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 int N = 300010, Mod = 1e9 + 7;
long long A, B, x, n, ans, A1;
long long power(long long x, long long y) {
  long long ans = 1, temp = x;
  while (y) {
    if (y & 1) ans = (1ll * ans * temp) % Mod;
    temp = (1ll * temp * temp) % Mod;
    y /= 2;
  }
  return ans;
}
long long mod_inverse(long long x) { return power(x, Mod - 2); }
int main() {
  cin >> A >> B >> n >> x;
  if (A == 1) {
    ans = (((n % Mod) * B) % Mod + x) % Mod;
    cout << ans << endl;
    return 0;
  }
  A1 = power(A, n);
  B = ((B * mod_inverse(A - 1)) % Mod * ((A1 - 1 + Mod) % Mod)) % Mod;
  ans = ((A1 * (x % Mod)) % Mod + B) % Mod;
  cout << ans << endl;
  return 0;
}
