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: Accepted)

#include "bits/stdc++.h"

using namespace std;

void solve()
{
    int n, m;
    cin >> n >> m;
    int ans = 0;
    map<int, int> mp;
    for (int i = 0; i < n; i++)
    {
        int x;
        cin >> x;
        mp[x]++;
    }
    vector<int> mods(m), used(m), pairs(m);
    for (auto &p : mp)
    {
        if (p.second)
        {
            mods[p.first % m] += p.second;
            pairs[p.first % m] += p.second / 2;
        }
    }
    ans += mods[0] / 2;
    for (int i = 1; i <= m / 2; i++)
    {
        if (i * 2 == m)
        {
            ans += mods[i] / 2;
            used[i] = mods[i];
        }
        else
        {
            int y = min(mods[i], mods[m - i]);
            ans += y;
            used[i] = used[m - i] = y;
        }
    }
    for (int i = 1; i < m; i++)
    {
        int z = (mods[i] - used[i]) / 2;
        ans += min(z, pairs[i]);
    }
    cout << ans << endl;
}

int main()
{
    solve();
    return 0;
}