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 = (int)1e9 + 7;
int pw(int x, long long k) {
  int res = 1;
  int mul = x;
  while (k > 0) {
    if (k & 1) res = 1LL * res * mul % mod;
    mul = 1LL * mul * mul % mod;
    k >>= 1;
  }
  return (res);
}
int inverse(int x) { return (pw(x, mod - 2)); }
int main(void) {
  int a, b, x;
  long long n;
  cin >> a >> b >> n >> x;
  if (a == 1)
    cout << (x + n % mod * b) % mod << endl;
  else
    cout << (1LL * pw(a, n) * x % mod +
             1LL * (pw(a, n) - 1 + mod) * inverse(a - 1) % mod * b) %
                mod
         << endl;
  return 0;
}
