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

namespace test
{
	class MainClass
	{
		public static void Main(string[] args)
		{
			string[] s = Console.ReadLine().Split(' ');
			int N = int.Parse(s[0]);
			int M = int.Parse(s[1]);
			int[] X = new int[N + 1];
			int maxM = 100000;
			int[] cnt = new int[maxM + 1];
			int ans = 0;
			s = Console.ReadLine().Split(' ');
			int max = 0;
			for (int i = 0; i < N; i++)
			{
				X[i] = int.Parse(s[i]);
				cnt[X[i]]++;
				if (X[i] > max)
					max = X[i];
			}
			for (int i = 0; i < max + 1; i++)
			{
				if (cnt[i] % 2 !=0)
				{
					for (int n = 1; n < max / M; n++)
					{
						while (cnt[i] %2 != 0)
						{
							if (n * M - i > 0 && n * M - i < maxM + 1 && cnt[n * M - i] != 0 && n * M - i != i)
							{
									ans++;
									cnt[n * M - i]--;
									cnt[i]--;
							}
							else
								break;
						}
					}
				}
			}
			for (int i = 0; i < maxM + 1; i++)
			{
				while(cnt[i] != 1 && cnt[i] != 0)
				{
					cnt[i] -= 2;
					ans++;
				}
			}
			Console.WriteLine(ans);
		}
	}
}