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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let v = read_vec::<usize>();
    let (n, m) = (v[0], v[1]);
    let mut x = read_vec::<usize>();
    x.sort();
    let mut i = 0;
    let mut pairs = HashMap::new();
    let mut paired_idx = HashSet::new();
    while i + 1 < n {
        if x[i] == x[i + 1] {
            *pairs.entry(x[i] % m).or_insert(0) += 1;
            paired_idx.insert(i);
            paired_idx.insert(i + 1);
            i += 2;
            continue;
        }
        i += 1;
    }
    debug!(paired_idx);

    let mut mod_dict = vec![0; m];
    for i in 0..n {
        if paired_idx.contains(&i) {
            continue;
        }
        mod_dict[x[i] % m] += 1;
    }

    let mut ans = paired_idx.len() / 2;
    debug!(ans, mod_dict);
    for i in 0..m {
        if i == m - i || i == 0 {
            ans += mod_dict[i] / 2;
            mod_dict[i] -= (mod_dict[i] / 2) * 2;
            continue;
        }
        let pairable = min(mod_dict[i], mod_dict[m - i]);
        ans += pairable;
        mod_dict[i] -= pairable;
        mod_dict[m - i] -= pairable;
    }
    debug!(ans, mod_dict);

    for &same_key in pairs.keys() {
        if same_key == 0 || same_key == m - same_key {
            continue;
        }
        let pairable = min(pairs[&same_key] * 2, mod_dict[m - (same_key % m)]);
        ans += pairable / 2;
        let paired = 2 * (pairable / 2);
        mod_dict[m - (same_key % m)] -= paired;
    }
    println!("{}", ans);
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}