Problem:
Score : 600 points

Problem Statement

You are given an integer sequence A of length N and an integer K.
You will perform the following operation on this sequence Q times:

Choose a contiguous subsequence of length K, then remove the smallest element among the K elements contained in the chosen subsequence (if there are multiple such elements, choose one of them as you like).

Let X and Y be the values of the largest and smallest element removed in the Q operations. You would like X-Y to be as small as possible.
Find the smallest possible value of X-Y when the Q operations are performed optimally.

Constraints

1 \leq N \leq 2000

1 \leq K \leq N

1 \leq Q \leq N-K+1

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K Q
A_1 A_2 ... A_N

Output

Print the smallest possible value of X-Y.

Sample Input 1

5 3 2
4 3 1 5 2

Sample Output 1

1

In the first operation, whichever contiguous subsequence of length 3 we choose, the minimum element in it is 1.
Thus, the first operation removes A_3=1 and now we have A=(4,3,5,2).
In the second operation, it is optimal to choose (A_2,A_3,A_4)=(3,5,2) as the contiguous subsequence of length 3 and remove A_4=2.
In this case, the largest element removed is 2, and the smallest is 1, so their difference is 2-1=1.

Sample Input 2

10 1 6
1 1 2 3 5 8 13 21 34 55

Sample Output 2

7

Sample Input 3

11 7 5
24979445 861648772 623690081 433933447 476190629 262703497 211047202 971407775 628894325 731963982 822804784

Sample Output 3

451211184

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

// Reads multiple ints in a line, separate by a space.
// It works even if the actual number of ints is smaller than n.
// WARNING: This function does not work for -2^31.
// NOTE: This function does not handle error cases.
fun fastReadInts(n: Int): IntArray {
  val xs = IntArray(n)
  val s = readLine()!!
  var currentValue = 0
  var isNegative = false
  var currentIndex = 0
  for (c in s) {
    if (c == ' ') {
      xs[currentIndex] = currentValue * if (isNegative) -1 else 1
      currentValue = 0
      isNegative = false
      currentIndex++
    } else if (c == '-') {
      isNegative = true
    } else {
      currentValue *= 10
      currentValue += c - '0'
    }
  }
  xs[currentIndex] = currentValue * if (isNegative) -1 else 1
  return xs
}

fun main(args: Array<String>) {
  val (n, k, q) = fastReadInts(3)
  val xs = fastReadInts(n)

  var ans = Int.MAX_VALUE

  // Define here for performance.
  val forbidden = BooleanArray(n)
  for (l in xs) {
    forbidden.fill(false)

    for (i in 0 until n) {
      if (xs[i] < l) {
        forbidden[i] = true
      }
    }

    val candidates = mutableListOf<Int>()
    var s = 0
    while (s < n) {
      if (forbidden[s]) {
        s++
      } else {
        var t = s
        while (t + 1 < n && !forbidden[t + 1]) {
          t++
        }
        // xs[s]..xs[t] is a valid range.
        val segmentLength = t - s + 1
        if (segmentLength >= k) {
          val segmentValues = mutableListOf<Int>()
          for (i in s..t) {
            segmentValues.add(xs[i])
          }
          segmentValues.sort()
          for (i in 0 until segmentLength - k + 1) {
            candidates.add(segmentValues[i])
          }
        }
        s = t + 1
      }
    }

    if (candidates.size < q) continue

    candidates.sort()
    val u = candidates[q - 1]
    ans = Math.min(u - l, ans)
  }
  println(ans)
}