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.

Input

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.

Output

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

Examples

Input

3 4 1 1


Output

7


Input

3 4 2 1


Output

25


Input

3 4 3 1


Output

79
#!/usr/bin/env python3


def g(a, b, n, x, mod=10 ** 9 + 7):
    if a == 1:
        return (x + b * n) % mod
    z = pow(a, n, mod)
    inv = pow(a - 1 + mod, mod - 2, mod)
    return (z * x + b * (z - 1 + mod) * inv) % mod

print(g(*[int(x) for x in input().split()]))
