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: Time Limit Exceeded)

def main():
  n,m=map(int,input().split())
  x=list(map(int,input().split()))
  xmod=[y%m for y in x]
  from collections import Counter
  cxmod=dict(Counter(xmod))
  cx=dict(Counter(x))
  keys=list(cxmod.keys())
  ans1,ans2=0,0 # ams1:m倍になるペア、ans2:同数のペア。ans1からもとめる
  d2={}
  for k in keys:
    if k==0:
      ans1+=cxmod[k]//2
      cxmod[k]-=2*(cxmod[k]//2)
    else:
      if k==m-k:
        ans1+=cxmod[k]//2
        cxmod[k]-=2*(cxmod[k]//2)
      elif m-k in keys:
        tmp=min(cxmod[k],cxmod[m-k])
        ans1+=tmp
        cxmod[k]-=tmp
        cxmod[m-k]-=tmp
  for k,v in cx.items():
    if v>=2 and cxmod[k%m]>=2:
      tmp=min(v//2,cxmod[k%m]//2)
      ans2+=tmp
      cxmod[k%m]-=tmp*2

  print(ans1+ans2)
if __name__=='__main__':
  main()