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 main():
	for line in sys.stdin:
		line = line.split()
		A = int(line[0])
		B = int(line[1])
		n = int(line[2])
		x = int(line[3])
		if(A==1):
			asum = n
		else:
			num = pow(A,n,1000000007*(A-1))
			asum = ((num)//(A-1))%1000000007
			if(num == 1 and A == 2):
				asum = 0
		print((B*asum%1000000007+ x*pow(A,n,1000000007))%1000000007)

if __name__ == "__main__":
   main()