#include <bits/stdc++.h>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;
using lint=long long;

const long long INF=1LL<<61;

int main(){
	int n;
	lint k; scanf("%d%lld",&n,&k);
	vector<lint> a(n);
	rep(i,n) scanf("%lld",&a[i]);

	auto b=a;
	rep(i,n) b[i]*=-1;

	sort(a.begin(),a.end());
	sort(b.begin(),b.end());

	lint lo=-INF,hi=INF;
	while(hi-lo>1){
		lint mi=(lo+hi)/2;

		lint cnt=0;
		rep(i,n){
			if(a[i]==0){
				if(mi>=0) cnt+=n;
			}
			else if(a[i]>0){
				lint num;
				if(mi>=0) num=mi/a[i];
				else      num=-((-mi+a[i]-1)/a[i]);
				cnt+=upper_bound(a.begin(),a.end(),num)-a.begin();
			}
			else{
				lint num;
				if(mi>=0) num=mi/-a[i];
				else      num=-((-mi-a[i]-1)/-a[i]);
				cnt+=upper_bound(b.begin(),b.end(),num)-b.begin();
			}
			if(a[i]*a[i]<=mi) cnt--;
		}
		cnt/=2;

		if(cnt<k) lo=mi;
		else      hi=mi;
	}
	printf("%lld\n",lo+1);

	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>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;
using lint=long long;

const long long INF=1LL<<61;

int main(){
	int n;
	lint k; scanf("%d%lld",&n,&k);
	vector<lint> a(n);
	rep(i,n) scanf("%lld",&a[i]);

	auto b=a;
	rep(i,n) b[i]*=-1;

	sort(a.begin(),a.end());
	sort(b.begin(),b.end());

	lint lo=-INF,hi=INF;
	while(hi-lo>1){
		lint mi=(lo+hi)/2;

		lint cnt=0;
		rep(i,n){
			if(a[i]==0){
				if(mi>=0) cnt+=n;
			}
			else if(a[i]>0){
				lint num;
				if(mi>=0) num=mi/a[i];
				else      num=-((-mi+a[i]-1)/a[i]);
				cnt+=upper_bound(a.begin(),a.end(),num)-a.begin();
			}
			else{
				lint num;
				if(mi>=0) num=mi/-a[i];
				else      num=-((-mi-a[i]-1)/-a[i]);
				cnt+=upper_bound(b.begin(),b.end(),num)-b.begin();
			}
			if(a[i]*a[i]<=mi) cnt--;
		}
		cnt/=2;

		if(cnt<k) lo=mi;
		else      hi=mi;
	}
	printf("%lld\n",lo+1);

	return 0;
}

```