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;
long long mod = 1e9 + 7;
pair<long long, long long> cc(pair<long long, long long> g,
                              pair<long long, long long> f) {
  return make_pair(f.first * g.first % mod,
                   (f.first * g.second + f.second) % mod);
}
int main() {
  long long A, B, e, first;
  cin >> A >> B >> e >> first;
  pair<long long, long long> ret(1, 0), b(A, B);
  while (e) {
    if (e & 1) ret = cc(ret, b);
    b = cc(b, b);
    e >>= 1;
  }
  cout << (ret.first * first + ret.second) % mod << endl;
}
