#include <bits/stdc++.h>
using namespace std;
#define int long long
const long long LINF=1e18;

signed main(){
  int n,k;cin>>n>>k;
  vector<int> v(n),w(n);
  for(int i=0;i<n;i++){cin>>v[i];w[i]=-v[i];}
  sort(v.begin(),v.end());sort(w.begin(),w.end());
  int ng=-LINF,ok=LINF;
  while(ok-ng>1){
    int mid=(ok+ng)>>1,tmp=0;
    for(int i=0;i<n;i++){
      if(v[i]>0){
        int l=-1,r=n;
        while(r-l>1){
          int m=(r+l)>>1;
          (v[i]*v[m]>mid?r:l)=m;
        }
        tmp+=r-(v[i]*v[i]<=mid);
      }
      if(!v[i]&&mid>=0)tmp+=n-1;
      if(v[i]<0){
        int l=-1,r=n;
        while(r-l>1){
          int m=(r+l)>>1;
          (-v[i]*w[m]>mid?r:l)=m;
        }
        tmp+=r-(v[i]*v[i]<=mid);
      }
    }
    if(tmp>=k*2)ok=mid;
    else ng=mid;
  }
  cout<<ok<<endl;
}

### Prompt

Please formulate a Cpp solution to 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 <bits/stdc++.h>
using namespace std;
#define int long long
const long long LINF=1e18;

signed main(){
  int n,k;cin>>n>>k;
  vector<int> v(n),w(n);
  for(int i=0;i<n;i++){cin>>v[i];w[i]=-v[i];}
  sort(v.begin(),v.end());sort(w.begin(),w.end());
  int ng=-LINF,ok=LINF;
  while(ok-ng>1){
    int mid=(ok+ng)>>1,tmp=0;
    for(int i=0;i<n;i++){
      if(v[i]>0){
        int l=-1,r=n;
        while(r-l>1){
          int m=(r+l)>>1;
          (v[i]*v[m]>mid?r:l)=m;
        }
        tmp+=r-(v[i]*v[i]<=mid);
      }
      if(!v[i]&&mid>=0)tmp+=n-1;
      if(v[i]<0){
        int l=-1,r=n;
        while(r-l>1){
          int m=(r+l)>>1;
          (-v[i]*w[m]>mid?r:l)=m;
        }
        tmp+=r-(v[i]*v[i]<=mid);
      }
    }
    if(tmp>=k*2)ok=mid;
    else ng=mid;
  }
  cout<<ok<<endl;
}

```