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 = 1000000007;
long long A, B, n;
long long x;
long long r1 = 1, r2;
int main() {
  cin >> A >> B >> n >> x;
  while (n > 0) {
    if (n & 1) {
      long long r3 = r1 * A % MOD;
      long long r4 = (A * r2 + B) % MOD;
      r1 = r3;
      r2 = r4;
    }
    long long C = A * A % MOD;
    long long D = (A * B + B) % MOD;
    A = C;
    B = D;
    n /= 2;
  }
  cout << (r1 * x + r2) % MOD << endl;
  return 0;
}
