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 math

t=input().split()
a=int(t[0])
b=int(t[1])
n=int(t[2])
x=int(t[3])
var=1000000007
ans=0
if n==1:
	ans=(a*x+b)%var
	print (ans)
	exit()
if a==1:
	ans=(x+b*n)%var
	print (ans)
	exit()
def f(a,n,var):
	res=1
	while n:
		if n & 1:
			res=(res*a)%var
		a=(a*a)%var
		n=n//2
	return res
ans=(f(a,n,var)*x)%var;
t=(b*(f(a,n,var)+var-1))%var
p=(t*f(a-1,var-2,var))%var
ans=(ans+p)%var;
print (ans)
exit()