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 GM(long long Num) { return Num % MOD; }
long long A, B, N, X;
long long PowLog(long long X, long long Y) {
  long long Ret = 1;
  for (; Y; Y >>= 1) {
    if (Y & 1) Ret = GM(Ret * X);
    X = GM(X * X);
  }
  return Ret;
}
int main() {
  cin >> A >> B >> N >> X;
  if (A == 1) {
    cout << GM(X + GM(B * GM(N))) << endl;
    return 0;
  }
  long long ANX = GM(PowLog(A, N) * X);
  long long SA = GM((PowLog(A, N) - 1) * PowLog(A - 1, MOD - 2));
  cout << GM(ANX + GM(B * SA)) << endl;
}
