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 pot(long long b, long long p, int m) {
  long long res = 1;
  b %= m;
  while (p) {
    if (p & 1) {
      res *= b;
      res %= m;
    }
    b *= b;
    b %= m;
    p /= 2;
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long a, b, x, n, m = 1e9 + 7;
  cin >> a >> b >> n >> x;
  if (a == 1) {
    cout << ((pot(a, n, m) * x) % m + (b * (n % m)) % m) % m << '\n';
    return 0;
  }
  cout << ((pot(a, n, m) * x) % m +
           (b * ((((((pot(a, n, m) - 1) % (m)) + (m)) % (m)) *
                  pot(((((a - 1) % (m)) + (m)) % (m)), m - 2, m)) %
                 m)) %
               m) %
              m
       << '\n';
  return 0;
}
