#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define MOD 1000000007 #define R 36041 #define _R 85227895 #define N 131072 #define INF 9212376920367300606LL int m, rm, _m, _rm, p; long long n; int modPow(int a, long long n) { int res(1); for (; n; n >>= 1, a = 1LL * a * a % MOD) if (n & 1) res = 1LL * res * a % MOD; return res; } int mod[N], rmod[N]; void build() { int i; for (m = 1; 4 * p >= m; m <<= 1); rm = modPow(m, MOD - 2); for (mod[0] = i = 1; i < N; i++) mod[i] = 1LL * mod[i - 1] * R % MOD; for (rmod[0] = i = 1; i < N; i++) rmod[i] = 1LL * rmod[i - 1] * _R % MOD; } inline int EXP(int d, int p, int m) { if (d > 0) return mod[N / m * p]; return rmod[N / m * p]; } void FFT(int *in, int *out, int step, int size, int d) { if (size == 1) { out[0] = in[0]; return; } size >>= 1; FFT(in, out, step * 2, size, d); FFT(in + step, out + size, step * 2, size, d); int i, even, odd; for (i = 0; i < size; i++) { even = out[i], odd = out[i + size]; out[i] = (1LL * EXP(d, i, size << 1) * odd + even) % MOD; out[i + size] = (1LL * EXP(d, i + size, size << 1) * odd + even) % MOD; } } int _a[N << 1], _b[N << 1], _ab[N << 1], _c[N << 1]; void multi(int *a, int *_b, int p, int *c, int st, int en) { for (_m = 1; 2 * p >= _m; _m <<= 1); _rm = modPow(_m, MOD - 2); for (int i = p; i < _m; i++) a[i] = 0; FFT(a, _a, 1, _m, 1); for (int i = 0; i < _m; i++) _ab[i] = 1LL * _a[i] * _b[i] % MOD; FFT(_ab, _c, 1, _m, -1); for (int i = 0; i < en - st; i++) c[i] = 1LL * _c[i + st] * _rm % MOD; for (int i = en - st; i < _m; i++) c[i] = 0; } void sqr(int *a, int p, int *b) { FFT(a, _a, 1, m, 1); for (int i = 0; i < m; i++) _ab[i] = 1LL * _a[i] * _a[i] % MOD; FFT(_ab, _b, 1, m, -1); for (int i = 0; i < p; i++) b[i] = 1LL * _b[i] * rm % MOD; } vector P; int a[N << 1], c[N << 1], _I[N << 1], I[N << 1], _Q[N << 1], Q[N << 1], C[N << 1], _S[N << 1], _C[N << 1], S[N << 1], _B[N << 1], A[N << 1], B[N << 1], D[N << 1]; long long int aa[6] = { 2, 3, 5, 7, 11, 13 }; long long int b[6] = { 4, 6, 8, 9, 10, 12 }; vector cc; class make{ public: vector v; #define MAX 102 bool dp[MAX][10][10]; //何回目,sump sums bool use[MAX]; #define MOD 1000000007 long long int a[MAX]; long long int n; make(){ cc.clear(); scanf("%lld", &n); int p, c; cin >> p >> c; dp[0][0][0] = true; for (int i = 0; i < MAX; i++){ for (int j = 0; j <= p; j++){ for (int k = 0; k <= c; k++){ if (dp[i][j][k]){ use[i] = true; for (int kk = 0; kk < 6; kk++){ if (j < p){ dp[i + aa[kk]][j + 1][k] = true; use[i + aa[kk]] = true; } if (k < c){ dp[i + b[kk]][j][k + 1] = true; use[i + b[kk]] = true; } } } } } } cc.clear(); for (int i = 1; i < MAX; i++){ if (use[i]){ cc.push_back(i); } } a[0] = 1LL; for (int i = 0; i < MAX; i++){ for (int j = 0; j < cc.size(); j++){ if (i + cc[j] < MAX){ a[i + cc[j]] += a[i]; a[i + cc[j]] %= MOD; } } } } }; make mk; int ccc[MAX]; int main() { int i, j, ans, cur; long