Problem: You are given two integers n and k. Find k-th smallest divisor of n, or report that it doesn't exist.

Divisor of n is any such natural number, that n can be divided by it without remainder.

Input

The first line contains two integers n and k (1 ≤ n ≤ 1015, 1 ≤ k ≤ 109).

Output

If n has less than k divisors, output -1.

Otherwise, output the k-th smallest divisor of n.

Examples

Input

4 2


Output

2


Input

5 3


Output

-1


Input

12 5


Output

6

Note

In the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.

In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
long long n, k;
std::deque<long long> q;
signed main() {
  std::cin >> n >> k;
  for (register long long i = sqrt(n); i >= 1; i--) {
    if (n % i == 0) {
      if (i * i != n)
        q.push_front(i), q.push_back(n / i);
      else
        q.push_front(i);
    }
  }
  if (q.size() < k)
    std::cout << -1;
  else
    std::cout << q[k - 1];
  return 0;
}