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

mod = int(1000000007)
def inv(a):
    a1 = pow(a, mod-2, mod)
    return a1
A, B, n, x = map(int, raw_input().split(' '))
A, B, n, x = [int(A), (int)(B), (int)(n), (int)(x)]
#print A,B, n, x

if A != 1:
    A_n = pow(A, n, mod)
    rev = inv(A-1)
    p1 = (A_n*x)%mod
    p2 = B*((((A_n*rev)%mod)-rev)%mod)
    ans = (p1 + p2)%mod
    print ans
else:
    ans = (x + (B*(n)%mod))%mod
    print ans



