Problem 344
Silver dollar game W(10^6, 100) mod 1000036000099 via CRT.
View problem on Project Euler
Performance comparison
| Metric | Our solution | Best known |
|---|
| Time complexity | O(n^3) | O(n log n) |
|---|
| Space complexity | O(n^2) | O(n) |
|---|
| Approach | Flow solution | Chinese Remainder Theorem |
|---|
| Verdict | Suboptimal |
|---|
Flow source
# Project Euler 344
# Silver dollar game W(10^6, 100) mod 1000036000099 via CRT.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function modpow(base: i64, exp: i64, mod: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = ((base % mod) + mod) % mod
let mut e: i64 = exp
while e > 0 {
if e % 2 == 1 { r = (r * b) % mod }
b = (b * b) % mod
e = e / 2
}
return r
}
function binom_mod(n: i64, k0: i64, prime: i64) -> i64 {
if k0 < 0 || k0 > n { return 0 }
let mut k: i64 = k0
if k > n - k { k = n - k }
let mut num: i64 = 1
let mut den: i64 = 1
let mut i: i64 = 1
while i <= k {
num = num * ((n - k + i) % prime) % prime
den = den * i % prime
i = i + 1
}
return num * modpow(den, prime - 2, prime) % prime
}
function build_ways(active: i64, passive: i64, mod: i64, ways: ptr<i64>) -> i32 {
let lim: i64 = active + passive
let mut i: i64 = 0
while i <= lim {
ways[i] = 0
i = i + 1
}
let mut aones: i64 = 0
while aones <= active {
let ac: i64 = binom_mod(active, aones, mod)
let mut pones: i64 = 0
while pones <= passive {
let ones: i64 = aones + pones
ways[ones] = (ways[ones] + ac * binom_mod(passive, pones, mod)) % mod
pones = pones + 1
}
aones = aones + 2
}
return 0
}
function count_with_ways(total_sum: i64, ways: ptr<i64>, wlen: i64, mod: i64) -> i64 {
# Collect nonzero terms
let terms_ones: ptr<i64> = calloc(wlen + 1, 8)
let terms_cnt: ptr<i64> = calloc(wlen + 1, 8)
let mut tc: i64 = 0
let mut ones: i64 = 0
while ones <= wlen {
if ways[ones] != 0 {
terms_ones[tc] = ones
terms_cnt[tc] = ways[ones]
tc = tc + 1
}
ones = ones + 1
}
let mut bits: i64 = 0
let mut tmp: i64 = total_sum
while tmp > 0 {
bits = bits + 1
tmp = tmp / 2
}
if bits < 1 { bits = 1 }
let mut dp: ptr<i64> = calloc(2, 8)
let mut dplen: i64 = 1
dp[0] = 1
let mut bit: i64 = 0
while bit < bits {
let target: i64 = (total_sum >> bit) & 1
let max_carry: i64 = dplen + wlen / 2 + 2
let next: ptr<i64> = calloc(max_carry + 1, 8)
let mut carry: i64 = 0
while carry < dplen {
let value: i64 = dp[carry]
if value != 0 {
let mut t: i64 = 0
while t < tc {
let col: i64 = carry + terms_ones[t]
if (col & 1) == target {
let nc: i64 = (col - target) / 2
next[nc] = (next[nc] + value * terms_cnt[t]) % mod
}
t = t + 1
}
}
carry = carry + 1
}
free(dp)
dp = next
dplen = max_carry + 1
bit = bit + 1
}
let ans: i64 = dp[0]
free(dp)
free(terms_ones)
free(terms_cnt)
return ans
}
function losing_count(n: i64, c: i64, mod: i64) -> i64 {
let coin_count: i64 = c + 1
let empty: i64 = n - coin_count
let active: i64 = (coin_count + 1) / 2
let passive: i64 = coin_count - active + 1
let wlen: i64 = active + passive
let ways: ptr<i64> = calloc(wlen + 1, 8)
let ways2: ptr<i64> = calloc(wlen + 1, 8)
build_ways(active, passive, mod, ways)
build_ways(active - 1, passive, mod, ways2)
let second: i64 = count_with_ways(empty, ways, wlen, mod)
let other: i64 = (count_with_ways(empty + 1, ways, wlen, mod) - count_with_ways(empty + 1, ways2, wlen, mod) + mod) % mod
free(ways)
free(ways2)
return (second + (coin_count - 2) % mod * other) % mod
}
function solve_prime(n: i64, c: i64, prime: i64) -> i64 {
let coin_count: i64 = c + 1
let total: i64 = coin_count % prime * binom_mod(n, coin_count, prime) % prime
return (total - losing_count(n, c, prime) + prime) % prime
}
function main() -> i32 {
let n: i64 = 1000000
let c: i64 = 100
let P1: i64 = 1000003
let P2: i64 = 1000033
let MOD: i64 = 1000036000099
let r1: i64 = solve_prime(n, c, P1)
let r2: i64 = solve_prime(n, c, P2)
let t: i64 = ((r2 - r1) % P2 + P2) % P2 * modpow(P1 % P2, P2 - 2, P2) % P2
let ans: i64 = (r1 + P1 * t) % MOD
printf("%lld\n", ans)
return 0
}
Generated C
#include <stdint.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
