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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import collections
n, m = map(int, input().split())
lists = list(map(int, input().split()))
data = dict(collections.Counter(lists))
ans = 0
dic = {i: [] for i in range(m)}
for some in lists:
    dic[some % m].append(some)
ans += len(dic[0])//2
if m % 2 == 0:
    for i in range(1, m//2):
        a = 0
        b = 0

        for num in dic[i]:

            a += data[num]//2

        for nums in dic[m-i]:

            b += data[nums]//2

        if len(dic[i]) > len(dic[m-i]):

            if len(dic[i])-2*a <= len(dic[m-i]):

                ans += (len(dic[i])+len(dic[m-i]))//2

            elif len(dic[i])-2*a > len(dic[m-i]):

                ans += a+len(dic[m-i])

        elif len(dic[i]) == len(dic[m-i]):
            ans += len(dic[i])

        elif len(dic[i]) < len(dic[m-i]):
            if len(dic[m-i])-2**b <= len(dic[i]):
                ans += (len(dic[i])+len(dic[m-i]))//2
            elif len(dic[m-i])-2**b > len(dic[i]):
                ans += b+len(dic[i])

    ans += len(dic[m//2])//2


elif m % 2 != 0:
    if m == 1:
        print(n//2)
        exit()
    for i in range(1, m//2+1):
        a = 0
        b = 0

        for num in dic[i]:

            a += data[num]//2

        for nums in dic[m-i]:

            b += data[nums]//2

        if len(dic[i]) > len(dic[m-i]):

            if len(dic[i])-2*a <= len(dic[m-i]):

                ans += (len(dic[i])+len(dic[m-i]))//2

            elif len(dic[i])-2*a > len(dic[m-i]):

                ans += a+len(dic[m-i])

        elif len(dic[i]) == len(dic[m-i]):
            ans += len(dic[i])

        elif len(dic[i]) < len(dic[m-i]):
            if len(dic[m-i])-2**b <= len(dic[i]):
                ans += (len(dic[i])+len(dic[m-i]))//2
            elif len(dic[m-i])-2**b > len(dic[i]):
                ans += b+len(dic[i])
print(ans)