#include<bits/stdc++.h>
using namespace std;
typedef long long i64;
const int N=2e5+5;
const i64 INF=1e18;

int a[N];
int n;
i64 m;

int bs1(int l,int r,i64 x,i64 y){
	int mid;
	while(l<=r){
		mid=(l+r)>>1;
		if(a[mid]*x>y)l=mid+1;
		else r=mid-1;
	}
	return r;
}

int bs2(int l,int r,i64 x,i64 y){
	int mid;
	while(l<=r){
		mid=(l+r)>>1;
		if(a[mid]*x<=y)l=mid+1;
		else r=mid-1;
	}
	return r;
}

int clc(i64 x,int v){
	if(a[v]==0){
		if(x>=0)return v-1;
		else return 0;
	}
	else if(a[v]<0){
		return v-1-bs1(1,v-1,a[v],x);
	}
	else{
		return bs2(1,v-1,a[v],x);
	}
}

bool chk(i64 x){
	int i;
	i64 s=0;
	for(i=1;i<=n;i++)
		s+=clc(x,i);
	return s>=m;
}

i64 bnsr(i64 l,i64 r){
	i64 mid;
	l+=INF,r+=INF;
	while(l<=r){
		mid=(l+r)>>1;
		if(chk(mid-INF))r=mid-1;
		else l=mid+1;
	}
	return l-INF;
}

int main()
{
	int i;
	scanf("%d%lld",&n,&m);
	for(i=1;i<=n;i++)
		scanf("%d",&a[i]);
	sort(a+1,a+n+1);
	printf("%lld",bnsr(-INF,INF));
	return 0;
}
### 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;
typedef long long i64;
const int N=2e5+5;
const i64 INF=1e18;

int a[N];
int n;
i64 m;

int bs1(int l,int r,i64 x,i64 y){
	int mid;
	while(l<=r){
		mid=(l+r)>>1;
		if(a[mid]*x>y)l=mid+1;
		else r=mid-1;
	}
	return r;
}

int bs2(int l,int r,i64 x,i64 y){
	int mid;
	while(l<=r){
		mid=(l+r)>>1;
		if(a[mid]*x<=y)l=mid+1;
		else r=mid-1;
	}
	return r;
}

int clc(i64 x,int v){
	if(a[v]==0){
		if(x>=0)return v-1;
		else return 0;
	}
	else if(a[v]<0){
		return v-1-bs1(1,v-1,a[v],x);
	}
	else{
		return bs2(1,v-1,a[v],x);
	}
}

bool chk(i64 x){
	int i;
	i64 s=0;
	for(i=1;i<=n;i++)
		s+=clc(x,i);
	return s>=m;
}

i64 bnsr(i64 l,i64 r){
	i64 mid;
	l+=INF,r+=INF;
	while(l<=r){
		mid=(l+r)>>1;
		if(chk(mid-INF))r=mid-1;
		else l=mid+1;
	}
	return l-INF;
}

int main()
{
	int i;
	scanf("%d%lld",&n,&m);
	for(i=1;i<=n;i++)
		scanf("%d",&a[i]);
	sort(a+1,a+n+1);
	printf("%lld",bnsr(-INF,INF));
	return 0;
}
```