#pragma GCC optimize ("O3") #pragma GCC target ("avx") #include typedef __int128_t int128; // worst: 1152921504606839475 300 300 => 610505353 // 1000000000000000000 300 300 => 817328043 // 今回は不使用 class NumberTheoreticTransform { public: int mod; int root; public: NumberTheoreticTransform(int mod, int root) : mod(mod), root(root) { } std::vector mul(std::vector a, std::vector b) { int s = a.size() + b.size() - 1; int t = 1; while (t < s) t *= 2; for (int i = 0; i < a.size(); i++) a[i] %= mod; for (int i = 0; i < b.size(); i++) b[i] %= mod; a.resize(t); b.resize(t); ntt(a); ntt(b); for (int i = 0; i < a.size(); i++) a[i] = mul(a[i], b[i]); ntt(a, true); a.resize(s); return a; } private: int mul(int x, int y) { return int64_t(x) * y % mod; } int add(int x, int y) { return (x += y) >= mod ? x - mod : x; } int pow(int x, int y) { int res = 1; for (; y > 0; x = mul(x, x), y >>= 1) if (y & 1) res = mul(res, x); return res; } int inv(int x) { return pow(x, mod - 2); } void ntt(std::vector &a, bool rev = false) { int n = a.size(); int h = 0; for (int i = 0; 1 << i < n; i++) h++; for (int i = 0; i < n; i++) { int j = 0; for (int k = 0; k < h; k++) j |= (i >> k & 1) << (h - 1 - k); if (i < j) std::swap(a[i], a[j]); } for (int i = 1; i < n; i *= 2) { int w = pow(root, (mod - 1) / (i * 2)); if (rev) w = inv(w); for (int j = 0; j < n; j += i * 2) { int wn = 1; for (int k = 0; k < i; k++) { int s = a[j + k + 0]; int t = mul(a[j + k + i], wn); a[j + k + 0] = add(s, t); a[j + k + i] = add(s, mod - t); wn = mul(wn, w); } } } int v = inv(n); if (rev) for (int i = 0; i < n; i++) a[i] = mul(a[i], v); } }; // 今回は不使用 // mod を取りつつ Karatsuba 法 class Karatsuba { private: int mod; public: Karatsuba(int mod) : mod(mod) {} std::vector mul(std::vector a, std::vector b) { int s = std::max(a.size(), b.size()); int t = 1; int u = a.size() + b.size() - 1; while (t < s) t *= 2; a.resize(t); b.resize(t); std::vector c(t * 6); mul(a.data(), b.data(), t, c.data()); c.resize(u); return c; } private: void mul(int a[], int b[], int n, int res[]) { int *a0 = a, *a1 = a + n / 2; int *b0 = b, *b1 = b + n / 2; int *c0 = res + n * 5, *c1 = res + n * 5 + n / 2; int *x0 = res, *x1 = res + n, *x2 = res + n * 2; if (n <= 8) { for (int i = 0; i < n * 2; i++) res[i] = 0; for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) upd(res[i + j], int64_t(a[i]) * b[j] % mod); return; } for (int i = 0; i < n / 2; i++) { c0[i] = add(a0[i], a1[i]); c1[i] = add(b0[i], b1[i]); } mul(a0, b0, n / 2, x0); mul(a1, b1, n / 2, x1); mul(c0, c1, n / 2, x2); for (int i = 0; i < n; i++) upd(x2[i], mod - add(x0[i], x1[i])); for (int i = 0; i < n; i++) upd(res[i + n / 2], x2[i]); } int add(int x, int y) { return (x += y) >= mod ? x - mod : x; } void upd(int &x, int y) { x = add(x, y); } }; // int128 を使って mod を省いた Karatsuba 法 class Karatsuba128 { private: int mod; public: Karatsuba128(int mod) : mod(mod) {} std::vector mul(std::vector a, std::vector b, int pmod = -1) { if (pmod == -1) pmod = a.size() + b.size() - 1; else { if (a.size() > pmod) a.resize(pmod); if (b.size() > pmod) b.resize(pmod); } int s = std::max(a.size(), b.size()); int t = 1; while (t < s) t *= 2; std::vector A(t), B(t), C(t * 6); for (int i = 0; i < a.size(); i++) A[i] = a[i]; for (int i = 0; i < b.size(); i++) B[i] = b[i]; mul(A.data(), B.data(), t, C.data()); std::vector c(pmod); for (int i = 0; i < std::min(pmod, C.size()); i++) { c[i] = C[i] % mod; if (c[i] < 0) c[i] += mod; } return c; } private: void mul(int128 a[], int128 b[], int n, int128 res[]) { if (n <= 8) { memset(res, 0, sizeof(res[0]) * n * 2); for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) { res[i + j] += a[i] * b[j]; } return; } int128 *a0 = a, *a1 = a + n / 2; int128 *b0 = b, *b1 = b + n / 2; int128 *c0 = res + n * 5, *c1 = res + n * 5 + n / 2; int128 *x0 = res, *x1 = res + n, *x2 = res + n * 2; for (int i = 0; i < n / 2; i++) { c0[i] = a0[i] + a1[i]; c1[i] = b0[i] + b1[i]; } mul(a0, b0, n / 2, x0); mul(a1, b1, n / 2, x1); mul(c0, c1, n / 2, x2); for (int i = 0; i < n; i++) x2[i] -= x0[i] + x1[i]; for (int i = 0; i < n; i++) res[i + n / 2] += x2[i]; } }; // 今回は不使用 // 3種の mod を使って CRT で復元する畳み込み class AnyModConvolution { private: std::vector ntt; std::vector mods; std::vector roots; int mod; public: AnyModConvolution(int