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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/*
                              _,add8ba,
                            ,d888888888b,
                           d8888888888888b                        _,ad8ba,_
                          d888888888888888)                     ,d888888888b,
                          I8888888888888888 _________          ,8888888888888b
                __________`Y88888888888888P"""""""""""baaa,__ ,888888888888888,
            ,adP"""""""""""9888888888P""^                 ^""Y8888888888888888I
         ,a8"^           ,d888P"888P^                           ^"Y8888888888P'
       ,a8^            ,d8888'                                     ^Y8888888P'
      a88'           ,d8888P'                                        I88P"^
    ,d88'           d88888P'                                          "b,
   ,d88'           d888888'                                            `b,
  ,d88'           d888888I                                              `b,
  d88I           ,8888888'            ___                                `b,
 ,888'           d8888888          ,d88888b,              ____            `b,
 d888           ,8888888I         d88888888b,           ,d8888b,           `b
,8888           I8888888I        d8888888888I          ,88888888b           8,
I8888           88888888b       d88888888888'          8888888888b          8I
d8886           888888888       Y888888888P'           Y8888888888,        ,8b
88888b          I88888888b      `Y8888888^             `Y888888888I        d88,
Y88888b         `888888888b,      `""""^                `Y8888888P'       d888I
`888888b         88888888888b,                           `Y8888P^        d88888
 Y888888b       ,8888888888888ba,_          _______        `""^        ,d888888
 I8888888b,    ,888888888888888888ba,_     d88888888b               ,ad8888888I
 `888888888b,  I8888888888888888888888b,    ^"Y888P"^      ____.,ad88888888888I
  88888888888b,`888888888888888888888888b,     ""      ad888888888888888888888'
  8888888888888698888888888888888888888888b_,ad88ba,_,d88888888888888888888888
  88888888888888888888888888888888888888888b,`"""^ d8888888888888888888888888I
  8888888888888888888888888888888888888888888baaad888888888888888888888888888'
  Y8888888888888888888888888888888888888888888888888888888888888888888888888P
  I888888888888888888888888888888888888888888888P^  ^Y8888888888888888888888'
  `Y88888888888888888P88888888888888888888888888'     ^88888888888888888888I
   `Y8888888888888888 `8888888888888888888888888       8888888888888888888P'
    `Y888888888888888  `888888888888888888888888,     ,888888888888888888P'
     `Y88888888888888b  `88888888888888888888888I     I888888888888888888'
       "Y8888888888888b  `8888888888888888888888I     I88888888888888888'
         "Y88888888888P   `888888888888888888888b     d8888888888888888'
            ^""""""""^     `Y88888888888888888888,    888888888888888P'
                             "8888888888888888888b,   Y888888888888P^
                              `Y888888888888888888b   `Y8888888P"^
                                "Y8888888888888888P     `""""^
                                  `"YY88888888888P'
                                       ^""""""""'
*/
#include <bits/stdc++.h>

#define pb push_back
#define pf push_front
#define in insert
#define F first
#define S second
#define sz(a) int (a.size ())
#define mp make_pair
#define GGWP return 0
#define all(a) (a).begin(), (a).end()
#define pii pair<int,int>
#define graph vector <vector <int> >
#define fname ""

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;

using namespace std;
const int inf = int (1e9);
const double eps = 0.0000000001, pi = 3.14159265358979323;
const int maxn = int (1e5 + 100);
int x[maxn];
int b[maxn], c[maxn];
ll ans;

int main () {
	ios::sync_with_stdio(0);
	cin.tie(0);
	#ifndef ONLINE_JUDGE
  //freopen (fname"in", "r", stdin);
	//freopen (fname"out", "w", stdout);
	#endif                                                

	int n, m;
	set <int> st;

	cin >> n >> m;

	for (int i=1; i<=n; ++i) 
		cin >> x[i],
			st.in (x[i]),
				c[x[i]]++;
	for(auto i : st) b[i % m]++;
	int cnt = 0;
	for(auto i : st){
		cnt = (m - i % m) % m;
		//cout << i << ' ' << cnt << ' ' << b[cnt] << endl;
		ans += b[cnt];
		if((i + i) % m == 0 && c[i] == 1){
			ans--;			
		} b[i % m]--;
 	} cout << ans;  	

	GGWP;
}