/* Flow runtime helpers */
typedef struct flow_temp_node { struct flow_temp_node* next; } flow_temp_node;
static flow_temp_node* flow_temp_head = NULL;
static int flow_temp_atexit_set = 0;
__attribute__((unused)) static void flow_temp_free_all(void) {
while (flow_temp_head) {
flow_temp_node* n = flow_temp_head;
flow_temp_head = n->next;
free(n);
}
}
__attribute__((unused)) static void* flow_temp_alloc(size_t nbytes) {
flow_temp_node* node = (flow_temp_node*)malloc(sizeof(flow_temp_node) + nbytes);
if (!node) return NULL;
node->next = flow_temp_head;
flow_temp_head = node;
if (!flow_temp_atexit_set) {
flow_temp_atexit_set = 1;
atexit(flow_temp_free_all);
}
return (void*)(node + 1);
}
#ifndef FLOW_DIAG
#define FLOW_DIAG(msg) fprintf(stderr, "%s", (msg))
#endif
#ifndef FLOW_LOG
#define FLOW_LOG(fmt, ...) printf(fmt, __VA_ARGS__)
#endif
#ifndef FLOW_LOG_EMPTY
#define FLOW_LOG_EMPTY(fmt) printf(fmt)
#endif
static char* flow_strcat(const char* a, const char* b) {
size_t la = strlen(a ? a : ""), lb = strlen(b ? b : "");
char* r = (char*)flow_temp_alloc(la + lb + 1);
if (!r) return NULL;
if (la) memcpy(r, a, la);
if (lb) memcpy(r + la, b, lb);
r[la + lb] = '\0';
return r;
}
#define __flow_in_arr(arr, val) __extension__ ({ \
int _found = 0; \
size_t _n = sizeof(arr)/sizeof((arr)[0]); \
for (size_t _i = 0; _i < _n; _i++) { \
if ((arr)[_i] == (val)) { _found = 1; break; } \
} _found; })
/* Unified fault handler (MISRA #279) — override with -DFLOW_FAULT_HANDLER=fn */
#ifndef FLOW_FAULT_HANDLER
__attribute__((unused)) static inline void flow_fault_handler(const char* msg) {
fprintf(stderr, "flow: %s\n", msg ? msg : "fault");
abort();
#if defined(__GNUC__) || defined(__clang__)
__builtin_unreachable();
#endif
}
#else
#define flow_fault_handler FLOW_FAULT_HANDLER
#endif
#define flow_div_by_zero_handler() flow_fault_handler("division by zero")
#define flow_shift_ub_handler() flow_fault_handler("invalid shift (amount out of range or left-shift of negative)")
#ifndef FLOW_CHECKED_DIV
#define FLOW_CHECKED_DIV(L, R) (((R) != 0) ? ((L) / (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_MOD
#define FLOW_CHECKED_MOD(L, R) (((R) != 0) ? ((L) % (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHL
#define FLOW_CHECKED_SHL(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull)) && ((L) >= 0)) ? ((L) << (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHR
#define FLOW_CHECKED_SHR(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull))) ? ((L) >> (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#include <math.h>
void* _ui_state = NULL;
static inline float i32_to_f32(int32_t v) { return (float)v; }
/* Host stub for @gpu kernels (device codegen replaces this). */
static inline int32_t gpu_thread_id(void) { return 0; }
int64_t modpow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
int64_t binom_mod_i64_i64_i64(int64_t n, int64_t k0, int64_t prime);
int32_t build_ways_i64_i64_i64_ptr_i64(int64_t active, int64_t passive, int64_t mod, int64_t* ways);
int64_t count_with_ways_i64_ptr_i64_i64_i64(int64_t total_sum, int64_t* ways, int64_t wlen, int64_t mod);
int64_t losing_count_i64_i64_i64(int64_t n, int64_t c, int64_t mod);
int64_t solve_prime_i64_i64_i64(int64_t n, int64_t c, int64_t prime);
int32_t main(void);
int64_t modpow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
int64_t r = 1;
int64_t b = FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD((base), (mod)) + mod)), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
r = FLOW_CHECKED_MOD(((r * b)), (mod));
}
b = FLOW_CHECKED_MOD(((b * b)), (mod));
e = FLOW_CHECKED_DIV((e), (2));
}
return r;
}
int64_t binom_mod_i64_i64_i64(int64_t n, int64_t k0, int64_t prime) {
if ((k0 < 0 || k0 > n)) {
return 0;
}
int64_t k = k0;
if (k > (n - k)) {
k = (n - k);
}
int64_t num = 1;
int64_t den = 1;
int64_t i = 1;
while (i <= k) {
num = FLOW_CHECKED_MOD(((num * FLOW_CHECKED_MOD((((n - k) + i)), (prime)))), (prime));
den = FLOW_CHECKED_MOD(((den * i)), (prime));
i = (i + 1);
}
return FLOW_CHECKED_MOD(((num * modpow_i64_i64_i64(den, (prime - 2), prime))), (prime));
