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
import sys

A, B, n, x = map(int, input().split())
mod = 10**9 + 7


def matmul(matA, matB):
    x, y, z = len(matA), len(matB[0]), len(matA[0])
    res = [[0]*y for _ in range(x)]

    for i in range(x):
        for j in range(y):
            for k in range(z):
                res[i][j] += matA[i][k] * matB[k][j]
            res[i][j] %= mod

    return res


matA = [
    [(A*x + B) % mod, 1],
    [x, 1]
]
matB = [
    [A, 0],
    [B, 1]
]
n -= 1

while n:
    if n & 1:
        matA = matmul(matA, matB)
    matB = matmul(matB, matB)
    n >>= 1

print(matA[0][0] % mod)
