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;
const long long c = 1e9 + 7;
long long a, b, x;
long long mod(long long num, long long n) {
  long long rec;
  if (n == 0) return 1;
  rec = mod(num, n / 2);
  if (n % 2 == 0) return (rec * rec) % c;
  return (((rec * num) % c) * rec) % c;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n;
  cin >> a >> b >> n >> x;
  if (a == 1) {
    cout << (((mod(a, n) % c) * (x % c)) % c + ((b % c) * (n % c)) % c) % c
         << endl;
    return 0;
  }
  cout << (((mod(a, n) * x) % c) +
           (((b * (mod(a, n) - 1)) % c) * (mod(a - 1, c - 2)) % c)) %
              c
       << endl;
  return 0;
}