}
int32_t build_ways_i64_i64_i64_ptr_i64(int64_t active, int64_t passive, int64_t mod, int64_t* ways) {
int64_t lim = (active + passive);
int64_t i = 0;
while (i <= lim) {
ways[i] = 0;
i = (i + 1);
}
int64_t aones = 0;
while (aones <= active) {
int64_t ac = binom_mod_i64_i64_i64(active, aones, mod);
int64_t pones = 0;
while (pones <= passive) {
int64_t ones = (aones + pones);
ways[ones] = FLOW_CHECKED_MOD(((ways[ones] + (ac * binom_mod_i64_i64_i64(passive, pones, mod)))), (mod));
pones = (pones + 1);
}
aones = (aones + 2);
}
return 0;
}
int64_t count_with_ways_i64_ptr_i64_i64_i64(int64_t total_sum, int64_t* ways, int64_t wlen, int64_t mod) {
int64_t* terms_ones = (int64_t*)(calloc((wlen + 1), 8));
int64_t* terms_cnt = (int64_t*)(calloc((wlen + 1), 8));
int64_t tc = 0;
int64_t ones = 0;
while (ones <= wlen) {
if (ways[ones] != 0) {
terms_ones[tc] = ones;
terms_cnt[tc] = ways[ones];
tc = (tc + 1);
}
ones = (ones + 1);
}
int64_t bits = 0;
int64_t tmp = total_sum;
while (tmp > 0) {
bits = (bits + 1);
tmp = FLOW_CHECKED_DIV((tmp), (2));
}
if (bits < 1) {
bits = 1;
}
int64_t* dp = (int64_t*)(calloc(2, 8));
int64_t dplen = 1;
dp[0] = 1;
int64_t bit = 0;
while (bit < bits) {
int64_t target = (FLOW_CHECKED_SHR((total_sum), (bit)) & 1);
int64_t max_carry = ((dplen + FLOW_CHECKED_DIV((wlen), (2))) + 2);
int64_t* next = (int64_t*)(calloc((max_carry + 1), 8));
int64_t carry = 0;
while (carry < dplen) {
int64_t value = dp[carry];
if (value != 0) {
int64_t t = 0;
while (t < tc) {
int64_t col = (carry + terms_ones[t]);
if ((col & 1) == target) {
int64_t nc = FLOW_CHECKED_DIV(((col - target)), (2));
next[nc] = FLOW_CHECKED_MOD(((next[nc] + (value * terms_cnt[t]))), (mod));
}
t = (t + 1);
}
}
carry = (carry + 1);
}
free(dp);
dp = next;
dplen = (max_carry + 1);
bit = (bit + 1);
}
int64_t ans = dp[0];
free(dp);
free(terms_ones);
free(terms_cnt);
return ans;
}
int64_t losing_count_i64_i64_i64(int64_t n, int64_t c, int64_t mod) {
int64_t coin_count = (c + 1);
int64_t empty = (n - coin_count);
int64_t active = FLOW_CHECKED_DIV(((coin_count + 1)), (2));
int64_t passive = ((coin_count - active) + 1);
int64_t wlen = (active + passive);
int64_t* ways = (int64_t*)(calloc((wlen + 1), 8));
int64_t* ways2 = (int64_t*)(calloc((wlen + 1), 8));
build_ways_i64_i64_i64_ptr_i64(active, passive, mod, ways);
build_ways_i64_i64_i64_ptr_i64((active - 1), passive, mod, ways2);
int64_t second = count_with_ways_i64_ptr_i64_i64_i64(empty, ways, wlen, mod);
int64_t other = FLOW_CHECKED_MOD((((count_with_ways_i64_ptr_i64_i64_i64((empty + 1), ways, wlen, mod) - count_with_ways_i64_ptr_i64_i64_i64((empty + 1), ways2, wlen, mod)) + mod)), (mod));
free(ways);
free(ways2);
return FLOW_CHECKED_MOD(((second + (FLOW_CHECKED_MOD(((coin_count - 2)), (mod)) * other))), (mod));
}
int64_t solve_prime_i64_i64_i64(int64_t n, int64_t c, int64_t prime) {
int64_t coin_count = (c + 1);
int64_t total = FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD((coin_count), (prime)) * binom_mod_i64_i64_i64(n, coin_count, prime))), (prime));
return FLOW_CHECKED_MOD((((total - losing_count_i64_i64_i64(n, c, prime)) + prime)), (prime));
}
int32_t main(void) {
int64_t n = 1000000;
int64_t c = 100;
int64_t P1 = 1000003;
int64_t P2 = 1000033;
int64_t MOD = 1000036000099;
int64_t r1 = solve_prime_i64_i64_i64(n, c, P1);
int64_t r2 = solve_prime_i64_i64_i64(n, c, P2);
int64_t t = FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((r2 - r1)), (P2)) + P2)), (P2)) * modpow_i64_i64_i64(FLOW_CHECKED_MOD((P1), (P2)), (P2 - 2), P2))), (P2));
int64_t ans = FLOW_CHECKED_MOD(((r1 + (P1 * t))), (MOD));
printf("%lld\n", ans);
return 0;
}
Generated MLIR
module {
llvm.func @printf(!llvm.ptr, ...) -> i32
llvm.mlir.global internal constant @str_0("%lld\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
func.func private @calloc(i64, i64) -> !llvm.ptr
func.func private @free(!llvm.ptr) -> ()
func.func @modpow(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
%0 = arith.constant 1 : i32
%1 = arith.extsi %0 : i32 to i64
