/* -*- coding: utf-8 -*- * * 718.cc: No.718 行列のできるフィボナッチ数列道場 (1) - yukicoder */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; /* constant */ const int N = 7; const int MOD = 1000000007; /* typedef */ typedef long long ll; typedef int vec[N]; typedef vec mat[N]; /* global variables */ /* g_i = f_i^2, h_i = f_i*f_i+1, F_i = sum_{j=0}^i g_j g_i+2 = (f_i+2)^2 = (f_i+f_i+1)^2 = f_i^2 + 2*f_i*f_i+1 + f_i+1^2 = g_i + 2*h_i + g_i+1 h_i+2 = f_i+2 * f_i+3 = f_i+2 * (f_i+1 + f_i+2) = f_i+1*f_i+2 + f_i+2^2 = h_i+1 + g_i+2 = h_i+1 + g_i + 2*h_i + g_i+1 f_i+1 |0 1 0 0 0 0 0| f_i f_i+2 |1 1 0 0 0 0 0| f_i+1 g_i+1 |0 0 0 1 0 0 0| g_i g_i+2 = |0 0 1 1 2 0 0| g_i+1 h_i+1 |0 0 0 0 0 1 0| h_i h_i+2 |0 0 1 1 2 1 0| h_i+1 F_i+1 |0 0 0 1 0 0 1| F_i f_i = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, g_i = 0, 1, 1, 4, 9, 25, 64, 169, 441, 1156, h_i = 0, 1, 2, 6, 15, 40, 104, 273, 714, F_i = 0, 1, 2, 6, 15, 40, 104, 273, 714, 0, 1, 0, 1, 0, 1, 0 1, 1, 1, 1, 1, 2, 1 1, 2, 1, 4, 2, 6, 2 2, 3, 4, 9, 6, 15, 6 */ const mat IM = {{0, 1, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 1, 1, 2, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 1, 1, 2, 1, 0}, {0, 0, 0, 1, 0, 0, 1}, }; const vec IV = {0, 1, 0, 1, 0, 1, 0}; /* subroutines */ inline void initvec(vec a) { fill(a, a + N, 0); } inline void initmat(mat a) { for (int i = 0; i < N; i++) initvec(a[i]); } inline void unitmat(mat a) { initmat(a); for (int i = 0; i < N; i++) a[i][i] = 1; } inline void copymat(const mat a, mat b) { memcpy(b, a, sizeof(mat)); } inline void addmat(const mat a, const mat b, mat c) { for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) c[i][j] = ((ll)a[i][j] + b[i][j]) % MOD; } inline void mulmat(const mat a, const mat b, mat c) { for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) { c[i][j] = 0; for (int k = 0; k < N; k++) c[i][j] = ((ll)c[i][j] + (ll)a[i][k] * b[k][j] % MOD) % MOD; } } inline void powmat(const mat a, ll b, mat c) { mat s, t; copymat(a, s); unitmat(c); while (b > 0) { if ((b & 1LL) != 0) { mulmat(c, s, t); copymat(t, c); } mulmat(s, s, t); copymat(t, s); b >>= 1; } } inline void mulmatvec(const mat a, const vec b, vec c) { for (int i = 0; i < N; i++) { c[i] = 0; for (int j = 0; j < N; j++) c[i] = ((ll)c[i] + (ll)a[i][j] * b[j] % MOD) % MOD; } } void printvec(const vec a) { for (int j = 0; j < N; j++) { if (j) putchar(' '); printf("%d", a[j]); } putchar('\n'); } void printmat(const mat a) { for (int i = 0; i < N; i++) printvec(a[i]); } /* main */ int main() { ll n; scanf("%lld", &n); mat m; powmat(IM, n, m); vec v; mulmatvec(m, IV, v); printf("%d\n", v[6]); //printvec(v); return 0; }