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

• $1 \leq N \leq 2000$
• $1 \leq K \leq N$
• $1 \leq Q \leq N-K+1$
• $1 \leq A_i \leq 10^9$
• 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 $X-Y$.