#include #include #include using namespace std; typedef unsigned uint; typedef unsigned long long uint64; typedef long long int64; uint dp[301][3901]; uint poly_P[4000]; uint poly_C[4000]; uint poly[8000]; uint poly_inv[8000]; uint counts[8000]; uint sums[8000]; uint rem[16000]; uint64 temp[16000]; const uint mod = 1000000007; const uint64 lim = (0x7FFFFFFFFFFFFFFFull / mod - mod) * mod; inline void add_mod(uint& a, uint b) { a += b; if (a >= mod) { a -= mod; } } void init_poly(const uint* dice, const uint T, uint* result) { for (uint i = 1; i <= T; ++i) { fill(dp[i], dp[i] + dice[5] * i + 1, 0); } dp[0][0] = 1; for (uint di = 0; di < 6; ++di) { const uint d = dice[di]; for (uint t = 0; t < T; ++t) { for (uint i = t * dice[0]; i <= t * dice[di]; ++i) { if (dp[t][i]) { add_mod(dp[t + 1][i + d], dp[t][i]); } } } } for (uint i = 0; i <= dice[5] * T; ++i) { result[i] = dp[T][i]; } } uint64 poly64[8000]; uint64 mods[2] __attribute__((aligned(16))); uint64 coefs[2] __attribute__((aligned(16))); uint64 naive[8000]; void sub_mod_sse2(uint64* src, uint size, uint64* dest, uint64 coef) { coefs[0] = coefs[1] = coef; __asm__( "movdqa (%0), %%xmm6\n\t" "movdqa (%1), %%xmm7\n\t" :: "r"(coefs), "r"(mods) ); for (uint i = size / 4 * 4; i < size; ++i) { dest[i] -= uint64(coef) * src[i]; if (int64(dest[i]) < 0) { dest[i] += mods[0]; } } for (uint i = 0; i < size / 4 * 4; i += 4) { __asm__( "movdqu (%0), %%xmm0\n\t" "movdqu (%1), %%xmm1\n\t" "pxor %%xmm2, %%xmm2\n\t" "pxor %%xmm5, %%xmm5\n\t" "movdqu (%2), %%xmm3\n\t" "movdqu (%3), %%xmm4\n\t" "pmuludq %%xmm6, %%xmm0\n\t" "pmuludq %%xmm6, %%xmm3\n\t" "psubq %%xmm0, %%xmm1\n\t" "psubq %%xmm3, %%xmm4\n\t" "pcmpgtd %%xmm1, %%xmm2\n\t" "pcmpgtd %%xmm4, %%xmm5\n\t" "pand %%xmm7, %%xmm2\n\t" "pand %%xmm7, %%xmm5\n\t" "paddd %%xmm2, %%xmm1\n\t" "paddd %%xmm5, %%xmm4\n\t" "movdqu %%xmm1, (%1)\n\t" "movdqu %%xmm4, (%3)\n\t" :: "r"(src + i), "r"(dest + i), "r"(src + i + 2), "r"(dest + i + 2) ); } } uint poly_square(uint* p1, uint s1, uint* res) { uint s = 2 * s1 - 1; fill(temp, temp + s, 0); for (uint i = 0; i < s1; ++i) { temp[2 * i] = uint64(p1[i]) * p1[i]; } copy(p1, p1 + s1, poly64); poly64[s1] = 0; for (uint i = 0; i < s1; ++i) { uint coef = poly64[i]; if (!coef) { continue; } coef = (coef << 1) % mod; coef = mod - coef; sub_mod_sse2(poly64 + i + 1, s1 - i - 1, temp + 2 * i + 1, coef); } for (uint i = 0; i < s; ++i) { res[i] = temp[i] % mod; } return s; } void poly_mul(uint* p1, uint s1, uint* p2, uint s2, uint* res) { uint s = s1 + s2 - 1; fill(temp, temp + s, 0); copy(p2, p2 + s2, poly64); poly64[s2] = 0; for (uint i = 0; i < s1; ++i) { uint64 coef = p1[i]; if (!coef) { continue; } coef = mod - coef; sub_mod_sse2(poly64, s2, temp + i, coef); } for (uint i = 0; i < s; ++i) { res[i] = temp[i] % mod; } } uint poly_rem(uint* p1, uint s1, const uint* p2, uint s2, uint ofs, uint* ret) { if (s1 < s2) { copy(p1, p1 + s1, ret); return s1; } copy(p1, p1 + s1, temp); copy(p2, p2 + s2, poly64); poly64[s2] = 0; uint dif = s1 - s2 + 1; for (uint i = 0; i < dif; ++i) { uint coef = temp[i] % mod; if (!coef) { continue; } sub_mod_sse2(poly64 + ofs, s2 - ofs, temp + i + ofs, coef); } for (uint i = dif; i < s1; ++i) { ret[i - dif] = temp[i] % mod; } return s2 - 1; } uint poly_power_rem(uint64 e, const uint* divisor, uint div_size, uint ofs, uint* ret) { uint64 mask = 1; while (mask <= e) { mask <<= 1; } mask >>= 1; ret[0] = 1; uint ret_size = 1; while (mask) { if (e & mask) { ret[ret_size++] = 0; } mask >>= 1; if (mask == 0) { break; } ret_size = poly_square(ret, ret_size, ret); ret_size = poly_rem(ret, ret_size, divisor, div_size, ofs, ret); } if (ret_size >= div_size) { ret_size = poly_rem(ret, ret_size, divisor, div_size, ofs, ret); } return ret_size; } void conv(uint* poly, uint size) { poly[0] = 1; for (uint i = 1; i < size; ++i) { if (poly[i]) { poly[i] = mod - poly[i]; } } } void init_mod() { mods[0] = mods[1] = uint64(mod) << 32; } int main() { init_mod(); const uint Ps[] = {2, 3, 5, 7, 11, 13}; const uint Cs[] = {4, 6, 8, 9, 10, 12}; uint64 N; uint P, C; while (~scanf("%llu %u %u", &N, &P, &C)) { init_poly(Ps, P, poly_P); init_poly(Cs, C, poly_C); uint size_p = 13 * P + 1; uint size_c = 12 * C + 1; poly_mul(poly_P, size_p, poly_C, size_c, poly); const uint poly_size = 13 * P + 12 * C + 1; conv(poly, poly_size); uint rem_size = poly_power_rem(N + poly_size - 2, poly, poly_size, 2 * P + 4 * C, rem); uint64 ans = 0; for (uint i = 0; i < rem_size; ++i) { ans += rem[i]; } printf("%llu\n", ans % mod); } return 0; }