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 sys import stdin, stderr, stdout, exit
from math import gcd

readl = lambda : list(map(int, stdin.readline().strip().split()))
MOD = 1000000007


def main():
    A, B, n, x = readl()
    if(A == 1):
        stdout.write(str((B*n + x) % MOD))
    else:
        An = pow(A, n, MOD)
        stdout.write(str((((An * x) % MOD) + (B * (1-An) * pow(1-A, MOD-2, MOD)) % MOD) % MOD))

if __name__ == '__main__':
    main()
