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)
xs = Array.new(1e5+1,0)
gets.split.each{ |a|
  xs[a.to_i] += 1
}
pairs = Array.new(M, 0)
singles = Array.new(M, 0)
xs.each_with_index { |n,i|
  pairs[i%M] += n/2
  singles[i%M] += n%2
}
#p pairs, singles

ans = 0
ans += pairs[0] + singles[0]/2
if M%2 == 0
  ans += pairs[M/2] + singles[M/2]/2
end
(1...(M+1)/2).each{ |k|
  #p ans
  le,ma = k,M-k
  if singles[k] > singles[M-k]
    le,ma = ma,le
  end
  ans += singles[le]
  ans += pairs[ma]
  ans += pairs[le]
  ans += [pairs[le], (singles[ma] - singles[le])/2].min
}
p ans