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 exprap(long long bb, long long n) {
  if (n == 0) return 1;
  if (n % 2 == 0)
    return exprap((bb * bb) % 1000000007, n / 2) % 1000000007;
  else
    return (bb * (exprap(bb, n - 1)) % 1000000007) % 1000000007;
}
long long somapg(long long q, long long n) {
  if (q == 1) return n % 1000000007;
  if (n >= 1)
    return ((exprap(q, n) - 1) * exprap(q - 1, 1000000007 - 2)) % 1000000007;
  else
    return 0;
}
int main() {
  long long a, b, n, x;
  scanf("%lld %lld %lld %lld", &a, &b, &n, &x);
  printf("%lld\n", (x * exprap(a, n) + b * somapg(a, n)) % 1000000007);
  return 0;
}
