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