Algorithm


A. k-th divisor
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 ≤ 10151 ≤ k ≤ 109).

Output

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

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

Examples
input
Copy
4 2
output
Copy
2
input
Copy
5 3
output
Copy
-1
input
Copy
12 5
output
Copy
6
Note

In the first example, number 4 has three divisors: 12 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.

 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include <bits/stdc++.h>

using namespace std;

vector<long long> d;
long long n, k;

int main() {
  scanf("%lld %lld", &n, &k);
  
  for(int i = 1; 1ll * i * i <= n; ++i) {
    if(n % i == 0) {
      d.push_back(i);
      
      if(n / i != i)
        d.push_back(n / i);
    }
  }
  
  sort(d.begin(), d.end());
  
  if(d.size() < k) {
    puts("-1");
    return 0;
  }
  
  printf("%lld\n", d[k - 1]);
  
  return 0;
}
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Input

x
+
cmd
4 2

Output

x
+
cmd
2
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Demonstration


Codeforces Solution-k-th divisor-Solution in C, C++, Java, Python

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