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
from sys import stdin
import sys
sys.setrecursionlimit(10**7)
A,B,n,x=map(int,stdin.readline().strip().split())
mod=10**9+7
"""
dp=[-1 for i in range(n+10)]
def f(x1):
    return (A*x1+B)%mod
def g(n,x):
    if n==0:
        return x
    if dp[n]!=-1:
       return dp[n]
    dp[n]=f(g(n-1,x))
    return dp[n]
"""
def geo(n):
    ans=(pow(A,n,mod)*x)%mod
    if(A!=1):
        ans1=(((B-B*pow(A,n,mod))%mod)*pow(1-A,mod-2,mod))%mod
    else:
        ans1=(B*n)
    return (ans+ans1)%mod
print(geo(n))
