LARMY - Lannister Army

"A Lannister Always Pays His Debts."

That's true, now here is a chance for you to get paid by Jaime Lannister.

In Jaime's army there are total N number of warriors.

And all them are standing in a single row.

Now Jaime wants to convey a message to his warriors. But it's very difficult to convey a message if warriors are standing in a single row.

So, Jaime wants to break that single row into K rows. Such that in each row at least one warrior should be there.

Also, there is an amount of unhappiness associated with each warrior x which is equal to : number of warriors in front of x (in his row) whose height is greater than the height of x. And, total unhappiness is sum of unhappiness of all warriors. Jaime wants that his army should be happy as much as possible.

Now, Jaime wants you to break the single row into K rows such that total unhappiness should be minimum.

Note: You just have to break the row, you are not allowed to change the position of the warriors.

Input

First line of input contain two integers N and K.

Second line of input contain N number of integers, ith of which denotes height of ith warrior standing in that single row (represented as H[i]).

Constraints

1 ≤ N ≤ 5000

1 ≤ K ≤ N

1 ≤ H[i] ≤ 105

Output

Output the minimum possible value of "total unhappiness".

Examples

Input:
6 3
20 50 30 60 40 100

Output:
0

Explanation

Break as:

Row 1 : 20 50

Row 2 : 30 60

Row 3 : 40 100

Input:
8 3
20 50 30 60 40 100 5 1

Output:
2

Explanation

Row 1 : 20 50 30 60, Unhappiness = 1

Row 2 : 40 100, Unhappiness = 0

Row 3 : 5 1, Unhappiness = 1

Total = 2


Added by:anupamwadhwa
Date:2017-11-10
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:Code Rush 2017, IIT (ISM), Dhanbad

hide comments
2022-05-06 23:41:57
try using knuth optimization
2020-07-09 13:52:31 moh.amr
Please modify the time limit, so that languages other than C++ pass.

Last edit: 2020-07-09 14:06:50
2020-06-18 08:54:49
Very cool problem.
2020-04-23 08:28:12
Nice problem :)
solve Codechef - CHEFAOR also.
2020-03-16 11:59:43
The time limit is tight. My O(n^2 logn + nklogn) solution TLEd, but O(n^2 + nklogn) one passed
2019-12-11 16:48:01
I don't know why it is giving TLE.... My solution is to use divide and conquer optimization.
2018-08-02 05:50:54 Shubhojeet Chakraborty
very strict time limit..!
P.S: Nice question though.
2018-07-22 20:15:48
O(nklogn) with fast i/o gives TLE!!
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