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 fastpow(a, n, b):
    #print(a, n, b)
    if a == 0:
        return 0
    base = 1
    m = a % b
    res = 1
    for i in range(64):
        if (n & base) > 0:
            res = (res * m) % b
        base = base*2
        m = (m * m) % b
        if base > n:
            break
    return res

if __name__ == '__main__':
    A, B, n, f0 = sys.stdin.read().split()
    A = int(A)
    B = int(B)
    n = int(n)
    f0 = int(f0)
    M = 1000000007

    if A == 1:
        res = ((B * n) % M + f0) % M
    else:
        t0 = fastpow(A, n, M)
        t1 = f0 % M
        t2 = (fastpow(A, n, M) + M - 1) % M
        t3 = fastpow(A-1, M-2, M)
        t4 = B % M

        res = ((t0 * t1) % M + ((t2 * t3) % M * t4) % M) % M
    print(res)
   			 	 	  		 	   			  		 		