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 os, sys
from io import BytesIO, IOBase
mod=10**9+7

input = lambda: sys.stdin.readline().rstrip("\r\n")

def pw(x,y):
    ans=1
    while y:
        if y%2:
            ans*=x
            y-=1
            ans%=mod
        else:
            x*=x
            y//=2
            x%=mod
    return ans

a,b,n,x=map(int,input().split())
ans=0
t=pw(a,n)
#print(t)
ans+=x*t
#print(ans)
ans%=mod
if a!=1:
    ans+=(b*(t-1))*pw((a-1),mod-2)
    ans%=mod
else:
    ans+=(n)*b
    ans%=mod
print(ans)