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
#include <bits/stdc++.h>
using namespace std;
long long a, b, x, n, ans;
const int mod = 1e9 + 7;
int main() {
  cin >> a >> b >> n >> x;
  while (n) {
    if ((n % 2) != 0) x = (a * x + b) % mod;
    b = (a * b + b) % mod;
    a = (a * a) % mod;
    n /= 2;
  }
  cout << x << endl;
  return 0;
}
