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 ≤ A_i ≤ 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