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 Ruby (2.3.3) (judge verdict: Accepted)

n,m=gets.split.map &:to_i
h=Array.new(m,0)
hh=Array.new(10**5+1,0)
hhh=Array.new(m,0)

gets.split.map{|i|
  g=i.to_i
  h[g%m]+=1
  hh[g]+=1
}
(10**5).times do |i|
  if hh[i]>=2
    hhh[i%m]+=hh[i]/2
  end
end
c=0
(m/2+1).times do |i|
  if i==0 || 2*i==m
    c+=h[i]/2
  else
    g=[h[i],h[m-i]].min
    c+=g
    c+=[(h[i]-g)/2,hhh[i]].min
    c+=[(h[m-i]-g)/2,hhh[m-i]].min
  end
end
p c