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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] x = new int[n];
		for(int i=0; i<n; i++){
			x[i] = sc.nextInt();
		}
		sc.close();
		
		int[] rem = new int[n];
		int[] num = new int[m];
		int[] same = new int[200000 + m + 100];
		for(int i=0; i<n; i++){
			rem[i] = x[i]%m;
		}
		
		int ans = 0;
		
		for(int i=0; i<n; i++){
			num[rem[i]]++;
			same[x[i]]++;
		}
		ans += num[0]/2;
		for(int i=1; i<=(m-1)/2; i++){
			ans += Math.min(num[i], num[m-i]);
			int nsam = (Math.max(num[i], num[m-i]) - Math.min(num[i], num[m-i])) / 2;
			int p = 0;
			while(nsam > 0){
				if(same[p*m + i] >= 2){
					ans += Math.min(nsam, same[p*m+i]/2);
					nsam -= same[p*m+i]/2;
				}
				if(nsam > 0){
					if(same[p*m + m - i] >= 2){
						ans += Math.min(nsam, same[p*m+m-i]/2);
						nsam -= same[p*m+m-i]/2;
					}
				}
				if(p*m > 100000){
					break;
				}
				p++;
			}
		}
		
		if(m%2 == 0){
			ans += num[m/2]/2;
		}
		
		System.out.println(ans);

	}

}