Discription

Levko has an array that consists of integers: a₁, a₂, ... , a_n. But he doesn’t like this array at all.

Levko thinks that the beauty of the array a directly depends on value c(a), which can be calculated by the formula:

The less value c(a) is, the more beautiful the array is.

It’s time to change the world and Levko is going to change his array for the better. To be exact, Levko wants to change the values of at most k array elements (it is allowed to replace the values by any integers). Of course, the changes should make the array as beautiful as possible.

Help Levko and calculate what minimum number c(a) he can reach.

Input

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 2000). The second line contains space-separated integers a₁, a₂, ... , a_n ( - 10⁹ ≤ a_i ≤ 10⁹).

Output

A single number — the minimum value of c(a) Levko can get.

Examples

Input

5 2 4 7 4 7 4

Output

0

Input

3 1 -100 0 100

Output

100

Input

6 3 1 2 3 7 8 9

Output

1

Note

In the first sample Levko can change the second and fourth elements and get array:4, 4, 4, 4, 4.

In the third sample he can get array: 1, 2, 3, 4, 5, 6.

 

 

   二分答案之后直接dp就行啦，水水水hhhh

 

#include
     
      #define ll long longusing namespace std;const int maxn=20005,inf=2*1e9;int n,a[maxn],f[maxn],k,mid;inline int mabs(int x){ return x<0?-x:x;}inline bool solve(){	for(int i=1;i<=n;i++){		f[i]=i-1;		for(int j=1;j
      
       >1;		if(solve()) r=mid-1,ans=mid;		else l=mid+1;	}		printf("%d\n",ans);	return 0;}