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: Wrong Answer)

require 'set'; require 'prime'; require 'pp'
INF=Float::INFINITY; MOD=10**9+7
n,m = gets.chomp.split.map(&:to_i)
x = gets.chomp.split.map(&:to_i)

h = Hash.new(0)
x.each do |num|
  h[num] += 1
end
onazi = Array.new(m, 0)
a = Array.new(m, 0)

x.each do |num|
  a[num % m] += 1
  o = h[num]
  o -= 1 if o.odd?
  onazi[num % m] += o
end

ans = 0

mid = m / 2
mid -= 1 if m.even?
1.upto(m/2) do |i|
  snum = [a[i], a[m - i]].min
  a[i] -= snum
  a[m-i] -= snum
  ans += snum
end
if m.even?
  ans += a[m/2] / 2
  a[m/2] = 0
end

m.times do |i|
  if onazi[i] > a[i]
    tmp = a[i]
    tmp -= 1 if tmp.odd?
    ans += tmp
  else
    ans += onazi[i]
  end
end
puts ans