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
def egcd(a, b):
    x = v = 0
    y = u = 1
    while a:
        q, r = divmod(b, a)
        a, b, x, y, u, v = r, a, u, v, x - u * q, y - v * q
    return x, y, b


def main():
    a, b, n, x = map(int, input().split())
    mod = 1000000007
    print(((x + b * n) if a == 1 else (pow(a, n, mod) * x + (pow(a, n, mod) - 1) * b * egcd(a - 1, mod)[0])) % mod)


if __name__ == '__main__':
    main()
