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
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Jul 11 16:49:52 2020

@author: shailesh
"""
#def power_sum(A,n):
#    if A == 1:
#        return 1


A,B,n,x = [int(i) for i in input().split()]

#n-=1

m = 10**9 + 7
#val = A**n*x + B*(A**n - 1)//(A-1)
if A != 1:
    val = pow(A,n,m)*x + B*(pow(A,n,m) - 1)*pow(A-1,m-2,m)
else:
    val = (x + n*B)
print(val%(m))