#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
const int INF = (1<<30);
const ll INFLL = (1ll<<60);
const ll MOD = (ll)(1e9+7);

#define l_ength size

void mul_mod(ll& a, ll b){
	a *= b;
	a %= MOD;
}

void add_mod(ll& a, ll b){
	a = (a<MOD)?a:(a-MOD);
	b = (b<MOD)?b:(b-MOD);
	a += b;
	a = (a<MOD)?a:(a-MOD);
}

int n;
ll k,a[225816];

bool judge(ll x){
	int i;
	ll y;
	ll cnt=0ll;
	for(i=0; i<n; ++i){
		if(a[i]>0){
			y = x/a[i];
			if(y*a[i]>x){
				--y;
			}
			cnt += (ll)(upper_bound(a,a+i,y)-a);
		}else if(a[i]<0){
			y = x/a[i];
			if(y*a[i]>x){
				++y;
			}
			cnt += (ll)(&a[i]-lower_bound(a,a+i,y));
		}else if(x>=0ll){
			cnt += i;
		}
	}
	return (cnt>=k);
}

int main(void){
	int i;
	ll l,r,m;
	cin >> n >> k;
	for(i=0; i<n; ++i){
		cin >> a[i];
	}
	sort(a,a+n);
	l = -INFLL;
	r = INFLL;
	while(r-l>1ll){
		m = (l+r)/2;
		if(judge(m)){
			r = m;
		}else{
			l = m;
		}
	}
	cout << r << endl;
	return 0;
}

### Prompt

Your challenge is to write 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;
const int INF = (1<<30);
const ll INFLL = (1ll<<60);
const ll MOD = (ll)(1e9+7);

#define l_ength size

void mul_mod(ll& a, ll b){
	a *= b;
	a %= MOD;
}

void add_mod(ll& a, ll b){
	a = (a<MOD)?a:(a-MOD);
	b = (b<MOD)?b:(b-MOD);
	a += b;
	a = (a<MOD)?a:(a-MOD);
}

int n;
ll k,a[225816];

bool judge(ll x){
	int i;
	ll y;
	ll cnt=0ll;
	for(i=0; i<n; ++i){
		if(a[i]>0){
			y = x/a[i];
			if(y*a[i]>x){
				--y;
			}
			cnt += (ll)(upper_bound(a,a+i,y)-a);
		}else if(a[i]<0){
			y = x/a[i];
			if(y*a[i]>x){
				++y;
			}
			cnt += (ll)(&a[i]-lower_bound(a,a+i,y));
		}else if(x>=0ll){
			cnt += i;
		}
	}
	return (cnt>=k);
}

int main(void){
	int i;
	ll l,r,m;
	cin >> n >> k;
	for(i=0; i<n; ++i){
		cin >> a[i];
	}
	sort(a,a+n);
	l = -INFLL;
	r = INFLL;
	while(r-l>1ll){
		m = (l+r)/2;
		if(judge(m)){
			r = m;
		}else{
			l = m;
		}
	}
	cout << r << endl;
	return 0;
}

```