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 (3.4.3) (judge verdict: Wrong Answer)

#!/usr/bin/env python3
# -*- coding:utf-8 -*-

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from __future__ import unicode_literals

from collections import Counter
N, M = map(int, input().split())
X = list(map(int, input().split()))
XX = [x % M for x in X]
# print(Counter(X))
cc = Counter(X)
c = Counter(XX)
cnt = c[0] // 2
c[0] -= cnt
if M % 2 == 1:
    to = M // 2 + 1
else:
    to = M // 2
for i in range(1, to):
    # print(i, M-i, c[i], c[M-i])
    tmp = min(c[i], c[M-i])
    cnt += tmp

    c[i] -= tmp
    c[M-i] -= tmp
tmp = c[M//2] // 2
c[M//2] -= tmp * 2
cnt += tmp
# print(c)
# print(cc)
for i in cc:
    if cc[i] >= 2:
        if c[i % M] >= 2:
            tmp =  c[i % M] // 2
            cnt += tmp
            c[i % M] -= tmp * 2
            # print(cc[i])
            # print(c[i % M],  i, cc[i])

print(cnt)