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
A, B, M = 0, 0, 10**9 + 7

def GP(A,n):
    if n == 0:
        return 1
    if A == 1:
        return (n * A) % M
    res = (pow(A,n,M)-1) * pow(A-1,M-2,M)
    return res % M

def f(n,x):
    res = pow(A,n,M) * x + B * GP(A,n)
    return res % M

def g(n,x):
    if n == 0:
        return x
    elif n == 1:
        return (A*x + B) % M
    return f(n,x) % M

A, B, n, x = map(int,input().split())
print(g(n,x))
