Given an array sequence [A1 , A2 ...An], the task is to find the maximum possible sum of increasing subsequence S of length K such that Si1<=Si2<=Si3.........<=Sin.

Example 1:

Input:
N = 8 K = 3
A[] = {8 5 9 10 5 6 19 8}
Output: 38
Explanation:
Possible increasing subsequence of
length 3 with maximum possible
sum is 9 10 19.

Example 2:

Input:
N = 2,K = 2
A[] = {10 5}
Output: -1
Explanation:
Can't make any increasing subsequence 
of length 2.

Your Task:
You don't need to read or print anything. Your task is to complete the function max_sum() which takes sequence A as the first parameter and K as the second parameter and returns the maximum possible sum of K-length increasing subsequnece. If not possible return -1.

Expected Time Complexity: O(max(Ai) * n * log(max(Ai)))
Expected Space Complexity: O(max(Ai))

Contraints:
1 <= n <= 100
1 <= A_i <= 100000