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)
X = gets.split.map(&:to_i)

mod_list = Hash.new { |h, k| h[k] = [] }

X.each do |x|
  mod_list[x % M] << x
end

ans = 0

0.upto(M / 2) do |m|
  listA = mod_list[m]
  listB = mod_list[M - m]
  a_size = listA.size
  b_size = listB.size

  if m == 0 || m == (M - m)
    ans += a_size / 2
  else
    counterA = Hash.new(0)
    counterB = Hash.new(0)

    listA.each do |a|
      counterA[a] += 1
    end

    listB.each do |b|
      counterB[b] += 1
    end

    pair_a_cnt = counterA.values.map { |c| c / 2 }.inject(:+) || 0
    pair_b_cnt = counterB.values.map { |c| c / 2 }.inject(:+) || 0

    match_cnt = [a_size, b_size].min
    ans += match_cnt

    ans += [(a_size - match_cnt) / 2, pair_a_cnt].min
    ans += [(b_size - match_cnt) / 2, pair_b_cnt].min
  end
end

puts ans