#include <iostream>
#include <vector>
#include <set>
#include <map>
#include <iomanip>
#include <stdio.h>
#include <algorithm>
#include <queue>
#include <string.h>
#define endl '\n'
#define pb push_back
#define mp make_pair
#define int long long
#define INF 0x3f3f3f3f
#define Inf 1000000000000000000LL
#define F first
#define S second
using namespace std;
typedef pair<int,int>pii;
int n,k;
int a[200010];
signed main(){
	cin>>n>>k;
	for(int i=0;i<n;i++)cin>>a[i];
	sort(a,a+n);
	int L=-Inf,R=Inf;
	while(L+1<R){
		int MID=(L+R)>>1,cnt=0;
		for(int i=0;i<n;i++){
			int l=i,r=n;
			while(l+1<r){
				int mid=(l+r)>>1;
				if(a[i]*a[mid]<=MID)(a[i]<0)?r=mid:l=mid;
				else (a[i]<0)?l=mid:r=mid;
			}
			cnt+=(a[i]<0)?n-r:l-i;
		}
		if(cnt<k)L=MID;
		else R=MID;
	}
	cout<<R<<endl;
	return 0;
}

### Prompt

Your task is to create 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 <iostream>
#include <vector>
#include <set>
#include <map>
#include <iomanip>
#include <stdio.h>
#include <algorithm>
#include <queue>
#include <string.h>
#define endl '\n'
#define pb push_back
#define mp make_pair
#define int long long
#define INF 0x3f3f3f3f
#define Inf 1000000000000000000LL
#define F first
#define S second
using namespace std;
typedef pair<int,int>pii;
int n,k;
int a[200010];
signed main(){
	cin>>n>>k;
	for(int i=0;i<n;i++)cin>>a[i];
	sort(a,a+n);
	int L=-Inf,R=Inf;
	while(L+1<R){
		int MID=(L+R)>>1,cnt=0;
		for(int i=0;i<n;i++){
			int l=i,r=n;
			while(l+1<r){
				int mid=(l+r)>>1;
				if(a[i]*a[mid]<=MID)(a[i]<0)?r=mid:l=mid;
				else (a[i]<0)?l=mid:r=mid;
			}
			cnt+=(a[i]<0)?n-r:l-i;
		}
		if(cnt<k)L=MID;
		else R=MID;
	}
	cout<<R<<endl;
	return 0;
}

```