#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

int main(void){
  int n,i;
  ll k,a[200005];
  
  cin >> n >> k;
  for (i=0;i<n;i++) cin >> a[i];
  
  sort(a,a+n);
  
  ll l,r,mid,trg,t;
  ll *p;
  l=-1e18;
  r=1e18;
  while (r-l>1){
    
    mid=(l+r)/2;
    t=0;
    for (i=0;i<n;i++){
      if (a[i]==0){
        if (mid>=0) t+=n-1;
      }else if (a[i]<0){
        if (mid>=0) trg=-(mid/(-a[i]));
        else trg=(-mid-a[i]-1)/(-a[i]);
        p=lower_bound(a,a+n,trg);
        if (p<=a+i) p++;
        t+=a+n-p;
      }else{
        if (mid>=0) trg=mid/a[i];
        else trg=(mid-a[i]+1)/a[i];
        p=upper_bound(a,a+n,trg);
        if (p>a+i) p--;
        t+=p-a;
      }
    }
    if (t/2>=k) r=mid;
    else l=mid;
    
  }
  
  cout << r << endl;
  
  return 0;
}
### Prompt

In cpp, your task is to solve the following problem:

We have N integers A_1, A_2, ..., A_N.

There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?

Constraints

* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:


N K
A_1 A_2 \dots A_N


Output

Print the answer.

Examples

Input

4 3
3 3 -4 -2


Output

-6


Input

10 40
5 4 3 2 -1 0 0 0 0 0


Output

6


Input

30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0


Output

448283280358331064

### Response

```cpp
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

int main(void){
  int n,i;
  ll k,a[200005];
  
  cin >> n >> k;
  for (i=0;i<n;i++) cin >> a[i];
  
  sort(a,a+n);
  
  ll l,r,mid,trg,t;
  ll *p;
  l=-1e18;
  r=1e18;
  while (r-l>1){
    
    mid=(l+r)/2;
    t=0;
    for (i=0;i<n;i++){
      if (a[i]==0){
        if (mid>=0) t+=n-1;
      }else if (a[i]<0){
        if (mid>=0) trg=-(mid/(-a[i]));
        else trg=(-mid-a[i]-1)/(-a[i]);
        p=lower_bound(a,a+n,trg);
        if (p<=a+i) p++;
        t+=a+n-p;
      }else{
        if (mid>=0) trg=mid/a[i];
        else trg=(mid-a[i]+1)/a[i];
        p=upper_bound(a,a+n,trg);
        if (p>a+i) p--;
        t+=p-a;
      }
    }
    if (t/2>=k) r=mid;
    else l=mid;
    
  }
  
  cout << r << endl;
  
  return 0;
}
```