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: Accepted)

n,m,*X=map(int,open(0).read().split())
E=[0]*(max(X)+1)
P=[0]*m
M=[0]*m
for x in X:E[x]+=1;M[x%m]+=1
for i,e in enumerate(E):P[i%m]+=e//2
ans=0
for i in range(m//2+1):
	if i==0 or i*2==m:
		ans+=M[i]//2
	else:
		l=min(M[i],M[(m-i)%m])
		ans+=l+min((M[i]-l)//2,P[i])+min((M[(m-i)%m]-l)//2,P[(m-i)%m])
print(ans)