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>
const int mod = 1e9 + 7;
using namespace std;
long long POW(long long bs, long long ex) {
  long long res = 1;
  while (ex) {
    if (ex % 2) res = (res * bs) % mod;
    bs = (bs * bs) % mod;
    ex /= 2LL;
  }
  return res % mod;
}
long long GS(long long r, long long n) {
  if (r == 1) return n % mod;
  return (1 - POW(r, n)) * POW(1 - r, mod - 2) % mod;
}
int main() {
  long long a, b, n, x;
  cin >> a >> b >> n >> x;
  cout << (POW(a, n) * x + b * GS(a, n)) % mod;
}
