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 mod = 1E9 + 7;
long long swift(long long n, long long x) {
  long long res = 1;
  while (n) {
    if (n & 1) res = res * x % mod;
    x = x * x % mod;
    n = n >> 1;
  }
  return res;
}
int main() {
  long long A, B, n, x, An = 0, AB = 0, Anx = 0, inv = 0;
  cin >> A >> B >> n >> x;
  if (A == 1) return cout << (x + n % mod * B % mod) % mod << endl, 0;
  An = swift(n, A);
  Anx = An % mod * x % mod;
  inv = swift(mod - 2, A - 1);
  AB = (An - 1) * inv % mod * B % mod;
  cout << (Anx + AB) % mod << endl;
  return 0;
}
