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 Python (3.8.2) (judge verdict: Wrong Answer)

import sys
from collections import defaultdict

sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7


def resolve():
    n, m = map(int, input().split())
    X = list(map(int, input().split()))

    MOD = [defaultdict(int) for _ in range(m + 1)]
    cnt = defaultdict(int)
    for x in X:
        MOD[x % m][x] += 1
        cnt[x % m] += 1

    res = cnt[0] // 2
    if m % 2 == 0:
        res += cnt[m // 2] // 2

    for i in range(1, (m + 1) // 2):
        res += min(cnt[i], cnt[m - i])
        if cnt[i] < cnt[m - i]:
            cnt[i], cnt[m - i] = cnt[m - i], cnt[i]
        
        if cnt[i] > cnt[m - i]:
            diff = (cnt[i] - cnt[m - i]) // 2
            for v in MOD[i].values():
                if diff == 0:
                    break
                t = min(diff, v // 2)
                diff -= t
                res += t

    print(res)


if __name__ == '__main__':
    resolve()