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, C, x, n, mod = 1e9 + 7;
long long power(long long a, long long n) {
  if (n == 0) return 1;
  long long p = power(a, n / 2) % mod;
  p = (p * p) % mod;
  if (n & 1) p = (p * a) % mod;
  return p;
}
int modInverse(long long a, long long m) { return power(a, m - 2); }
int main() {
  cin >> A >> B >> n >> x;
  long long z = power(A, n), y;
  if (A == 1)
    y = (n % mod) * (B) % mod;
  else
    y = B * (z - 1) % mod * modInverse(A - 1, mod) % mod;
  cout << ((z * x) % mod + y) % mod;
}
