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;
long long quick(long long a, long long b) {
  long long ret = 1;
  while (b) {
    if (b & 1) ret = ret * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return ret;
}
int main() {
  long long A, B, n, x;
  cin >> A >> B >> n >> x;
  long long ai = quick(A, n);
  long long ax;
  if (A != 1) ax = quick(A - 1, mod - 2);
  long long res1 = ai * x % mod;
  long long res2;
  if (A != 1)
    res2 = (B * (((ai - 1) * ax) % mod)) % mod;
  else
    res2 = ((B % mod) * (n % mod)) % mod;
  long long res = (res2 + res1) % mod;
  cout << res << endl;
}
