Problem Statement

There is a piece of yokan with a left-to-right length of $L$ [cm].
The yokan has $N$ notches, and the $i$-th notch from the left is located $A_i$ [cm] from the left end.

Sei and Hikaru play a game using this yokan. The game proceeds as follows.
1. Hikaru chooses $K$ of the $N$ notches and divides the yokan into $K + 1$ pieces.
2. Sei chooses any one of the $K + 1$ pieces of yokan.
3. Hikaru chooses any one of the remaining $K$ pieces of yokan. Let $H$ be the size of the piece chosen here.

Hikaru acts to maximize $H$, and Sei acts to minimize $H$.
Find the value of $H$ when both players act optimally.

Constraints

• $1 \leq K \leq N \leq 2 \times 10^5$
• $1 \leq A_1 < A_2 < A_3 < \cdots < A_N < L \leq 10^9$
• All inputs are integers.

Input

$N$ $L$
$K$
$A_1$ $A_2$ $A_3$ $\cdots$ $A_N$

Sample