Marisa has $n$ books, with the $i$-th book located at position $A_i$. She wants to select $k$ books to read.
Marisa believes that if she selects two books too close to each other, it will affect the aesthetic value of the books. Therefore, she wants to find a way to choose $k$ books such that the minimum distance between any two consecutive books selected is as large as possible.
For example, if Marisa selects books at positions $1, 3, 7, 10$, the minimum distance between any two consecutive books is $2$, which is the distance between the books at positions $1$ and $3$.
### Input
- The first line contains two integers $n, k$.
- The second line contains $n$ integers $A_i$. No two books occupy the same position.
### Output
- The maximum distance ensuring she can select exactly $k$ books.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le A_i , k\le 10^9$.
### Sample
Input:
```
5 3
10 4 2 3 1
```
Output:
```
3
```
