#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define F first
#define S second
#define mkp make_pair
#define pii pair<int,int>
typedef long long ll;
const int maxn=2e5+5;
const int mod=1e9+7;
ll n,k,ling;
ll a[maxn];
bool check(ll x){
	ll cnt=0;
	for(int i=0;i<n;i++){
		if(a[i]==0){
			if(x>=0)cnt+=n-1;
			continue;
		}
		else if(a[i]<0){
			ll tmp=0;
			if(x>=0)tmp=x/a[i];//a[i]*tmp<=x
			else {
				if(x%a[i]==0)tmp=x/a[i];
				else tmp=x/a[i]+1;
			}
			cnt+=n-(lower_bound(a,a+n,tmp)-a);
		}
		else if(a[i]>0){
			ll tmp=0;
			if(x>=0)tmp=x/a[i];
			else{
				if(x%a[i]==0)tmp=x/a[i];
				else tmp=x/a[i]-1;
			}
			cnt+=upper_bound(a,a+n,tmp)-a;
		}
		if(a[i]*a[i]<=x)cnt--;
		//cout<<cnt<<endl;
	}
	return cnt/2>=k;
}
int main(){
	scanf("%lld%lld",&n,&k);
	for(int i=0;i<n;i++){
		scanf("%lld",&a[i]);
	}
	sort(a,a+n);
	ll l=-1e18,r=1e18,ans=0;
	while(l<=r){
		ll mid=(l+r)/2;
		if(check(mid))r=mid-1,ans=mid;
		else l=mid+1;
	}

	//check(-6);
	cout<<ans<<endl;
}

### Prompt

Generate 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 pb push_back
#define F first
#define S second
#define mkp make_pair
#define pii pair<int,int>
typedef long long ll;
const int maxn=2e5+5;
const int mod=1e9+7;
ll n,k,ling;
ll a[maxn];
bool check(ll x){
	ll cnt=0;
	for(int i=0;i<n;i++){
		if(a[i]==0){
			if(x>=0)cnt+=n-1;
			continue;
		}
		else if(a[i]<0){
			ll tmp=0;
			if(x>=0)tmp=x/a[i];//a[i]*tmp<=x
			else {
				if(x%a[i]==0)tmp=x/a[i];
				else tmp=x/a[i]+1;
			}
			cnt+=n-(lower_bound(a,a+n,tmp)-a);
		}
		else if(a[i]>0){
			ll tmp=0;
			if(x>=0)tmp=x/a[i];
			else{
				if(x%a[i]==0)tmp=x/a[i];
				else tmp=x/a[i]-1;
			}
			cnt+=upper_bound(a,a+n,tmp)-a;
		}
		if(a[i]*a[i]<=x)cnt--;
		//cout<<cnt<<endl;
	}
	return cnt/2>=k;
}
int main(){
	scanf("%lld%lld",&n,&k);
	for(int i=0;i<n;i++){
		scanf("%lld",&a[i]);
	}
	sort(a,a+n);
	ll l=-1e18,r=1e18,ans=0;
	while(l<=r){
		ll mid=(l+r)/2;
		if(check(mid))r=mid-1,ans=mid;
		else l=mid+1;
	}

	//check(-6);
	cout<<ans<<endl;
}

```