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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static Reader;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;

public static class P
{
    public static void Main()
    {
        var nk = Console.ReadLine().Split().Select(long.Parse).ToArray();
        var k = nk[1];
        var a = Console.ReadLine().Split().Select(long.Parse).OrderBy(x => x).ToArray();
        var Valid = -(long)1e18 + 1;
        var Invalid = (long)1e18 + 1;
        //小さい数の個数
        while (Invalid - Valid > 1)
        {
            var target = (Valid + Invalid) / 2;
            var res = 0L;
            //res = Enumerable.Range(0, a.Length).Sum(ind => Count(ind, mid));
            for (int ind = 0; ind < a.Length; ind++)
            {
                int valid, invalid;
                //負
                if (a[ind] < 0) { valid = a.Length; invalid = ind; }
                //正
                else{ invalid = a.Length; valid = ind; }

                while (Abs(valid - invalid) > 1)
                {
                    var mid = (valid + invalid) / 2;
                    if (a[ind] * a[mid] <= target) valid = mid;
                    else invalid = mid;
                }
                if (a[ind] < 0) res += a.Length - valid;
                else res += valid - ind;
            }
            if (res < k) Valid = target;
            else Invalid = target;
        }
        Console.WriteLine(Invalid);
    }
}


static class Reader
{
    const int BUF_SIZE = 1 << 12;
    static Stream Stream = Console.OpenStandardInput();
    static byte[] Buffer = new byte[BUF_SIZE];
    static int ptr = BUF_SIZE - 1;
    static void Move() { if (++ptr >= Buffer.Length) { Stream.Read(Buffer, 0, BUF_SIZE); ptr = 0; } }

    public static int NextInt
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        get
        {
            int res = 0; int sign = 1; while (Buffer[ptr] < 45) Move();
            if (Buffer[ptr] == 45) { Move(); sign = -1; }
            do { res = res * 10 + (Buffer[ptr] ^ 48); Move(); } while (48 <= Buffer[ptr]);
            return res * sign;
        }
    }
}