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.