#include<bits/stdc++.h>
using namespace std;
const long long INF = 1ll<< 61;
int main(){
  int64_t n,k;
  cin >> n >> k;
  int64_t a[n];
  for(int i=0;i<n;i++){
    cin >> a[i];
  }
  sort(a,a+n);
  long long Left=-INF,Right=INF;
  while(Right-Left>1){
    int64_t x=(Left+Right)/2;
    int64_t S=0,T=0;    
    for(int64_t i=0;i<n;i++){
      if(a[i]>0){
        int l2=-1,r2=n;
        while(r2-l2>1){
          int m=(l2+r2)/2;
          if(a[i]*a[m]<=x)l2=m;
          else r2=m;
        }
        S+=r2;
      }else if(a[i]<0){
        int l2=-1,r2=n;
        while(r2-l2>1){
          int m=(l2+r2)/2;
          if(a[i]*a[m]<=x)r2=m;
          else l2=m;
        }
        S+=n-r2;
      }else if(x>=0)S+=n;
      if(a[i]*a[i]<=x)T++;
    }
    int64_t num=(S-T)/2;
    if(num>=k)Right=x;
    else Left=x;
  }
  cout << Right << endl;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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;
const long long INF = 1ll<< 61;
int main(){
  int64_t n,k;
  cin >> n >> k;
  int64_t a[n];
  for(int i=0;i<n;i++){
    cin >> a[i];
  }
  sort(a,a+n);
  long long Left=-INF,Right=INF;
  while(Right-Left>1){
    int64_t x=(Left+Right)/2;
    int64_t S=0,T=0;    
    for(int64_t i=0;i<n;i++){
      if(a[i]>0){
        int l2=-1,r2=n;
        while(r2-l2>1){
          int m=(l2+r2)/2;
          if(a[i]*a[m]<=x)l2=m;
          else r2=m;
        }
        S+=r2;
      }else if(a[i]<0){
        int l2=-1,r2=n;
        while(r2-l2>1){
          int m=(l2+r2)/2;
          if(a[i]*a[m]<=x)r2=m;
          else l2=m;
        }
        S+=n-r2;
      }else if(x>=0)S+=n;
      if(a[i]*a[i]<=x)T++;
    }
    int64_t num=(S-T)/2;
    if(num>=k)Right=x;
    else Left=x;
  }
  cout << Right << endl;
}

```