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 = gets.split.map(&:to_i).sort
all = Array.new(M, 0)
pair = Array.new(M, 0)
while xs.length > 0
    num = xs.shift
    sum = 1
    while xs.length > 0 && xs[0] == num
        xs.shift
        sum += 1
    end
    all[num % M] += sum
    pair[num % M] += sum / 2 * 2
end

ans = 0
(M/2+1).times do |i|
    if i == 0 || i*2 == M
        ans += all[i] / 2
    else
        j = M - i
        result = [all[i], all[j]].min
        ans += result
        ans += [all[i] - result, pair[i]].min / 2
        ans += [all[j] - result, pair[j]].min / 2
    end
end
puts ans