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)

import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time

sys.setrecursionlimit(10**7)
inf = 10**10
mod = 10**9 + 7

def f():
    n,m = list(map(int, input().split()))
    b = [[] for _ in range(m)]
    for c in map(int, input().split()):
        b[c%m].append(c)
    t = 0
    for i in range(m//2):
        if i+1 > m-i-1:
            break
        if i+1 == m-i-1:
            l = len(b[i+1])
            t += l//2
            break

        l = len(b[i+1])
        r = len(b[m-i-1])
        if l > r:
            t += r
            bt = b[i+1]
            sa = l-r

        else:
            t += l
            bt = b[m-i-1]
            sa = r-l

        bt.sort()
        lt = 0
        i = 0
        sa = sa // 2
        while i < l-1 and lt < sa:
            if bt[i] == bt[i+1]:
                lt += 1
                i += 2
            else:
                i += 1
        t += lt
    l = len(b[0])
    t += l//2

    return t


print(f())