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 A, B, n, x;
long long Pow(long long x, long long y) {
  long long temp = 1;
  while (y) {
    if (y & 1) temp = (temp * x) % MOD;
    x = (x * x) % MOD;
    y >>= 1;
  }
  return temp;
}
int main() {
  cin >> A >> B >> n >> x;
  if (A == 1) {
    cout << (x + (n % MOD * B % MOD)) % MOD;
  } else {
    long long ni = Pow(A - 1, MOD - 2);
    long long A_n = Pow(A, n);
    long long temp1 = B * ni % MOD * (A_n - 1) % MOD;
    temp1 = (temp1 + MOD) % MOD;
    temp1 = (temp1 + A_n * x % MOD) % MOD;
    cout << temp1 << endl;
  }
  return 0;
}
