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
mod=10**9+7
def ans(n,a,b):
    if n==0:
        return 1,0
    elif n==1:
        return a,b
    elif n%2==1:
        p,q=ans(n-1,a,b)
        return (a*p)%mod,(a*q+b)%mod
    else:
        p,q=ans(n/2,a,b)
        return (p*p)%mod,(p*q+q)%mod
a,b,n,x=map(int,raw_input().split())
p,q=ans(n,a,b)
print (x*p+q)%mod
        