## 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;
}``````
Copy The Code &

Input

cmd
4 2

Output

cmd
2

## Demonstration

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