%2 = llvm.mlir.constant(1 : i64) : i64
%3 = llvm.alloca %2 x i64 : (i64) -> !llvm.ptr
llvm.store %1, %3 : i64, !llvm.ptr
%4 = arith.remsi %arg0, %arg2 : i64
%5 = arith.addi %4, %arg2 : i64
%6 = arith.remsi %5, %arg2 : i64
%7 = llvm.mlir.constant(1 : i64) : i64
%8 = llvm.alloca %7 x i64 : (i64) -> !llvm.ptr
llvm.store %6, %8 : i64, !llvm.ptr
%9 = llvm.mlir.constant(1 : i64) : i64
%10 = llvm.alloca %9 x i64 : (i64) -> !llvm.ptr
llvm.store %arg1, %10 : i64, !llvm.ptr
cf.br ^bb0
^bb0:
%11 = llvm.load %10 : !llvm.ptr -> i64
%12 = arith.constant 0 : i32
%14 = arith.extsi %12 : i32 to i64
%13 = arith.cmpi sgt, %11, %14 : i64
cf.cond_br %13, ^bb1, ^bb2
^bb1:
%15 = llvm.load %10 : !llvm.ptr -> i64
%16 = arith.constant 2 : i32
%18 = arith.extsi %16 : i32 to i64
%17 = arith.remsi %15, %18 : i64
%19 = arith.constant 1 : i32
%21 = arith.extsi %19 : i32 to i64
%20 = arith.cmpi eq, %17, %21 : i64
cf.cond_br %20, ^bb3, ^bb4
^bb3:
%22 = llvm.load %3 : !llvm.ptr -> i64
%23 = llvm.load %8 : !llvm.ptr -> i64
%24 = arith.muli %22, %23 : i64
%25 = arith.remsi %24, %arg2 : i64
llvm.store %25, %3 : i64, !llvm.ptr
cf.br ^bb5
^bb4:
cf.br ^bb5
^bb5:
%26 = llvm.load %8 : !llvm.ptr -> i64
%27 = llvm.load %8 : !llvm.ptr -> i64
%28 = arith.muli %26, %27 : i64
%29 = arith.remsi %28, %arg2 : i64
llvm.store %29, %8 : i64, !llvm.ptr
%30 = llvm.load %10 : !llvm.ptr -> i64
%31 = arith.constant 2 : i32
%33 = arith.extsi %31 : i32 to i64
%32 = arith.divsi %30, %33 : i64
llvm.store %32, %10 : i64, !llvm.ptr
cf.br ^bb0
^bb2:
%34 = llvm.load %3 : !llvm.ptr -> i64
func.return %34 : i64
}
func.func @binom_mod(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
%35 = arith.constant 0 : i32
%37 = arith.extsi %35 : i32 to i64
%36 = arith.cmpi slt, %arg1, %37 : i64
%38 = scf.if %36 -> (i1) {
%39 = arith.constant true
scf.yield %39 : i1
} else {
%40 = arith.cmpi sgt, %arg1, %arg0 : i64
scf.yield %40 : i1
}
cf.cond_br %38, ^bb6, ^bb7
^bb6:
%41 = arith.constant 0 : i32
%42 = arith.extsi %41 : i32 to i64
func.return %42 : i64
^bb7:
cf.br ^bb8
^bb8:
%43 = llvm.mlir.constant(1 : i64) : i64
%44 = llvm.alloca %43 x i64 : (i64) -> !llvm.ptr
llvm.store %arg1, %44 : i64, !llvm.ptr
%45 = llvm.load %44 : !llvm.ptr -> i64
%46 = llvm.load %44 : !llvm.ptr -> i64
%47 = arith.subi %arg0, %46 : i64
%48 = arith.cmpi sgt, %45, %47 : i64
cf.cond_br %48, ^bb9, ^bb10
^bb9:
%49 = llvm.load %44 : !llvm.ptr -> i64
%50 = arith.subi %arg0, %49 : i64
llvm.store %50, %44 : i64, !llvm.ptr
cf.br ^bb11
^bb10:
cf.br ^bb11
^bb11:
%51 = arith.constant 1 : i32
%52 = arith.extsi %51 : i32 to i64
%53 = llvm.mlir.constant(1 : i64) : i64
%54 = llvm.alloca %53 x i64 : (i64) -> !llvm.ptr
llvm.store %52, %54 : i64, !llvm.ptr
%55 = arith.constant 1 : i32
%56 = arith.extsi %55 : i32 to i64
%57 = llvm.mlir.constant(1 : i64) : i64
%58 = llvm.alloca %57 x i64 : (i64) -> !llvm.ptr
llvm.store %56, %58 : i64, !llvm.ptr
%59 = arith.constant 1 : i32
%60 = arith.extsi %59 : i32 to i64
%61 = llvm.mlir.constant(1 : i64) : i64
%62 = llvm.alloca %61 x i64 : (i64) -> !llvm.ptr
llvm.store %60, %62 : i64, !llvm.ptr
cf.br ^bb12
^bb12:
%63 = llvm.load %62 : !llvm.ptr -> i64
%64 = llvm.load %44 : !llvm.ptr -> i64
%65 = arith.cmpi sle, %63, %64 : i64
cf.cond_br %65, ^bb13, ^bb14
^bb13:
%66 = llvm.load %54 : !llvm.ptr -> i64
%67 = llvm.load %44 : !llvm.ptr -> i64
%68 = arith.subi %arg0, %67 : i64
%69 = llvm.load %62 : !llvm.ptr -> i64
%70 = arith.addi %68, %69 : i64
%71 = arith.remsi %70, %arg2 : i64
%72 = arith.muli %66, %71 : i64
%73 = arith.remsi %72, %arg2 : i64
llvm.store %73, %54 : i64, !llvm.ptr
%74 = llvm.load %58 : !llvm.ptr -> i64
%75 = llvm.load %62 : !llvm.ptr -> i64
%76 = arith.muli %74, %75 : i64
%77 = arith.remsi %76, %arg2 : i64
llvm.store %77, %58 : i64, !llvm.ptr
%78 = llvm.load %62 : !llvm.ptr -> i64
%79 = arith.constant 1 : i32
%81 = arith.extsi %79 : i32 to i64
%80 = arith.addi %78, %81 : i64
llvm.store %80, %62 : i64, !llvm.ptr
cf.br ^bb12
^bb14:
%82 = llvm.load %54 : !llvm.ptr -> i64
%84 = llvm.load %58 : !llvm.ptr -> i64
