Best Time to Buy and Sell Stock atmost B times

Given an array of integers A of size N in which ith element is the price of the stock on day i,

You can complete atmost B transactions.

Find the maximum profit you can achieve.

NOTE: You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).



Input Format

The First argument given is the integer array A.
The Second argument is integer B.

Output Format

Return the maximum profit you can achieve by doing atmost B transactions.

Constraints

1 <= N <= 500
0 <= A[i] <= 10^6
0 <= B <= 10^9

For Example

Input 1:
    A = [2, 4, 1]
    B = 2
Output 1:
    2
    Explanation 1:
        Buy on day 1 (price = 2) and sell on day 2 (price = 4), 
        profit = 4 - 2 = 2

Input 2:
    A = [3, 2, 6, 5, 0, 3]
    B = 2
Output 2:
    7
    Explanation 1:
        Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6 - 2 = 4.
        Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3 - 0 = 3.
NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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