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, stdout


def multy(A, B):
    sze = 2
    result = [[0, 0], [0, 0]]
    
    for i in range(sze):
        for j in range(sze):
            for z in range(sze):
                result[i][j] = (result[i][j] + A[i][z] * B[z][j]) % MOD
    
    return result


def power(matr, pw):
    result = [[1, 0], [0, 1]]
    
    while pw:
        if pw & 1:
            result = multy(result, matr)
        
        pw >>= 1
        matr = multy(matr, matr)
    
    return result


a, b, n, x = map(int, stdin.readline().split())
matrix = [[a, b], [0, 1]]
MOD = 10 ** 9 + 7


matrix = power(matrix, n)
stdout.write(str((x * matrix[0][0] + matrix[0][1]) % MOD))