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

MAXN = 10 ** 9 + 7
f = sys.stdin
A, B, n, x = map(int, f.readline().strip().split(' '))
if A == 1:
    print((x + n * B) % MAXN)
else:
    ans = x
    while n > 0:
        if n % 2:
            ans = (A * ans + B) % MAXN;
        B = B * (A + 1) % MAXN;
        A = A * A % MAXN;
        n /= 2
    print(ans)
