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 = (long long)(1e9) + 7;
long long power(long long x, long long y) {
  long long p = mod;
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res % p;
}
int main() {
  std::ios_base::sync_with_stdio(0);
  std::cin.tie(0);
  std::cout.tie(0);
  int t = 1;
  while (t--) {
    long long a, b, n, x;
    cin >> a >> b >> n >> x;
    if (a == 1) {
      cout << ((b % mod) * (n % mod) + x % mod) % mod << endl;
      continue;
    }
    long long p = power(a, n);
    long long pp = power(a - 1, mod - 2);
    long long ans =
        ((p * x) % mod + (((b * (p - 1LL)) % mod) * pp) % mod) % mod;
    cout << (long long)(ans % mod);
  }
  return 0;
}
