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 fun(long long a, long long b, long long c) {
  long long ans = 1;
  while (b != 0) {
    if (b % 2 == 1) ans = (ans * a) % c;
    a = (a * a) % c;
    b /= 2;
  }
  return ans;
}
int main() {
  long long n, a, b, x, ans, c = 1000000007, an;
  scanf("%lld %lld %lld %lld", &a, &b, &n, &x);
  long long k = (fun(a, n, c) * x) % c;
  if (a > 1) {
    long long f = ((fun(a, n, c) * b) % c - b + c) % c;
    long long h = fun(a - 1, c - 2, c);
    an = (f * h) % c;
  } else if (a == 1)
    an = (n % c * b) % c;
  ans = (k + an) % c;
  printf("%lld\n", ans);
  return 0;
}
