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() {
  unsigned long long n, k;
  cin >> n >> k;
  vector<unsigned long long> factors;
  factors.push_back(1);
  if (n != 1) factors.push_back(n);
  for (int i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) {
      factors.push_back(i);
      if (i != sqrt(n)) factors.push_back(n / i);
    }
  }
  sort(factors.begin(), factors.end());
  if (k <= factors.size())
    cout << factors[k - 1];
  else
    cout << -1;
}