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 math
[A,B,n,x]=[int(x) for x in raw_input().split()]
q=pow(10,9)+7
total=pow(A,n,q)*x
total%=q
if A==1:
    total=x+n*B
    total%=q
    print total
else:
    m=pow(A,n,q)-1
    m*= pow(A-1,q-2,q)
    m*=B
    total+=m
    total%=q
    print total