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 (2.7.6) (judge verdict: Wrong Answer)

n,m=map(int,raw_input().split())
x=map(int,raw_input().split())
same=[0]*(max(x)+1)
for i in xrange(n):
    same[x[i]]+=1
samemod=[0]*m
for i in xrange(n):
    samemod[x[i]%m]+=1
ans=0
for i in xrange((m+1)/2):
    if i==0:
        ans+=samemod[0]/2
        samemod[0]=0
    else:
        ans+=min(samemod[i],samemod[m-i])
        if samemod[i]>=samemod[m-i]:
            samemod[i]-=samemod[m-i]
        else:
            samemod[m-i]-=samemod[i]
if (m+1)%2==1:
    ans+=samemod[(m+1)/2]/2
    samemod[(m+1)/2]=0
for i in xrange(n):
    if same[x[i]]>=2:
        if samemod[x[i]%m]>=same[x[i]]:
            ans+=same[x[i]]/2
            samemod[x[i]%m]-=same[x[i]]
print(ans)