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 ow(long long a, long long n) {
  if (n == 0) return 1;
  long long t = ow(a, n / 2);
  t = (t * t) % 1000000007;
  if (n % 2) t = (t * a) % 1000000007;
  return t % 1000000007;
}
int main() {
  long long int a, b, n, x;
  cin >> a >> b >> n >> x;
  if (a != 1) {
    long long po = ow(a, n);
    long long in = ow(a - 1, 1000000007 - 2);
    long long m = 0;
    m = ((po - 1) * in) % 1000000007;
    m = (m * b) % 1000000007;
    m = (m % 1000000007 + (po * x) % 1000000007) % 1000000007;
    cout << m << endl;
  } else {
    long long m = 0;
    b = b % 1000000007;
    n = n % 1000000007;
    x = x % 1000000007;
    m = (b * n) % 1000000007;
    m = (m + x) % 1000000007;
    cout << m << endl;
  }
}
