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,raw_input().split())

M = 1000000007

def exp(a,b):
	if b==0:
		return 1
	if b%2==1:
		return (a*exp(a,b-1))%M
	else:
		p = exp(a,b/2)
		return (p*p)%M


if a==1:
	res = (x+b*n)%M
else:
	res = ((exp(a,n)*x)%M + (((b*(exp(a,n)-1))%M) * exp(a-1,M-2))%M)%M

print res