#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
const ll INF = 1LL<<61;

long long pairs(ll n, ll k, vector<ll> a) {
  sort(a.begin(), a.end());

  long long left = -INF, right = INF;

  while(right > left + 1) {
    long long x = (left + right) / 2;
    long long s = 0, t = 0;

    for(int i=0;i<n;i++) {
      if(a[i] > 0) {
	ll l2 = -1, r2 = n;
	while(r2 > l2 + 1) {
	  ll m = (l2 + r2) / 2;
	  if(a[i] * a[m] <= x) l2 = m;
	  else r2 = m;
	}
	s += r2;
      }
      else if (a[i] < 0) {
	ll l2 = -1, r2 = n;
	while(r2 > l2 + 1) {
	  ll m = (l2 + r2) / 2;
	  if(a[i] * a[m] <= x) {
	    r2 = m;
	  } else l2 = m;
	}
	s += n - r2;
      }
      else if (x >= 0) s+= n;
      if(a[i] * a[i] <= x) ++ t;
    }
    long long num = (s-t) / 2;
    if(num >= k) right = x;
    else left = x;
  }

  return right;
}
int main() {
  ll n, k;
  cin >> n;
  cin >> k;
  vector<long long> a(n);
  for(ll i=0;i<n;i++) {
    cin >> a[i];
  }
  cout << pairs(n, k, a);
}
### Prompt

Please create a solution in CPP 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>
typedef long long ll;
using namespace std;
const ll INF = 1LL<<61;

long long pairs(ll n, ll k, vector<ll> a) {
  sort(a.begin(), a.end());

  long long left = -INF, right = INF;

  while(right > left + 1) {
    long long x = (left + right) / 2;
    long long s = 0, t = 0;

    for(int i=0;i<n;i++) {
      if(a[i] > 0) {
	ll l2 = -1, r2 = n;
	while(r2 > l2 + 1) {
	  ll m = (l2 + r2) / 2;
	  if(a[i] * a[m] <= x) l2 = m;
	  else r2 = m;
	}
	s += r2;
      }
      else if (a[i] < 0) {
	ll l2 = -1, r2 = n;
	while(r2 > l2 + 1) {
	  ll m = (l2 + r2) / 2;
	  if(a[i] * a[m] <= x) {
	    r2 = m;
	  } else l2 = m;
	}
	s += n - r2;
      }
      else if (x >= 0) s+= n;
      if(a[i] * a[i] <= x) ++ t;
    }
    long long num = (s-t) / 2;
    if(num >= k) right = x;
    else left = x;
  }

  return right;
}
int main() {
  ll n, k;
  cin >> n;
  cin >> k;
  vector<long long> a(n);
  for(ll i=0;i<n;i++) {
    cin >> a[i];
  }
  cout << pairs(n, k, a);
}
```