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
M = 10**9 + 7
def le(A, n):
    if(A == 1):
        return n
    else:
        return (((pow(A, n, M) % M) - (1 % M)) % M) * pow(A - 1, M-2, M)
A,B,n,x = map(int,input().split())
first = (pow(A, n, M) * x) % M
second = (B * le(A, n)) % M
if(n == 1):
    print((A * x + B) % M)
else:
    print((first + second) % M)