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 (2.4.0) (judge verdict: Accepted)

from collections import Counter
n,m=map(int,input().split())
x=[int(i) for i in input().split()]
v=[[] for i in range(m)]
for i in x:v[i%m].append(i)
a=0
for i in range(1,m//2+m%2):
  x,y=v[i],v[m-i]
  d=len(x)-len(y)
  if d<0:d,x,y=-d,y,x
  c=sorted([p[1] for p in Counter(x).items()])
  p=0
  for t in c:p+=t//2
  a+=len(y)+min(p,d//2)
a+=len(v[0])//2+(1-m%2)*len(v[m//2])//2
print(a)