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 md = 1e9 + 7;
long long pow_mod(long long x, long long n) {
  long long tmp = x, ans = 1;
  while (n > 0) {
    if (n & (long long)1) ans = ans * tmp % md;
    tmp = tmp * tmp % md;
    n >>= 1;
  }
  return ans;
}
void init() {
  long long A, B, n, x;
  cin >> A >> B >> n >> x;
  long long An = pow_mod(A, n);
  long long ans;
  if (A == 1) {
    ans = An * x % md + n % md * B % md;
    ans %= md;
  } else {
    long long inv = pow_mod(A - 1, md - 2);
    ans = An * x % md;
    long long tmp = (An - 1) * inv % md;
    ans = (ans + B * tmp % md) % md;
  }
  cout << ans << "\n";
  return;
}
int main() {
  init();
  return 0;
}
