Problem:
Score: 400 points

Problem Statement

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.

Sample Input 1

4 3
3 3 -4 -2

Sample Output 1

-6

There are six ways to form a pair. The products of those pairs are 9, -12, -6, -12, -6, 8.

Sorting those numbers in ascending order, we have -12, -12, -6, -6, 8, 9. The third number in this list is -6.

Sample Input 2

10 40
5 4 3 2 -1 0 0 0 0 0

Sample Output 2

6

Sample Input 3

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

Sample Output 3

448283280358331064

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
 
class Test{
  public static void Main(){
    var NK =  Console.ReadLine().Split(' ').Select(n => int.Parse(n)).ToList();
    int N = NK[0];
    int K = NK[1];
    var nums =  Console.ReadLine().Split(' ').Select(n => long.Parse(n)).ToList();
    var pos = new List<long>();
    var neg = new List<long>();
    var zero = new List<long>();
    for(int i=0; i<N; i++){
      if(nums[i]>0){
        pos.Add(nums[i]);
      }else if(nums[i]==0){
        zero.Add(nums[i]);
      }else{
        neg.Add(nums[i]);
      }
    }
    int cntNeg = pos.Count()*neg.Count();
    int cntZero = pos.Count()*zero.Count() 
                  + neg.Count()*zero.Count() 
                  + zero.Count()*(zero.Count()-1)/2;
    if(K<=cntNeg){
      var list = new List<long>();
      for(int i=0; i<pos.Count(); i++){
        for(int j=0; j<neg.Count(); j++){
           list.Add(pos[i]*neg[j]);
        }
      }
      list.Sort();
      Console.WriteLine(list[K-1]);
    }else if(K<=cntNeg+cntZero){
      Console.WriteLine(0);
    }else{
      var list = new List<long>();
      int L = Math.Max(pos.Count(),neg.Count());
      for(int i=0; i<L; i++){
        for(int j=i+1; j<L; j++){
          if(j<pos.Count()){
            list.Add(pos[i]*pos[j]);
          }
          if(j<neg.Count()){
            list.Add(neg[i]*neg[j]);
          }
        }
      }
      list.Sort();
      Console.WriteLine(list[K-cntNeg-cntZero-1]);
    }
  }
}