#include<bits/stdc++.h>
#define rep(i, n) for(i = 0; i < n; i++)
#define int long long
 
using namespace std;
 
int n, k;
int a[200000];
 
int Count(int x) {
	int i;
	
	int ret = 0;
	
	int ok, ng, mid;
	
	rep(i, n) {
		if (a[i] >= 0) {
			ok = -1; ng = n;
			while (ng - ok >= 2) {
				mid = (ok + ng) / 2;
				if (a[i] * a[mid] <= x) { ok = mid; }
				else { ng = mid; }
			}
			if (ok >= i) ret += ok;
			else ret += ok + 1;
			
		}
		else {
			ng = -1; ok = n;
			while (ok - ng >= 2) {
				mid = (ok + ng) / 2;
				if (a[i] * a[mid] <= x) { ok = mid; }
				else { ng = mid; }
			}
			if (ok <= i) ret += n - 1 - ok;
			else ret += n - ok;
		}
	}
	return ret / 2;
}
 
signed main() {
	int i, j;
	
	cin >> n >> k;
	rep(i, n) cin >> a[i];
	sort(a, a + n);
	
	int INF = 2 * (1e+18);
	int st = -INF, ed = INF, mid;
	while (ed - st >= 2) {
		mid = (st + ed) / 2;
		if (Count(mid) < k) st = mid;
		else ed = mid;
	}
	cout << ed << endl;
	return 0; 
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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(i = 0; i < n; i++)
#define int long long
 
using namespace std;
 
int n, k;
int a[200000];
 
int Count(int x) {
	int i;
	
	int ret = 0;
	
	int ok, ng, mid;
	
	rep(i, n) {
		if (a[i] >= 0) {
			ok = -1; ng = n;
			while (ng - ok >= 2) {
				mid = (ok + ng) / 2;
				if (a[i] * a[mid] <= x) { ok = mid; }
				else { ng = mid; }
			}
			if (ok >= i) ret += ok;
			else ret += ok + 1;
			
		}
		else {
			ng = -1; ok = n;
			while (ok - ng >= 2) {
				mid = (ok + ng) / 2;
				if (a[i] * a[mid] <= x) { ok = mid; }
				else { ng = mid; }
			}
			if (ok <= i) ret += n - 1 - ok;
			else ret += n - ok;
		}
	}
	return ret / 2;
}
 
signed main() {
	int i, j;
	
	cin >> n >> k;
	rep(i, n) cin >> a[i];
	sort(a, a + n);
	
	int INF = 2 * (1e+18);
	int st = -INF, ed = INF, mid;
	while (ed - st >= 2) {
		mid = (st + ed) / 2;
		if (Count(mid) < k) st = mid;
		else ed = mid;
	}
	cout << ed << endl;
	return 0; 
}

```