Mike runs a hot dog stand on Pluto. There are $$$N$$$ Plutonians in line to buy hot dogs and the $$$i^{th}$$$ Plutonian wants to buy $$$M_i$$$ hot dogs. Mike also has $$$D$$$ discount tickets which he wants to distribute among the Plutonians. Each Plutonian can have at most $$$1$$$ discount ticket. If Mike chooses to give a discount ticket to the $$$i^{th}$$$ Plutonian, all consecutive $$$j$$$ Plutonians after the $$$i^{th}$$$ Plutonian where $$$M_j \leq M_i$$$ will also get a discount.
Mike is feeling nice today and wants as many people to get discounts as possible. Please help Mike find the maximum number of people who can get a discount if he distributes the $$$D$$$ discount tickets optimally.
The first line of input contains the integers $$$N \space D$$$. $$$(1 \leq N \leq 10^5, \space 1 \leq D \leq \min(N, 100))$$$
The next line contains $$$N$$$ integers where the $$$i^{th}$$$ integer represents $$$M_i$$$. $$$(1 \leq M_i \leq N)$$$
Please output one integer, the maximum number of people who can get a discount.
8 2 1 5 7 3 8 2 1 4
6
10 3 1 2 3 4 5 6 7 8 9 10
3
10 3 10 9 8 7 6 5 4 3 2 1
10
$$$\textbf{For sample test case #1}$$$:
There are 8 Plutonians in line. We have 2 discount tickets to distribute.
We can give the 1st ticket to the 5th Plutonian in line. Then, all Plutonians after (6th, 7th, and 8th) also get a discount. We can give the 2nd ticket to the 3rd Plutonian. Then, the 4th Plutonian will also receive a discount. Thus, a maximum of 6 Plutonians can get a discount.
$$$\textbf{For sample test case #2}$$$:
No matter how we distribute the 3 discount tickets, no other Plutonians in line will benefit from additional discounts.
$$$\textbf{For sample test case #3}$$$:
Mike can give the 1st ticket to the 1st Plutonian. Then, every other Plutonian in line will get a discount, regardless of how he distributes the other 2 tickets. Thus, all 10 Plutonians get a discount.
