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;
int pwr(int base, long long exp) {
  if (exp == 0) return 1;
  if (exp == 1) return base;
  int res = (1LL * base * base) % 1000000007;
  return (1LL * pwr(res, exp >> 1LL) * pwr(base, exp & 1LL)) % 1000000007;
}
int main() {
  int a, b, x, an;
  long long n;
  cin >> a >> b >> n >> x;
  an = pwr(a, n);
  n %= 1000000007;
  int res1 = (1LL * an * x) % 1000000007;
  int res2 = (an - 1 + 1000000007) % 1000000007;
  if (a != 1) {
    res2 = (1LL * res2 * b) % 1000000007;
    res2 = (1LL * res2 * pwr(a - 1, 1000000007 - 2)) % 1000000007;
  } else
    res2 = (1LL * n * b) % 1000000007;
  cout << (res1 + res2) % 1000000007 << endl;
  return 0;
}
