# 3206. Aggressive cows

Farmer John has built a new long barn, with $N$ $(2 \leq N \leq 100~000)$ stalls. The stalls are located along a straight line at positions $x_1,\ldots,x_N$ $(0 \leq xi \leq 10^9)$.

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?

### 输入格式

• Line $1$: Two space-separated integers: $N$ and $C$
• Lines $2$..$N+1$: Line $i+1$ contains an integer stall location, $x_i$

### 输出格式

One integer: the largest minimum distance

### 样例

Input
5 3
1
2
8
4
9

Output
3


### 提示

OUTPUT DETAILS:

FJ can put his 3 cows in the stalls at positions 1, 4 and 8, resulting in a minimum distance of 3.

Huge input data, scanf is recommended.

22 人解决，22 人已尝试。

26 份提交通过，共有 50 份提交。

3.4 EMB 奖励。