removemq

Title

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 ≤ N ≤ 2000
  • 1 ≤ K ≤ N
  • 1 ≤ Q ≤ N-K+1
  • 1 ≤ Ai ≤ 109
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K Q
A1 A2 ... AN

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 A3=1 and now we have A=(4,3,5,2). In the second operation, it is optimal to choose (A2,A3,A4)=(3,5,2) as the contiguous subsequence of length 3 and remove A4=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

Submitting .cpp to 'removemq'


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Time Limit: 1 Seconds
Memory Limit: 1024MB
No. of ACs: 3
Your best score: 0
Source: ARC 098E

Subtask Score
1 100
2 0