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
from collections import defaultdict
import sys

def mpow(base, p):
    temp = 1
    while p:
        if (p & 1):
            temp = (temp * base) % MOD
        p //= 2
        base = (base * base) % MOD
    return temp % MOD
if __name__ == "__main__":
    #n, m = list(map(int, input().split()))
    a, b, n, x = map(int, input().split())
    MOD = 10 ** 9 + 7
    temp = mpow(a, n)
    if a > 1:
        ans = ((temp * x % MOD) + (b * (temp - 1) % MOD) * mpow(a - 1, MOD - 2) % MOD) % MOD
    else:
        ans = ((temp * x % MOD) + b * (n % MOD) % MOD) % MOD
    print(ans)   