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 = 1e9 + 7;
int qpow(int x, long long int k) {
  int ans = 1;
  while (k) {
    if (k & 1) ans = ((long long int)ans * x) % mod;
    x = ((long long int)x * x) % mod;
    k >>= 1;
  }
  return ans;
}
int main() {
  long long int a, b, n, x;
  cin >> a >> b >> n >> x;
  long long int t1 = ((long long int)qpow(a, n) * x) % mod;
  if (a == 1) {
    cout << (t1 + (long long int)(n % mod) * b) % mod << endl;
  } else {
    long long int t2 = (long long int)(qpow(a, n) - 1);
    long long int t3 = qpow(a - 1, mod - 2);
    long long int t4 = (((t2 * t3) % mod) * b) % mod;
    cout << (t1 + t4) % mod << endl;
  }
  return 0;
}
