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
mod=1000000007
def power(x,y):
	res=1
	x=x%mod
	while(y>0):
		if((y&1)==1):
			res=(res*x)%mod
		y=y>>1
		x=(x*x)%mod
	return res
def modularinverse(a):
	return power(a,mod-2)
a,b,n,x=map(int,input().split())
if(a==1):
	print((x*power(a,n)+b*n)%1000000007)
else:
	print((x*power(a,n)+(b*(power(a,n)-1)*modularinverse(a-1)))%1000000007)