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

def r():
	return sys.stdin.readline()

mod = 1000000007

def q(n,a,b):
	if n == 0:
		return 1,0
	if n == 1:
		return a,b
	if n % 2 == 1:
		xa,xb = q(n-1,a,b)
		return a*xa % mod, (a*xb + b) % mod
	else:
		xa,xb = q(n/2,a,b)
		return xa*xa % mod, (xa*xb + xb) % mod

a,b,n,x = map(int, r().split())

xa,xb = q(n,a,b)
print (x*xa+xb) % mod

