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 MOD = 1000000007;
long long a, b;
long long mod(long long x) { return (x % MOD + MOD) % MOD; }
long long power(long long x, long long y) {
  long long res = 1;
  while (y) {
    if (y & 1) {
      --y;
      res = mod(res * x);
    }
    y /= 2;
    x = mod(x * x);
  }
  return res;
}
int main() {
  long long n, x;
  cin >> a >> b >> n >> x;
  if (a == 1) {
    cout << mod(x + mod(b * mod(n))) << endl;
    return 0;
  }
  long long res = mod(x * power(a, n));
  long long r = power(a, n) - 1;
  long long re = power(a - 1, MOD - 2);
  res = mod(res + mod(b * mod(r * re)));
  cout << res << endl;
}
