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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define per1(i,n) for(int i=n;i>0;i--)
#define all(v) v.begin(), v.end()
typedef long long ll;
typedef pair<ll,ll> P;
typedef vector<ll> vec;
typedef vector<vec> mat;
ll num[200001],numm[200001][2];
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    ll n,m,X[200001];
    cin>>n>>m;
    rep(i,n) cin>>X[i],num[X[i]]++,numm[X[i]%m][0]++;
    rep1(i,100000) numm[i%m][1]+=num[X[i]]/2*2;
    ll ans=0;
    rep(i,m/2+1){
        if(i==0||i==m-i) ans+=numm[i][0]/2;
        else{
            if(numm[i][0]>numm[m-i][0]) swap(numm[i],numm[m-i]);
            ans+=numm[i][0];
            numm[m-i][0]-=numm[i][0];
            if(numm[m-i][0]<numm[m-i][1]) ans+=numm[m-i][0]/2;
            else ans+=numm[m-i][1]/2;
        }
    }
    cout<<ans;
}