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 sys
from math import *

a, b, n, x = map(int, input().split())
inf = int(1e9 + 7)

def pow(x, n):
	ans = x % inf
	res = int(1)
	while (n):
		if (n & 1):
			res *= ans
			res %= inf
		ans *= ans
		ans %= inf 
		n >>= 1
	return res
r = (pow(a,n) - 1) % inf * pow(a - 1, int(inf) - 2) if a != 1 else n
print((pow(a,n) * x % inf + b * r % inf + inf * inf) % inf) 