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;
using System.Text;
using System.Threading.Tasks;

namespace ABC155_D
{
    class Program
    {
        static void Main(string[] args)
        {
            var nk = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var n = nk[0];
            var k = nk[1];
            var a = Console.ReadLine().Split().Select(long.Parse).ToArray();

            var aPos = a.Where(x => x > 0).ToList();
            var aNeg = a.Where(x => x < 0).ToList();
            var aZer = a.Where(x => x == 0).ToList();
            var nPos = aPos.Count();
            var nNeg = aNeg.Count();
            var nZer = aZer.Count();

            if (nPos * nNeg >= k)
            {
                var ans = new PriorityQueue<long>(nPos * nNeg, 0);
                for (int i = 0; i < nPos; i++)
                {
                    for (int j = 0; j < nNeg; j++)
                    {
                        ans.Push(aPos[i] * aNeg[j]);
                    }
                }

                var array = ans.ToArray();
                Console.WriteLine(ans.ToArray()[k - 1]);
            }
            else if (NPair(nPos) + NPair(nNeg) >= NPair(n) - k)
            {
                aNeg = aNeg.Select(x => x * -1).ToList();
                var ans = new PriorityQueue<long>(NPair(nPos + nNeg), 1);

                for (int i = 0; i < nPos; i++)
                {
                    for (int j = i + 1; j < nPos; j++)
                    {
                        ans.Push(aPos[i] * aPos[j]);
                    }
                }

                for (int i = 0; i < nNeg; i++)
                {
                    for (int j = i + 1; j < nNeg; j++)
                    {
                        ans.Push(aNeg[i] * aNeg[j]);
                    }
                }

                var array = ans.ToArray();
                Console.WriteLine(ans.ToArray()[NPair(n) - k]);
            }
            else
            {
                Console.WriteLine(0);
            }
        }

        static int NPair(int i)
        {
            return i * (i - 1) / 2;
        }
    }
    public class PriorityQueue<T> where T : IComparable
    {
        private IComparer<T> _comparer = null;
        private int _type = 0;

        private T[] _heap;
        private int _sz = 0;

        private int _count = 0;

        /// <summary>
        /// Priority Queue with custom comparer
        /// </summary>
        public PriorityQueue(int maxSize, IComparer<T> comparer)
        {
            _heap = new T[maxSize];
            _comparer = comparer;
        }

        /// <summary>
        /// Priority queue
        /// </summary>
        /// <param name="maxSize">max size</param>
        /// <param name="type">0: asc, 1:desc</param>
        public PriorityQueue(int maxSize, int type = 0)
        {
            _heap = new T[maxSize];
            _type = type;
        }

        private int Compare(T x, T y)
        {
            if (_comparer != null) return _comparer.Compare(x, y);
            return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        }

        public void Push(T x)
        {
            _count++;

            //node number
            var i = _sz++;

            while (i > 0)
            {
                //parent node number
                var p = (i - 1) / 2;

                if (Compare(_heap[p], x) <= 0) break;

                _heap[i] = _heap[p];
                i = p;
            }

            _heap[i] = x;
        }

        public T Pop()
        {
            _count--;

            T ret = _heap[0];
            T x = _heap[--_sz];

            int i = 0;
            while (i * 2 + 1 < _sz)
            {
                //children
                int a = i * 2 + 1;
                int b = i * 2 + 2;

                if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                if (Compare(_heap[a], x) >= 0) break;

                _heap[i] = _heap[a];
                i = a;
            }

            _heap[i] = x;

            return ret;
        }

        public int Count()
        {
            return _count;
        }

        public T Peek()
        {
            return _heap[0];
        }

        public bool Contains(T x)
        {
            for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
            return false;
        }

        public void Clear()
        {
            while (this.Count() > 0) this.Pop();
        }

        public IEnumerator<T> GetEnumerator()
        {
            var ret = new List<T>();

            while (this.Count() > 0)
            {
                ret.Add(this.Pop());
            }

            foreach (var r in ret)
            {
                this.Push(r);
                yield return r;
            }
        }

        public T[] ToArray()
        {
            T[] array = new T[_sz];
            int i = 0;

            foreach (var r in this)
            {
                array[i++] = r;
            }

            return array;
        }
    }

}