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
a,b,n,x=map(int, input().split());
m=1000000007;
def modex(a,n):
	ans=1
	while n:
		if n&1:
			ans=(ans%m*a%m)%m
		a=(a%m*a%m)%m
		n>>=1
	return ans
if a==1:
	print((x%m+(b%m*n%m)%m)%m)
else:
	print(((modex(a,n)%m*x%m)%m+(b%m*((modex(a,n)%m-1%m)%m)%m*(modex(a-1,m-2)))%m)%m)