Iterated Linear Function

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 10⁹ + 7.

The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 10⁹, 1 ≤ n ≤ 10¹⁸) — 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.

Print the only integer s — the value g⁽ⁿ⁾(x) modulo 10⁹ + 7.

3 4 1 1

7

3 4 2 1

25

3 4 3 1

79