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: Accepted)

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

namespace codefestival_2016_final_d
{
	class Program
	{
		static void Main(string[] args)
		{
			int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
			int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
			int[] remain = new int[x[1]];
			Dictionary<int, int>[] cards = new Dictionary<int, int>[x[1]];
			for (int i = 0; i < x[1]; i++) cards[i] = new Dictionary<int, int>();
			for (int i = 0; i < x[0]; i++)
			{
				int n = a[i] % x[1];
				remain[n]++;
				if (!cards[n].ContainsKey(a[i])) cards[n][a[i]] = 0;
				cards[n][a[i]]++;
			}
			int ret = 0;
			for (int i = 0; i < x[1]; i++)
			{
				int min = 0;
				if (i == 0 || i == x[1] - i)
				{
					min = remain[i] / 2;
				}
				else
				{
					min = Math.Min(remain[i], remain[x[1] - i]);
				}
				ret += min;
				remain[i] -= min; remain[(x[1] - i) % x[1]] -= min;
				int same = 0;
				foreach (var card in cards[i])
				{
					same += card.Value / 2;
				}
				ret += Math.Min(remain[i] / 2, same);
				remain[i] -= Math.Min(remain[i] / 2, same) * 2;
			}
			Console.WriteLine(ret);
		}
	}
}