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 calc(A, n, M):
    if n == 0:
        return 1
    if n == 1:
        return A % M
    res = calc(A, n/2, M)
    nr = (res * res) % M
    if n % 2 == 1:
        return (nr * A) % M
    return nr


if __name__ == "__main__":
    M = 10**9 + 7
    for line in sys.stdin:
        tokens = line.strip("\n").split()
        A = int(tokens[0])
        B = int(tokens[1])
        n = int(tokens[2])
        x = int(tokens[3])
        if A == 1:
            print ((x % M) + ((n%M) * (B%M)) % M) % M
        else:
            A_n = calc(A, n, M)
            A_M = calc(A-1, M-2, M)
            print (((A_n % M) * x) % M + ((B%M) * ((A_n-1)%M) * (A_M%M)) % M) % M
        # r = x
        # while True:
        #     if n == 0:
        #         break
        #     r = (((A%M) * (r%M)) % M + B % M) % M
        #     n -= 1
        # print r
 		       		 		       					 	 	