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>
using namespace std;
int main(void) {
  long long int n, k;
  vector<long long int> v;
  cin >> n >> k;
  int square_root = sqrt(n) + 1;
  for (long long int i = 1; i < square_root; i++) {
    if (n % i == 0 && i * i != n) {
      v.push_back(i);
      v.push_back(n / i);
    }
    if (n % i == 0 && i * i == n) v.push_back(i);
  }
  sort(v.begin(), v.end());
  if (k > v.size())
    cout << "-1";
  else
    cout << v[k - 1];
  return 0;
}