%85 = arith.constant 2 : i32
%87 = arith.extsi %85 : i32 to i64
%86 = arith.subi %arg2, %87 : i64
%83 = func.call @modpow(%84, %86, %arg2) : (i64, i64, i64) -> i64
%88 = arith.muli %82, %83 : i64
%89 = arith.remsi %88, %arg2 : i64
func.return %89 : i64
}
func.func @build_ways(%arg0: i64, %arg1: i64, %arg2: i64, %arg3: !llvm.ptr) -> i32 {
%90 = arith.addi %arg0, %arg1 : i64
%91 = arith.constant 0 : i32
%92 = arith.extsi %91 : i32 to i64
%93 = llvm.mlir.constant(1 : i64) : i64
%94 = llvm.alloca %93 x i64 : (i64) -> !llvm.ptr
llvm.store %92, %94 : i64, !llvm.ptr
cf.br ^bb15
^bb15:
%95 = llvm.load %94 : !llvm.ptr -> i64
%96 = arith.cmpi sle, %95, %90 : i64
cf.cond_br %96, ^bb16, ^bb17
^bb16:
%97 = arith.constant 0 : i32
%98 = llvm.load %94 : !llvm.ptr -> i64
%99 = arith.extsi %97 : i32 to i64
%100 = llvm.getelementptr %arg3[%98] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %99, %100 : i64, !llvm.ptr
%101 = llvm.load %94 : !llvm.ptr -> i64
%102 = arith.constant 1 : i32
%104 = arith.extsi %102 : i32 to i64
%103 = arith.addi %101, %104 : i64
llvm.store %103, %94 : i64, !llvm.ptr
cf.br ^bb15
^bb17:
%105 = arith.constant 0 : i32
%106 = arith.extsi %105 : i32 to i64
%107 = llvm.mlir.constant(1 : i64) : i64
%108 = llvm.alloca %107 x i64 : (i64) -> !llvm.ptr
llvm.store %106, %108 : i64, !llvm.ptr
cf.br ^bb18
^bb18:
%109 = llvm.load %108 : !llvm.ptr -> i64
%110 = arith.cmpi sle, %109, %arg0 : i64
cf.cond_br %110, ^bb19, ^bb20
^bb19:
%112 = llvm.load %108 : !llvm.ptr -> i64
%111 = func.call @binom_mod(%arg0, %112, %arg2) : (i64, i64, i64) -> i64
%113 = arith.constant 0 : i32
%114 = arith.extsi %113 : i32 to i64
%115 = llvm.mlir.constant(1 : i64) : i64
%116 = llvm.alloca %115 x i64 : (i64) -> !llvm.ptr
llvm.store %114, %116 : i64, !llvm.ptr
cf.br ^bb21
^bb21:
%117 = llvm.load %116 : !llvm.ptr -> i64
%118 = arith.cmpi sle, %117, %arg1 : i64
cf.cond_br %118, ^bb22, ^bb23
^bb22:
%119 = llvm.load %108 : !llvm.ptr -> i64
%120 = llvm.load %116 : !llvm.ptr -> i64
%121 = arith.addi %119, %120 : i64
%123 = llvm.getelementptr %arg3[%121] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%122 = llvm.load %123 : !llvm.ptr -> i64
%125 = llvm.load %116 : !llvm.ptr -> i64
%124 = func.call @binom_mod(%arg1, %125, %arg2) : (i64, i64, i64) -> i64
%126 = arith.muli %111, %124 : i64
%127 = arith.addi %122, %126 : i64
%128 = arith.remsi %127, %arg2 : i64
%129 = llvm.getelementptr %arg3[%121] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %128, %129 : i64, !llvm.ptr
%130 = llvm.load %116 : !llvm.ptr -> i64
%131 = arith.constant 1 : i32
%133 = arith.extsi %131 : i32 to i64
%132 = arith.addi %130, %133 : i64
llvm.store %132, %116 : i64, !llvm.ptr
cf.br ^bb21
^bb23:
%134 = llvm.load %108 : !llvm.ptr -> i64
%135 = arith.constant 2 : i32
%137 = arith.extsi %135 : i32 to i64
%136 = arith.addi %134, %137 : i64
llvm.store %136, %108 : i64, !llvm.ptr
cf.br ^bb18
^bb20:
%138 = arith.constant 0 : i32
func.return %138 : i32
}
func.func @count_with_ways(%arg0: i64, %arg1: !llvm.ptr, %arg2: i64, %arg3: i64) -> i64 {
%140 = arith.constant 1 : i32
%142 = arith.extsi %140 : i32 to i64
%141 = arith.addi %arg2, %142 : i64
%143 = arith.constant 8 : i32
%144 = arith.extsi %143 : i32 to i64
%139 = func.call @calloc(%141, %144) : (i64, i64) -> !llvm.ptr
%146 = arith.constant 1 : i32
%148 = arith.extsi %146 : i32 to i64
%147 = arith.addi %arg2, %148 : i64
%149 = arith.constant 8 : i32
%150 = arith.extsi %149 : i32 to i64
%145 = func.call @calloc(%147, %150) : (i64, i64) -> !llvm.ptr
%151 = arith.constant 0 : i32
%152 = arith.extsi %151 : i32 to i64
%153 = llvm.mlir.constant(1 : i64) : i64
%154 = llvm.alloca %153 x i64 : (i64) -> !llvm.ptr
llvm.store %152, %154 : i64, !llvm.ptr
%155 = arith.constant 0 : i32
%156 = arith.extsi %155 : i32 to i64
%157 = llvm.mlir.constant(1 : i64) : i64
%158 = llvm.alloca %157 x i64 : (i64) -> !llvm.ptr
llvm.store %156, %158 : i64, !llvm.ptr
cf.br ^bb24
^bb24:
%159 = llvm.load %158 : !llvm.ptr -> i64
%160 = arith.cmpi sle, %159, %arg2 : i64
cf.cond_br %160, ^bb25, ^bb26
^bb25:
