Given an array, A, having N integers, an increasing subsequence of this array of length k is a set of k indices \(i_1, i_2, ... i_k\), such that \(1 \le i_1 \lt i_2 \lt ... i_k \le N\) and \(A[i_1] \lt A[i_2] \lt A[i_3] \lt ... \lt A[i_k]\).
Energy of a subsequence is defined as sum of difference of consecutive numbers in the subsequence. For a given integer k, you need to find out the maximum value of energy among energies of all increasing subsequences of length k.

Hint: Among all increasing sequences of length k ending at an index, find the sequence with minimum value of starting point

Input:
First line consists of two space separated integer denoting N and k.
Second line consists of N space separated integers denoting the array A.

Output:
Print the maximum value of energy among energies of all increasing subsequences of length k.
If there are no increasing subsequences of length k in the array, print "-1" (without quotes")

Input Constraints:

\(1 \le k \times N \le 10^6\)
\(2 \le k \le N\)
\(1 \le A[i] \le 10^9\)