# p03343 AtCoder Regular Contest 098 - Range Minimum Queries

## Problem Description
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.

Examples

Input

5 3 2
4 3 1 5 2


Output

1


Input

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


Output

7


Input

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


Output

451211184

## Contest Information
- **Contest ID**: 0
- **Problem Index**: 
- **Points**: 0.0
- **Rating**: 0
- **Tags**: 
- **Time Limit**: {'seconds': 2, 'nanos': 0} seconds
- **Memory Limit**: 1073741824 bytes

## Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.