Problem:
Score : 700 points

Problem Statement

Takahashi is playing with N cards.

The i-th card has an integer X_i on it.

Takahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:

The integers on the two cards are the same.

The sum of the integers on the two cards is a multiple of M.

Find the maximum number of pairs that can be created.

Note that a card cannot be used in more than one pair.

Constraints

2≦N≦10^5

1≦M≦10^5

1≦X_i≦10^5

Input

The input is given from Standard Input in the following format:

N M
X_1 X_2 ... X_N

Output

Print the maximum number of pairs that can be created.

Sample Input 1

7 5
3 1 4 1 5 9 2

Sample Output 1

3

Three pairs (3,2), (1,4) and (1,9) can be created.

It is possible to create pairs (3,2) and (1,1), but the number of pairs is not maximized with this.

Sample Input 2

15 10
1 5 6 10 11 11 11 20 21 25 25 26 99 99 99

Sample Output 2

6

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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


static class P
{
    static void Main()
    {
        var nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var X = Console.ReadLine().Split().Select(int.Parse).ToArray();

        int res = 0;
        List<int>[] modList = Enumerable.Repeat(0, nm[1]).Select(_ => new List<int>()).ToArray();

        foreach (var item in X) modList[item % nm[1]].Add(item);

        res += modList[0].Count / 2;
        if (nm[1] % 2 == 0) res += modList[nm[1] / 2].Count / 2;

        for (int i = 1; i <= (nm[1] - 1) / 2; i++)
        {
            res += Min(modList[i].Count, modList[nm[1] - i].Count);
            res += Max(0, Abs(modList[i].Count - modList[nm[1] - i].Count) / 2 - modList[modList[i].Count > modList[nm[1] - i].Count ? i : nm[1] - i].GroupBy(x => x).Sum(x => x.Count() / 2));
        }
        Console.WriteLine(res);
    }
}