%162 = llvm.load %158 : !llvm.ptr -> i64
%163 = llvm.getelementptr %arg1[%162] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%161 = llvm.load %163 : !llvm.ptr -> i64
%164 = arith.constant 0 : i32
%166 = arith.extsi %164 : i32 to i64
%165 = arith.cmpi ne, %161, %166 : i64
cf.cond_br %165, ^bb27, ^bb28
^bb27:
%167 = llvm.load %158 : !llvm.ptr -> i64
%168 = llvm.load %154 : !llvm.ptr -> i64
%169 = llvm.getelementptr %139[%168] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %167, %169 : i64, !llvm.ptr
%171 = llvm.load %158 : !llvm.ptr -> i64
%172 = llvm.getelementptr %arg1[%171] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%170 = llvm.load %172 : !llvm.ptr -> i64
%173 = llvm.load %154 : !llvm.ptr -> i64
%174 = llvm.getelementptr %145[%173] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %170, %174 : i64, !llvm.ptr
%175 = llvm.load %154 : !llvm.ptr -> i64
%176 = arith.constant 1 : i32
%178 = arith.extsi %176 : i32 to i64
%177 = arith.addi %175, %178 : i64
llvm.store %177, %154 : i64, !llvm.ptr
cf.br ^bb29
^bb28:
cf.br ^bb29
^bb29:
%179 = llvm.load %158 : !llvm.ptr -> i64
%180 = arith.constant 1 : i32
%182 = arith.extsi %180 : i32 to i64
%181 = arith.addi %179, %182 : i64
llvm.store %181, %158 : i64, !llvm.ptr
cf.br ^bb24
^bb26:
%183 = arith.constant 0 : i32
%184 = arith.extsi %183 : i32 to i64
%185 = llvm.mlir.constant(1 : i64) : i64
%186 = llvm.alloca %185 x i64 : (i64) -> !llvm.ptr
llvm.store %184, %186 : i64, !llvm.ptr
%187 = llvm.mlir.constant(1 : i64) : i64
%188 = llvm.alloca %187 x i64 : (i64) -> !llvm.ptr
llvm.store %arg0, %188 : i64, !llvm.ptr
cf.br ^bb30
^bb30:
%189 = llvm.load %188 : !llvm.ptr -> i64
%190 = arith.constant 0 : i32
%192 = arith.extsi %190 : i32 to i64
%191 = arith.cmpi sgt, %189, %192 : i64
cf.cond_br %191, ^bb31, ^bb32
^bb31:
%193 = llvm.load %186 : !llvm.ptr -> i64
%194 = arith.constant 1 : i32
%196 = arith.extsi %194 : i32 to i64
%195 = arith.addi %193, %196 : i64
llvm.store %195, %186 : i64, !llvm.ptr
%197 = llvm.load %188 : !llvm.ptr -> i64
%198 = arith.constant 2 : i32
%200 = arith.extsi %198 : i32 to i64
%199 = arith.divsi %197, %200 : i64
llvm.store %199, %188 : i64, !llvm.ptr
cf.br ^bb30
^bb32:
%201 = llvm.load %186 : !llvm.ptr -> i64
%202 = arith.constant 1 : i32
%204 = arith.extsi %202 : i32 to i64
%203 = arith.cmpi slt, %201, %204 : i64
cf.cond_br %203, ^bb33, ^bb34
^bb33:
%205 = arith.constant 1 : i32
%206 = arith.extsi %205 : i32 to i64
llvm.store %206, %186 : i64, !llvm.ptr
cf.br ^bb35
^bb34:
cf.br ^bb35
^bb35:
%208 = arith.constant 2 : i32
%209 = arith.constant 8 : i32
%210 = arith.extsi %208 : i32 to i64
%211 = arith.extsi %209 : i32 to i64
%207 = func.call @calloc(%210, %211) : (i64, i64) -> !llvm.ptr
%212 = llvm.mlir.constant(1 : i64) : i64
%213 = llvm.alloca %212 x !llvm.ptr : (i64) -> !llvm.ptr
llvm.store %207, %213 : !llvm.ptr, !llvm.ptr
%214 = arith.constant 1 : i32
%215 = arith.extsi %214 : i32 to i64
%216 = llvm.mlir.constant(1 : i64) : i64
%217 = llvm.alloca %216 x i64 : (i64) -> !llvm.ptr
llvm.store %215, %217 : i64, !llvm.ptr
%218 = arith.constant 1 : i32
%219 = llvm.load %213 : !llvm.ptr -> !llvm.ptr
%220 = arith.constant 0 : i32
%221 = arith.extsi %218 : i32 to i64
%222 = arith.extsi %220 : i32 to i64
%223 = llvm.getelementptr %219[%222] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %221, %223 : i64, !llvm.ptr
%224 = arith.constant 0 : i32
%225 = arith.extsi %224 : i32 to i64
%226 = llvm.mlir.constant(1 : i64) : i64
%227 = llvm.alloca %226 x i64 : (i64) -> !llvm.ptr
llvm.store %225, %227 : i64, !llvm.ptr
cf.br ^bb36
^bb36:
%228 = llvm.load %227 : !llvm.ptr -> i64
%229 = llvm.load %186 : !llvm.ptr -> i64
%230 = arith.cmpi slt, %228, %229 : i64
cf.cond_br %230, ^bb37, ^bb38
^bb37:
%231 = llvm.load %227 : !llvm.ptr -> i64
%232 = arith.shrsi %arg0, %231 : i64
%233 = arith.constant 1 : i32
%235 = arith.extsi %233 : i32 to i64
%234 = arith.andi %232, %235 : i64
%236 = llvm.load %217 : !llvm.ptr -> i64
%237 = arith.constant 2 : i32
%239 = arith.extsi %237 : i32 to i64
%238 = arith.divsi %arg2, %239 : i64
