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
from sys import stdin

mod = 10**9+7

def geo(x, n, m):
    return (pow(x, n+1, m) - 1)*pow(x-1, m-2, m)

p, q, n, a = [int(x) for x in stdin.readline().rstrip().split()]
if p <= 1:
    print((a + q * n) % mod)
else:
    ans = (a * pow(p, n, mod) + q * (geo(p, n-1, mod) % mod)) % mod
    print(ans)
