Consider a linear function f(x) = Ax + B. Let's define g^{(0)}(x) = x and g^{(}n)(x) = f(g^{(}n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g^{(}n)(x) modulo 10^9 + 7.

-----Input-----

The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 10^9, 1 ≤ n ≤ 10^18) — the parameters from the problem statement.

Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.

-----Output-----

Print the only integer s — the value g^{(}n)(x) modulo 10^9 + 7.

-----Examples-----

Input 3 4 1 1

Output 7

Input 3 4 2 1

Output 25

Input 3 4 3 1

Output 79