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
def solve(A,B,n,x):
    m = 10**9 + 7
    # A^n*x + B*(1-A^n)/(1-A) -> A^n*x + B*(1-A^n)*(1-A)^-1 -> A^n*x + B*(1-A^n)*(1-A)^(m-2)
    if A == 1:
        return (x + n*B)% m
    return (pow(A,n,m)*x + B*((1 - pow(A,n,m)) * pow(1-A,m-2,m))) % m
print(solve(*list(map(int,input().split()))))