mod) : mod(mod) { mods.push_back(469762049); mods.push_back(167772161); mods.push_back(754974721); roots.push_back(3); roots.push_back(3); roots.push_back(11); for (int i = 0; i < 3; i++) { ntt.emplace_back(mods[i], roots[i]); } } std::vector mul(std::vector a, std::vector b) { std::vector> res(ntt.size()); for (int i = 0; i < ntt.size(); i++) { res[i] = ntt[i].mul(a, b); } for (int i = 0; i < res[0].size(); i++) { std::vector x; for (int j = 0; j < ntt.size(); j++) { x.push_back(res[j][i]); } res[0][i] = linear_congruence(x, mods, mod); } return res[0]; } int pow(int64_t x, int64_t y, int mod) { int64_t res = 1; for (; y > 0; x = x * x % mod, y >>= 1) if (y & 1) res = res * x % mod; return res; } int inv(int x, int mod) { return pow(x, mod - 2, mod); } int linear_congruence(std::vector x, std::vector m, int mod) { m.push_back(mod); std::vector u(x.size()); for (int i = 0; i <= x.size(); i++) { int64_t s = 0, v = 1; for (int j = 0; j < i; j++) { (s += u[j] * v) %= m[i]; (v *= m[j]) %= m[i]; } if (i == x.size()) return s; u[i] = (x[i] + m[i] - s) * inv(v, m[i]) % m[i]; } abort(); return -1; } }; class AnyModPolynomial { private: int mod; Karatsuba128 kara128; std::vector t; public: AnyModPolynomial(int mod) : mod(mod), kara128(mod) {} std::vector mul(const std::vector &a, const std::vector &b) { return kara128.mul(a, b); } std::vector add(const std::vector &a, const std::vector &b) { std::vector res(std::max(a.size(), b.size())); for (int i = 0; i < res.size(); i++) { res[i] = add(i < a.size() ? a[i] : 0, i < b.size() ? b[i] : 0); } return res; } std::vector sub(const std::vector &a, const std::vector &b) { std::vector res(std::max(a.size(), b.size())); for (int i = 0; i < res.size(); i++) { res[i] = add(i < a.size() ? a[i] : 0, i < b.size() ? (mod - b[i]) : 0); } return res; } std::vector quot(std::vector a, std::vector b) { if (a.size() < b.size()) return{ 0 }; while (b.back() == 0) b.pop_back(); int s = a.size() - b.size() + 1; while (!is_pow2(a.size() - b.size() + 1)) a.push_back(0); int n = a.size() - b.size() + 1; if (t.empty()) t = inv(rev(b), n); std::vector q = rev(mul(rev(a), t, n)); q.resize(s); return q; } std::vector rem(std::vector a, std::vector b) { while (b.back() == 0) b.pop_back(); std::vector r = sub(a, mul(quot(a, b), b, b.size() - 1)); r.resize(b.size() - 1); return r; } std::vector remmul(std::vector a, std::vector b, std::vector c) { return rem(mul(a, b), c); } private: int pow(int64_t x, int64_t y, int mod) { int64_t res = 1; for (; y > 0; x = x * x % mod, y >>= 1) if (y & 1) res = res * x % mod; return res; } int inv(int x, int mod) { return pow(x, mod - 2, mod); } int is_pow2(int n) { return (n & (n - 1)) == 0; } int mul(int x, int y) { return int64_t(x) * y % mod; } int add(int x, int y) { return (x += y) >= mod ? x - mod : x; } void upd(int &x, int y) { x = add(x, y); } int pow(int x, int y) { int res = 1; for (; y > 0; x = mul(x, x), y >>= 1) if (y & 1) res = mul(res, x); return res; } int inv(int x) { return pow(x, mod - 2); } std::vector mul(std::vector a, std::vector b, int n) { return kara128.mul(a, b, n); } std::vector inv(std::vector a, int n) { assert(is_pow2(n)); std::vector b(n); b[0] = inv(a[0]); for (int i = 0; (1 << i) < a.size(); i++) { b = sub(add(b, b), mul(mul(b, b, n), a, n)); } return b; } std::vector rev(std::vector a) { reverse(a.begin(), a.end()); return a; } }; const int mod = 1e9 + 7; int64_t dp[2][301][4000], way[10000]; void calc(int64_t dp[301][4000], int64_t n, std::vector dice) { dp[0][0] = 1; for (int k = 0; k < dice.size(); k++) { for (int i = 0; i < n; i++) { for (int j = 0; j < 3910; j++) { (dp[i + 1][j + dice[k]] += dp[i][j]) %= mod; } } } } int main() { using namespace std; int64_t N, P, C; cin >> N >> P >> C; calc(dp[0], P, { 2, 3, 5, 7, 11, 13 }); calc(dp[1], C, { 4, 6, 8, 9, 10, 12 }); for (int i = 0; i <= 3900; i++) { for (int j = 0; j <= 3900; j++) { (way[i + j] += dp[0][P][i] * dp[1][C][j]) %= mod; } } int64_t K = P * 13 + C * 12 + 1; vector a(K + 1); for (int i = 0; i < K; i++) a[i] = mod - way[K - i]; a[K] = 1; int64_t M = N + K - 1; AnyModPolynomial poly(mod); vector f = { 1 }, g = { 0, 1 }; for (; M > 0; g = poly.remmul(g, g, a), M >>= 1) if (M & 1) f = poly.remmul(f, g, a); int64_t ans = 0; for (int i = 0; i < K; i++) ans += int64_t(f[i]); cout << ans % mod << endl; }