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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.ABC_155
{
    class D
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            long[] nk = ReadLongs();
            long n = nk[0];
            long k = nk[1];
            long[] array = ReadLongs();
            Array.Sort(array);
            long[] revArray = new long[n];
            for (int i = 0; i < n; i++)
            {
                revArray[i] = array[n - i - 1];
            }
            long bottom = long.MinValue / 2;
            long top = long.MaxValue / 2;
            while (bottom + 1 < top)
            {
                long mid = (bottom + top) / 2;
                long cnt = 0;
                for (int i = 1; i < n; i++)
                {
                    long bottom2 = 0;
                    long top2 = n;
                    if (array[i] < 0)
                    {
                        bottom2 = n - i;
                        if (array[i] * revArray[bottom2] > mid)
                        {
                            continue;
                        }
                        while (bottom2 + 1 < top2)
                        {
                            long mid2 = (bottom2 + top2) / 2;
                            if (array[i] * revArray[mid2] <= mid)
                            {
                                bottom2 = mid2;
                            }
                            else
                            {
                                top2 = mid2;
                            }
                        }
                        cnt += bottom2 - (n - i) + 1;
                    }
                    else
                    {
                        top2 = i;
                        if (array[i] * array[bottom2] > mid)
                        {
                            continue;
                        }
                        while (bottom2 + 1 < top2)
                        {
                            long mid2 = (bottom2 + top2) / 2;
                            if (array[i] * array[mid2] <= mid)
                            {
                                bottom2 = mid2;
                            }
                            else
                            {
                                top2 = mid2;
                            }
                        }
                        cnt += bottom2 + 1;
                    }
                }
                if (cnt < k)
                {
                    bottom = mid;
                }
                else
                {
                    top = mid;
                }
            }
            WriteLine(top);
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}