Title description

Farmer John has built a new long barn, with $n \ (2 \leq n \leq 10^5)$ stalls. The stalls are located along a straight line at positions $x_1,\dots ,x_n \ (0 \leq x_i \leq 10^9)$. His $c \ (2 \leq c \leq n)$ cows don't like this barn layout and become aggressive towards each other once put into a stall. To prevent the cows from hurting each other, FJ want to assign the cows to the stalls, such that the minimum distance between any two of them is as large as possible. What is the largest minimum distance?

Input

• Line $1$: Two space-separated integers: $n$ and $c$.
• Lines $2\dots n+1$: Line $i+1$ contains an integer stall location,$x_i$.

Output

• Line $1$: One integer：the largest minimum distance.

5 3
1
2
8
4
9

3

Sample description

Put the cows at $1$, $4$ and $8$ so that the minimum distance is $3$.

Data scale and convention

For data of $100\%$，$2 \le n \le 10^5$，$0 \le x_i \le 10^9$，$2 \le c \le n$。

Topic source

Gold