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;
vector<long long> div(long long x) {
  vector<long long> divisors;
  for (long long i = 1; i * i <= x; i++) {
    if (x % i == 0) {
      divisors.emplace_back(i);
      if (i != x / i) divisors.emplace_back(x / i);
    }
  }
  sort(divisors.begin(), divisors.end());
  return divisors;
}
long long n, k;
vector<long long> Ans;
int main() {
  scanf("%lld%lld", &n, &k);
  Ans = div(n);
  if (Ans.size() < k)
    printf("-1\n");
  else
    printf("%lld", Ans[k - 1]);
}