Problem:
Score : 300 points

Problem Statement

In some other world, today is Christmas Eve.

There are N trees planted in Mr. Takaha's garden. The height of the i-th tree (1 \leq i \leq N) is h_i meters.

He decides to choose K trees from these trees and decorate them with electric lights. To make the scenery more beautiful, the heights of the decorated trees should be as close to each other as possible.

More specifically, let the height of the tallest decorated tree be h_{max} meters, and the height of the shortest decorated tree be h_{min} meters. The smaller the value h_{max} - h_{min} is, the better. What is the minimum possible value of h_{max} - h_{min}?

Constraints

2 \leq K < N \leq 10^5

1 \leq h_i \leq 10^9

h_i is an integer.

Input

Input is given from Standard Input in the following format:

N K
h_1
h_2
:
h_N

Output

Print the minimum possible value of h_{max} - h_{min}.

Sample Input 1

5 3
10
15
11
14
12

Sample Output 1

2

If we decorate the first, third and fifth trees, h_{max} = 12, h_{min} = 10 so h_{max} - h_{min} = 2. This is optimal.

Sample Input 2

5 3
5
7
5
7
7

Sample Output 2

0

If we decorate the second, fourth and fifth trees, h_{max} = 7, h_{min} = 7 so h_{max} - h_{min} = 0. This is optimal.

There are not too many trees in these sample inputs, but note that there can be at most one hundred thousand trees (we just can't put a sample with a hundred thousand lines here).

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

struct Combo<T> {
    data_len: usize,
    chunk_len: usize,
    min: usize,
    mask: usize,
    data: Vec<T>,
}

impl<T: Clone> Combo<T> {
    fn new(chunk_len: i32, data: Vec<T>) -> Self {
        let d_len = data.len();
        let min = 2usize.pow(chunk_len as u32) - 1;
        let max = 2usize.pow(d_len as u32) - 2usize.pow((d_len - chunk_len as usize) as u32);

        Combo {
            data_len: d_len,
            chunk_len: chunk_len as usize,
            min: min,
            mask: max,
            data: data,
        }
    }

    fn get_chunk(&self) -> Vec<T> {
        let b = format!("{:01$b}", self.mask, self.data_len);
        b
            .chars()
            .enumerate()
            .filter(|&(_, e)| e == '1')
            .map(|(i, _)| self.data[i].clone())
            .collect()
    }
}

impl<T: Clone> Iterator for Combo<T> {
    type Item = Vec<T>;
    fn next(&mut self) -> Option<Self::Item> {
        while self.mask >= self.min {
            if self.mask.count_ones() == self.chunk_len as u32 {
                let res = self.get_chunk();
                self.mask -= 1;
                return Some(res);
            }
            self.mask -= 1;
        }
        None
    }
}

fn main() {
    let s = {
        let mut s = String::new(); // バッファを確保
        std::io::stdin().read_line(&mut s).unwrap(); // 一行読む。失敗を無視
        s.trim_right().to_owned() // 改行コードが末尾にくっついてくるので削る
    };

    let (n, k) = {
        let mut ws = s.split_whitespace(); // 空白区切りの単語に分解する
        let n: i32 = ws.next().unwrap().parse().unwrap();
        let k: i32 = ws.next().unwrap().parse().unwrap();
        (n, k)
    };

    let mut hs: Vec<i32> = Vec::new();
    for _ in 0..n {
        hs.push(read());
    }

    let mut min_h = 1000000000;
    let combo = Combo::new(k, hs);
    for c in combo.into_iter() {
        if let Some(mi) = c.iter().min() {
            if let Some(ma) = c.iter().max() {
                if min_h > ma - mi {
                    min_h = ma - mi;
                }
            }
        }
    }
    println!("{}", min_h);
}