long q; p = cc.back(); n = mk.n; n++; // scanf("%d%lld", &p, &n); for (int i = 0; i < p; i++){ a[i] = mk.a[i]; } for (int i = 0; i < cc.size(); i++){ ccc[p-cc[i]]=true; } for (int i = 0; i < p; i++){ c[i] = ccc[i]; } // for (i = 0; i < p; i++) scanf("%d", &a[i]); //for (i = 0; i < p; i++) scanf("%d", &c[i]); if (n <= p) { printf("%d\n", a[n - 1]); return 0; } if (p == 1) { ans = 1LL * a[0] * modPow(c[0], n - 1) % MOD; printf("%d\n", ans); return 0; } build(); n--; for (j = 1; j <= p; j++) _I[j] = c[j - 1]; FFT(_I, I, 1, m, 1); for (C[0] = 1, j = 1; j < p; j++) C[j] = (MOD - c[j - 1]) % MOD; for (q = 2 * p - 1; q; q >>= 1) P.push_back(q); for (i = P.size() - 1; i >= 0; i--) { q = P[i]; if (q == 1) { S[0] = 1; for (j = 1; j <= p; j++) Q[j] = c[j - 1]; continue; } Q[0] = (Q[0] + 1) % MOD; for (j = 2 * p - 1; j < m; j++) S[j] = Q[j] = 0; FFT(Q, _Q, 1, m, 1); FFT(S, _S, 1, m, 1); for (j = 0; j < m; j++) _S[j] = 1LL * _S[j] * _Q[j] % MOD; FFT(_S, S, 1, m, -1); for (j = 0; j < 2 * p - 1; j++) S[j] = 1LL * S[j] * rm % MOD; Q[0] = (Q[0] + MOD - 1) % MOD; for (j = 0; j < m; j++) { _Q[j] = 1LL * (_Q[j] - 1) * (_Q[j] - 1) % MOD; if (_Q[j] < 0) _Q[j] += MOD; } FFT(_Q, Q, 1, m, -1); for (j = 0; j < 2 * p - 1; j++) Q[j] = 1LL * Q[j] * rm % MOD; if (q & 1) { for (j = 0; j < 2 * p - 1; j++) S[j] = (S[j] + Q[j]) % MOD; for (j = 2 * p - 1; j < m; j++) Q[j] = 0; FFT(Q, _Q, 1, m, 1); for (j = 0; j < m; j++) _Q[j] = 1LL * _Q[j] * I[j] % MOD; FFT(_Q, Q, 1, m, -1); for (j = 0; j < 2 * p - 1; j++) Q[j] = 1LL * Q[j] * rm % MOD; } } for (i = 2 * p - 1; i < m; i++) S[i] = 0; int _m = m >> 1, _rm = modPow(_m, MOD - 2); FFT(S, _S, 1, m, 1); FFT(C, _C, 1, _m, 1); P.clear(); for (q = n; q; q >>= 1) P.push_back(q); A[p - 1] = 1; for (i = P.size() - 1; i >= 0; i--) { q = P[i]; if (q < 2 * p - 1) { for (j = 0; j < p; j++) A[j] = ((q + j >= p - 1) ? S[q + j - p + 1] : 0); continue; } multi(A, _C, p, B, 0, p); for (j = _m; j < m; j++) B[j] = 0; FFT(B, D, 1, _m, 1); for (j = 0; j < _m; j++) D[j] = 1LL * D[j] * D[j] % MOD; FFT(D, B, 1, _m, -1); for (j = 0; j < 2 * p - 1; j++) B[j] = 1LL * B[j] * _rm % MOD; FFT(B, D, 1, m, 1); for (j = 0; j < m; j++) D[j] = 1LL * D[j] * _S[j] % MOD; FFT(D, A, 1, m, -1); for (j = 0; j < p; j++) A[j] = 1LL * A[j + p - 1] * rm % MOD; if (q & 1) { for (cur = 1LL * A[0] * c[p - 1] % MOD, j = 0; j < p - 1; j++) A[j] = A[j + 1]; for (j = 0; j < p - 1; j++) cur = (1LL * A[j] * c[p - 2 - j] + cur) % MOD; A[p - 1] = cur; } } FFT(a, _a, 1, _m, 1); for (i = 0; i < _m; i++) _a[i] = 1LL * _a[i] * _C[i] % MOD; FFT(_a, D, 1, _m, -1); for (i = 0; i < p; i++) D[i] = 1LL * D[i] * _rm % MOD; for (i = p; i < _m; i++) A[i] = D[i] = 0; FFT(A, _a, 1, _m, 1); FFT(D, a, 1, _m, 1); for (i = 0; i < _m; i++) _a[i] = 1LL * _a[i] * a[i] % MOD; FFT(_a, B, 1, _m, -1); ans = 1LL * B[p - 1] * _rm % MOD; printf("%d\n", ans); return 0; }