| # 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. |