Teacher assigns a programming assignment to all the students in their computer programming lab. One of the students is your friend and he asks you to help him solve the problem.

Teacher gave students an Array \(A\) of size \(N\) and an integer \(K\). Now the students have to remove exactly \(K\) elements from the array such that the array obtained after removing exactly \(K\) elements have \(\sum_{i=1}^{i=L-1}abs(a[i]-a[i+1])\) as maximum.

Here \(L\) is the length of the array after removing exactly \(K\) elements. So if the initial array size is \(N\) and \(K\) elements are removed from it then \(L=N-K.\)

Suppose our original array \(A\) is \([1,2,3,4]\) and we remove \(2^{nd}\) and \(4^{th}\) element from the array then length of the new array formed is \(2\) and the array is \([1,3]\).

Now the student's task is to output the maximum value of  \(\sum_{i=1}^{i=L-1}abs(a[i]-a[i+1])\).

Input
First line contains 2 integers \(N\) and \(K\) denoting the size of the array and the elements to be removed respectively.

Next line contains \(N\) space separated integers denoting the array \(A\).

Output
Output the required answer.

Constraints

\(1 \leq N \leq {10^4}\)

\(1 \leq K \leq min(N,20)\)

\(1 \leq A[i] \leq {10^5}\)