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 -*-

import time


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

start = time.time()

md  = 1000000007

if A!=1 :
    an  = pow(A, n, md*(A-1))
    bn  = B*(an-1)//(A-1)
    ans = (an*x+bn)%md
else:
    ans = (x+B*n)%md
print(ans)

finish = time.time()
#print(finish - start)