%240 = arith.addi %236, %238 : i64
%241 = arith.constant 2 : i32
%243 = arith.extsi %241 : i32 to i64
%242 = arith.addi %240, %243 : i64
%245 = arith.constant 1 : i32
%247 = arith.extsi %245 : i32 to i64
%246 = arith.addi %242, %247 : i64
%248 = arith.constant 8 : i32
%249 = arith.extsi %248 : i32 to i64
%244 = func.call @calloc(%246, %249) : (i64, i64) -> !llvm.ptr
%250 = arith.constant 0 : i32
%251 = arith.extsi %250 : i32 to i64
%252 = llvm.mlir.constant(1 : i64) : i64
%253 = llvm.alloca %252 x i64 : (i64) -> !llvm.ptr
llvm.store %251, %253 : i64, !llvm.ptr
cf.br ^bb39
^bb39:
%254 = llvm.load %253 : !llvm.ptr -> i64
%255 = llvm.load %217 : !llvm.ptr -> i64
%256 = arith.cmpi slt, %254, %255 : i64
cf.cond_br %256, ^bb40, ^bb41
^bb40:
%258 = llvm.load %213 : !llvm.ptr -> !llvm.ptr
%259 = llvm.load %253 : !llvm.ptr -> i64
%260 = llvm.getelementptr %258[%259] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%257 = llvm.load %260 : !llvm.ptr -> i64
%261 = arith.constant 0 : i32
%263 = arith.extsi %261 : i32 to i64
%262 = arith.cmpi ne, %257, %263 : i64
cf.cond_br %262, ^bb42, ^bb43
^bb42:
%264 = arith.constant 0 : i32
%265 = arith.extsi %264 : i32 to i64
%266 = llvm.mlir.constant(1 : i64) : i64
%267 = llvm.alloca %266 x i64 : (i64) -> !llvm.ptr
llvm.store %265, %267 : i64, !llvm.ptr
cf.br ^bb45
^bb45:
%268 = llvm.load %267 : !llvm.ptr -> i64
%269 = llvm.load %154 : !llvm.ptr -> i64
%270 = arith.cmpi slt, %268, %269 : i64
cf.cond_br %270, ^bb46, ^bb47
^bb46:
%271 = llvm.load %253 : !llvm.ptr -> i64
%273 = llvm.load %267 : !llvm.ptr -> i64
%274 = llvm.getelementptr %139[%273] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%272 = llvm.load %274 : !llvm.ptr -> i64
%275 = arith.addi %271, %272 : i64
%276 = arith.constant 1 : i32
%278 = arith.extsi %276 : i32 to i64
%277 = arith.andi %275, %278 : i64
%279 = arith.cmpi eq, %277, %234 : i64
cf.cond_br %279, ^bb48, ^bb49
^bb48:
%280 = arith.subi %275, %234 : i64
%281 = arith.constant 2 : i32
%283 = arith.extsi %281 : i32 to i64
%282 = arith.divsi %280, %283 : i64
%285 = llvm.getelementptr %244[%282] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%284 = llvm.load %285 : !llvm.ptr -> i64
%287 = llvm.load %267 : !llvm.ptr -> i64
%288 = llvm.getelementptr %145[%287] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%286 = llvm.load %288 : !llvm.ptr -> i64
%289 = arith.muli %257, %286 : i64
%290 = arith.addi %284, %289 : i64
%291 = arith.remsi %290, %arg3 : i64
%292 = llvm.getelementptr %244[%282] : (!llvm.ptr, i64) -> !llvm.ptr, i64
llvm.store %291, %292 : i64, !llvm.ptr
cf.br ^bb50
^bb49:
cf.br ^bb50
^bb50:
%293 = llvm.load %267 : !llvm.ptr -> i64
%294 = arith.constant 1 : i32
%296 = arith.extsi %294 : i32 to i64
%295 = arith.addi %293, %296 : i64
llvm.store %295, %267 : i64, !llvm.ptr
cf.br ^bb45
^bb47:
cf.br ^bb44
^bb43:
cf.br ^bb44
^bb44:
%297 = llvm.load %253 : !llvm.ptr -> i64
%298 = arith.constant 1 : i32
%300 = arith.extsi %298 : i32 to i64
%299 = arith.addi %297, %300 : i64
llvm.store %299, %253 : i64, !llvm.ptr
cf.br ^bb39
^bb41:
%302 = llvm.load %213 : !llvm.ptr -> !llvm.ptr
func.call @free(%302) : (!llvm.ptr) -> ()
llvm.store %244, %213 : !llvm.ptr, !llvm.ptr
%303 = arith.constant 1 : i32
%305 = arith.extsi %303 : i32 to i64
%304 = arith.addi %242, %305 : i64
llvm.store %304, %217 : i64, !llvm.ptr
%306 = llvm.load %227 : !llvm.ptr -> i64
%307 = arith.constant 1 : i32
%309 = arith.extsi %307 : i32 to i64
%308 = arith.addi %306, %309 : i64
llvm.store %308, %227 : i64, !llvm.ptr
cf.br ^bb36
^bb38:
%311 = llvm.load %213 : !llvm.ptr -> !llvm.ptr
%312 = arith.constant 0 : i32
%313 = arith.extsi %312 : i32 to i64
%314 = llvm.getelementptr %311[%313] : (!llvm.ptr, i64) -> !llvm.ptr, i64
%310 = llvm.load %314 : !llvm.ptr -> i64
%316 = llvm.load %213 : !llvm.ptr -> !llvm.ptr
func.call @free(%316) : (!llvm.ptr) -> ()
func.call @free(%139) : (!llvm.ptr) -> ()
func.call @free(%145) : (!llvm.ptr) -> ()
func.return %310 : i64
}
func.func @losing_count(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
