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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

fun main(args: Array<String>) {
    abc115c()
}

/*
 先頭から木を1本ずつ選んでいく → それぞれ、他の木から高さの差の少ないものをK-1本選び、hmax-hminを計算
 その中から最小のものを選ぶ
 */

fun abc115c() {
    val (n, k) = readLine()!!.split(" ").map { it.toInt() }
    val treeHeights = (1..n).map { readLine()!!.toLong() }

    val diffsMemo = mutableListOf<List<Long>>()
    val selectedTreeDiffsMemo = mutableListOf<List<Long>>()
    val minDiffs = treeHeights.map { treeHeight ->
        // 選んだ基準の木からの高さの差を計算
        val diffs = treeHeights.map { it - treeHeight }

        // 高さの差のメモに含まれる＝計算済みの場合は無効値を返す そうでない場合はメモに追加
        if (diffsMemo.contains(diffs)) {
            return@map Long.MAX_VALUE
        } else {
            diffsMemo.add(diffs)
        }

        // 高さの差が小さいものからK-1本選ぶ
        val selectedTreeDiffs = diffs.sortedBy { Math.abs(it) }.take(k)

        // 選ばれた木のメモに含まれる＝計算済みの場合は無効値を返す そうでない場合はメモに追加
        if (selectedTreeDiffsMemo.contains(selectedTreeDiffs)) {
            return@map Long.MAX_VALUE
        } else {
            selectedTreeDiffsMemo.add(selectedTreeDiffs)
        }

        // hmax-hminを計算
        Math.abs(selectedTreeDiffs.max()!! - selectedTreeDiffs.min()!!)
    }

    val answer = minDiffs.min()

    println(answer)
}