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)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define all(x) (x).begin(),(x).end()
const int mod=998244353,MAX=1<<18,INF=1<<30;

int main(){
    
    int N,M;cin>>N>>M;
    vector<int> X(N),cnt(M);
    map<int,int> MA;
    for(int i=0;i<N;i++){
        cin>>X[i];
        cnt[X[i]%M]++;
        MA[X[i]]++;
    }
    int ans=0;
    for(int i=0;i<M;i++){
        if(i==0){
            ans+=cnt[i]/2;
            cnt[i]%=2;
        }else if(i+i==M){
            ans+=cnt[i]/2;
            cnt[i]%=2;
        }else{
            int a=min(cnt[i],cnt[M-i]);
            ans+=a;
            cnt[i]-=a;cnt[M-i]-=a;
            
            for(int j=i;j<=100000;j+=M){
                if(MA[j]>=2){
                    ans+=min(cnt[i],MA[j])/2;
                    cnt[i]-=min(cnt[i],MA[j])/2;
                }
            }
            
        }
    }
    
    cout<<ans<<endl;
}