%319 = arith.constant 1 : i32
%321 = arith.extsi %319 : i32 to i64
%320 = arith.addi %arg1, %321 : i64
%322 = arith.subi %arg0, %320 : i64
%323 = arith.constant 1 : i32
%325 = arith.extsi %323 : i32 to i64
%324 = arith.addi %320, %325 : i64
%326 = arith.constant 2 : i32
%328 = arith.extsi %326 : i32 to i64
%327 = arith.divsi %324, %328 : i64
%329 = arith.subi %320, %327 : i64
%330 = arith.constant 1 : i32
%332 = arith.extsi %330 : i32 to i64
%331 = arith.addi %329, %332 : i64
%333 = arith.addi %327, %331 : i64
%335 = arith.constant 1 : i32
%337 = arith.extsi %335 : i32 to i64
%336 = arith.addi %333, %337 : i64
%338 = arith.constant 8 : i32
%339 = arith.extsi %338 : i32 to i64
%334 = func.call @calloc(%336, %339) : (i64, i64) -> !llvm.ptr
%341 = arith.constant 1 : i32
%343 = arith.extsi %341 : i32 to i64
%342 = arith.addi %333, %343 : i64
%344 = arith.constant 8 : i32
%345 = arith.extsi %344 : i32 to i64
%340 = func.call @calloc(%342, %345) : (i64, i64) -> !llvm.ptr
%346 = func.call @build_ways(%327, %331, %arg2, %334) : (i64, i64, i64, !llvm.ptr) -> i32
%348 = arith.constant 1 : i32
%350 = arith.extsi %348 : i32 to i64
%349 = arith.subi %327, %350 : i64
%347 = func.call @build_ways(%349, %331, %arg2, %340) : (i64, i64, i64, !llvm.ptr) -> i32
%351 = func.call @count_with_ways(%322, %334, %333, %arg2) : (i64, !llvm.ptr, i64, i64) -> i64
%353 = arith.constant 1 : i32
%355 = arith.extsi %353 : i32 to i64
%354 = arith.addi %322, %355 : i64
%352 = func.call @count_with_ways(%354, %334, %333, %arg2) : (i64, !llvm.ptr, i64, i64) -> i64
%357 = arith.constant 1 : i32
%359 = arith.extsi %357 : i32 to i64
%358 = arith.addi %322, %359 : i64
%356 = func.call @count_with_ways(%358, %340, %333, %arg2) : (i64, !llvm.ptr, i64, i64) -> i64
%360 = arith.subi %352, %356 : i64
%361 = arith.addi %360, %arg2 : i64
%362 = arith.remsi %361, %arg2 : i64
func.call @free(%334) : (!llvm.ptr) -> ()
func.call @free(%340) : (!llvm.ptr) -> ()
%365 = arith.constant 2 : i32
%367 = arith.extsi %365 : i32 to i64
%366 = arith.subi %320, %367 : i64
%368 = arith.remsi %366, %arg2 : i64
%369 = arith.muli %368, %362 : i64
%370 = arith.addi %351, %369 : i64
%371 = arith.remsi %370, %arg2 : i64
func.return %371 : i64
}
func.func @solve_prime(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
%372 = arith.constant 1 : i32
%374 = arith.extsi %372 : i32 to i64
%373 = arith.addi %arg1, %374 : i64
%375 = arith.remsi %373, %arg2 : i64
%376 = func.call @binom_mod(%arg0, %373, %arg2) : (i64, i64, i64) -> i64
%377 = arith.muli %375, %376 : i64
%378 = arith.remsi %377, %arg2 : i64
%379 = func.call @losing_count(%arg0, %arg1, %arg2) : (i64, i64, i64) -> i64
%380 = arith.subi %378, %379 : i64
%381 = arith.addi %380, %arg2 : i64
%382 = arith.remsi %381, %arg2 : i64
func.return %382 : i64
}
func.func @main() -> i32 {
%383 = arith.constant 1000000 : i32
%384 = arith.extsi %383 : i32 to i64
%385 = arith.constant 100 : i32
%386 = arith.extsi %385 : i32 to i64
%387 = arith.constant 1000003 : i32
%388 = arith.extsi %387 : i32 to i64
%389 = arith.constant 1000033 : i32
%390 = arith.extsi %389 : i32 to i64
%391 = arith.constant 995741032803 : i32
%392 = arith.extsi %391 : i32 to i64
%393 = func.call @solve_prime(%384, %386, %388) : (i64, i64, i64) -> i64
%394 = func.call @solve_prime(%384, %386, %390) : (i64, i64, i64) -> i64
%395 = arith.subi %394, %393 : i64
%396 = arith.remsi %395, %390 : i64
%397 = arith.addi %396, %390 : i64
%398 = arith.remsi %397, %390 : i64
%400 = arith.remsi %388, %390 : i64
%401 = arith.constant 2 : i32
%403 = arith.extsi %401 : i32 to i64
%402 = arith.subi %390, %403 : i64
%399 = func.call @modpow(%400, %402, %390) : (i64, i64, i64) -> i64
%404 = arith.muli %398, %399 : i64
%405 = arith.remsi %404, %390 : i64
%406 = arith.muli %388, %405 : i64
%407 = arith.addi %393, %406 : i64
%408 = arith.remsi %407, %392 : i64
%409 = llvm.mlir.addressof @str_0 : !llvm.ptr
%410 = llvm.call @printf(%409, %408) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
%411 = arith.constant 0 : i32
func.return %411 : i32
}
}