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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
  val (n, m) = readLine()!!.split(" ").map { it.toInt() }
  val x = readLine()!!.split(" ").map { it.toInt() }.sorted()
  var mpc = Array(m) { 0 }
  var mc = Array(m) { 0 }
  var p = 0
  for (i in 0 until n) {
    p++
    mc[x[i] % m]++
    if (i < n - 1 && x[i] == x[i + 1]) continue
    mpc[x[i] % m] += p / 2
    p = 0
  }
  var ans = mc[0] / 2
  if (m % 2 == 0) ans += mc[m / 2] / 2
  for (i in 1..(m - 1) / 2) {
    ans += if (mc[i] < mc[m - i]) {
      mc[i] + arrayOf((mc[m - i] - mc[i]) / 2, mpc[m - i]).min()!!
    } else {
      mc[m - i] + arrayOf((mc[i] - mc[m - i]) / 2, mpc[i]).min()!!
    }
  }
  println(ans)
}