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, N, X;
const long long MOD = 1e9 + 7;
long long pow_mod(long long x, long long n, long long a, long long b) {
  if (n == 0) {
    return x;
  } else if (n & 1) {
    return pow_mod((a * x + b) % MOD, n - 1, a, b);
  } else {
    return pow_mod(x, n >> 1, (a * a) % MOD, (a * b + b) % MOD);
  }
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> A >> B >> N >> X;
  cout << pow_mod(X, N, A, B) << endl;
  return 0;
}
