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.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		int[] Cnt = new int[M];
		int[] Same = new int[M];
		Dictionary<int,int> D = new Dictionary<int,int>();
		for(int i=0;i<N;i++){
			if(D.ContainsKey(A[i]) == false) D.Add(A[i],0);
			D[A[i]]++;
		}
		foreach(var k in D.Keys){
			Cnt[k%M] += D[k];
			Same[k%M] += D[k]/2;
		}
		int ans = 0;
		for(int i=0;i<M;i++){
			int j = M - i;
			if(j < i) continue;
			j %= M;
			if(i == j){
				ans += Cnt[i]/2;
			}else{
				int ma = Cnt[i] > Cnt[j] ? i : j;
				int mi = ma == i ? j : i;
				
				ans += Cnt[mi];
				int rest = Cnt[ma] - Cnt[mi];
				int add = Math.Min(rest/2,Same[ma]*2);
				
				ans += add;
			}
		}
		Console.WriteLine(ans);
		
	}
	int N,M;
	int[] A;
	public Sol(){
		var d = ria();
		N = d[0]; M = d[1];
		A = ria();
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}