#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int main(){
	long long n,k;
	cin>>n>>k;
	vector<long long>a(n);
	for(int i=0;i<n;i++)
		cin>>a[i];
	sort(a.begin(),a.end());
	long long ub=2e18,lb=-2e18;
	while(ub-lb>1){
		ll mid=(ub+lb)/2,cnt=0;
		for(int i=0;i<n-1;i++)
			if(a[i]>0)
				if(a[n-1]*a[i]<=mid)
					cnt+=(n-1)-(i+1)+1;
				else if(a[i+1]*a[i]>mid)
					continue;
				else{
					long long ub2=n-1,lb2=i+1;
					while(ub2-lb2>1){
						long long mid2=(ub2+lb2)/2;
						if(a[i]*a[mid2]<=mid)
							lb2=mid2;
						else
							ub2=mid2;
					}
					cnt+=ub2-(i+1);	  
				}
			else{
				if(a[i+1]*a[i]<=mid)
					cnt+=(n-1)-(i+1)+1;
				else if(a[n-1]*a[i]>mid)
					continue;
				else{
					long long ub2=n-1,lb2=i+1;
					while(ub2-lb2>1){
						long long mid2=(ub2+lb2)/2;
						if(a[i]*a[mid2]>mid)
							lb2=mid2;
						else
							ub2=mid2;
					}
				cnt+=n-1-lb2;
				}
			}
		if(cnt<k)
			lb=mid;
		else
			ub=mid;
	}
	cout<<ub<<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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
int main(){
	long long n,k;
	cin>>n>>k;
	vector<long long>a(n);
	for(int i=0;i<n;i++)
		cin>>a[i];
	sort(a.begin(),a.end());
	long long ub=2e18,lb=-2e18;
	while(ub-lb>1){
		ll mid=(ub+lb)/2,cnt=0;
		for(int i=0;i<n-1;i++)
			if(a[i]>0)
				if(a[n-1]*a[i]<=mid)
					cnt+=(n-1)-(i+1)+1;
				else if(a[i+1]*a[i]>mid)
					continue;
				else{
					long long ub2=n-1,lb2=i+1;
					while(ub2-lb2>1){
						long long mid2=(ub2+lb2)/2;
						if(a[i]*a[mid2]<=mid)
							lb2=mid2;
						else
							ub2=mid2;
					}
					cnt+=ub2-(i+1);	  
				}
			else{
				if(a[i+1]*a[i]<=mid)
					cnt+=(n-1)-(i+1)+1;
				else if(a[n-1]*a[i]>mid)
					continue;
				else{
					long long ub2=n-1,lb2=i+1;
					while(ub2-lb2>1){
						long long mid2=(ub2+lb2)/2;
						if(a[i]*a[mid2]>mid)
							lb2=mid2;
						else
							ub2=mid2;
					}
				cnt+=n-1-lb2;
				}
			}
		if(cnt<k)
			lb=mid;
		else
			ub=mid;
	}
	cout<<ub<<endl;
	return 0;
}
```