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 Pow(long long a, long long b) {
  long long ans = 1LL, base = a % 1000000007;
  while (b != 0) {
    if (b & 1LL != 0) ans = ans * base % 1000000007;
    base = base * base % 1000000007;
    b >>= 1LL;
  }
  return ans;
}
long long A, B, n, x;
long long ans;
int main() {
  scanf("%lld %lld %lld %lld", &A, &B, &n, &x);
  long long ppow = Pow(A, n) % 1000000007;
  if (A == 1LL)
    ans = (x % 1000000007 + n % 1000000007 * B % 1000000007) % 1000000007;
  else
    ans = (ppow * x % 1000000007 + B % 1000000007 * (ppow - 1LL) % 1000000007 *
                                       Pow(A - 1LL, 1000000007 - 2) %
                                       1000000007) %
          1000000007;
  cout << ans;
}
