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 int exp(long long int a, long long int p) {
  if (p == 0) {
    return 1;
  }
  if (p == 1) {
    return a;
  }
  long long int temp = exp(a, p / 2);
  temp = (temp * temp) % 1000000007;
  if (p % 2) {
    temp = (temp * a) % 1000000007;
  }
  return temp;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int a, b, n, x;
  long long int temp, t1, t2;
  cin >> a >> b >> n >> x;
  if (n == 0) {
    cout << x;
    return 0;
  }
  if (a == 1) {
    cout << ((x + (n % 1000000007) * b) % 1000000007);
    return 0;
  }
  temp = exp(a, n);
  t1 = (temp * x) % 1000000007;
  t2 = ((temp - 1) * exp(a - 1, 1000000007 - 2)) % 1000000007;
  t2 = (t2 * b) % 1000000007;
  cout << ((t1 + t2) % 1000000007);
  return 0;
}
