/* -*- coding: utf-8 -*- * * 1559.cc: No.1559 Next Rational - 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 MOD = 1000000007; /* typedef */ typedef long long ll; typedef int vec[2]; typedef vec mat[2]; /* global variables */ mat ma, mb; /* subroutines */ inline void initvec(vec a) { memset(a, 0, sizeof(vec)); } inline void initmat(mat a) { memset(a, 0, sizeof(mat)); } inline void unitmat(mat a) { a[0][0] = a[1][1] = 1; a[0][1] = a[1][0] = 0; } inline void copymat(const mat a, mat b) { memcpy(b, a, sizeof(mat)); } inline void mulmat(const mat a, const mat b, mat c) { for (int i = 0; i < 2; i++) for (int j = 0; j < 2; j++) { c[i][j] = 0; for (int k = 0; k < 2; k++) c[i][j] = (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 & 1) { mulmat(c, s, t); copymat(t, c); } mulmat(s, s, t); copymat(t, s); b >>= 1; } } int powmod(int a, int n) { // a^n % MOD int pm = 1; while (n > 0) { if (n & 1) pm = (ll)pm * a % MOD; a = (ll)a * a % MOD; n >>= 1; } return pm; } /* main */ int main() { ll n; int a, b, k; scanf("%lld%d%d%d", &n, &a, &b, &k); int x = (((ll)a * a % MOD + (ll)b * b % MOD) % MOD + k) % MOD; int y = (ll)a * b % MOD; ma[0][0] = 0, ma[0][1] = 1; ma[1][0] = (MOD - 1), ma[1][1] = (ll)x * powmod(y, MOD - 2) % MOD; powmat(ma, n - 1, mb); int v = ((ll)mb[0][0] * a % MOD + (ll)mb[0][1] * b % MOD) % MOD; printf("%d\n", v); return 0; }