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 a, b, n, x;
const int mod = 1e9 + 7;
long long ans;
long long aced(long long i, long long k) {
  if (k == 0) return 1;
  long long tmp = aced(i, k / 2);
  if (k % 2 == 1)
    return 1LL * tmp * tmp % mod * i % mod;
  else
    return 1LL * tmp * tmp % mod;
}
int main() {
  cin >> a >> b >> n >> x;
  if (a == 1) {
    cout << 1LL * (x + 1LL * b * (n % mod)) % mod;
    return 0;
  }
  ans = 1LL * (ans + 1LL * aced(a, n) * x % mod) % mod;
  long long tmp =
      1LL * (aced(a, n) % mod - 1) % mod * aced(a - 1, mod - 2) % mod * b % mod;
  ans = 1LL * (ans + tmp) % mod;
  cout << ans << endl;
}
