PQUEUE - Printer Queue

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The only printer in the computer science students' union is experiencing an extremely heavy workload. Sometimes there are a hundred jobs in the printer queue and you may have to wait for hours to get a single page of output.

Because some jobs are more important than others, the Hacker General has invented and implemented a simple priority system for the print job queue. Now, each job is assigned a priority between 1 and 9 (with 9 being the highest priority, and 1 being the lowest), and the printer operates as follows.

  • The first job J in queue is taken from the queue.
  • If there is some job in the queue with a higher priority than job J, then move J to the end of the queue without printing it.
  • Otherwise, print job J (and do not put it back in the queue).

In this way, all those important muffin recipes that the Hacker General is printing get printed very quickly. Of course, those annoying term papers that others are printing may have to wait for quite some time to get printed, but that's life.

Your problem with the new policy is that it has become quite tricky to determine when your print job will actually be completed. You decide to write a program to figure this out. The program will be given the current queue (as a list of priorities) as well as the position of your job in the queue, and must then calculate how long it will take until your job is printed, assuming that no additional jobs will be added to the queue. To simplify matters, we assume that printing a job always takes exactly one minute, and that adding and removing jobs from the queue is instantaneous.

Input

One line with a positive integer: the number of test cases (at most 100). Then for each test case:

  • One line with two integers n and m, where n is the number of jobs in the queue (1 ≤ n ≤ 100) and m is the position of your job (0 ≤ m ≤ n-1). The first position in the queue is number 0, the second is number 1, and so on.
  • One line with n integers in the range 1 to 9, giving the priorities of the jobs in the queue. The first integer gives the priority of the first job, the second integer the priority of the second job, and so on.

Output

For each test case, print one line with a single integer; the number of minutes until your job is completely printed, assuming that no additional print jobs will arrive.

Example

Input:
3
1 0
5
4 2
1 2 3 4
6 0
1 1 9 1 1 1

Output:
1
2
5

hide comments
malcolm123_ssj: 2018-10-11 22:45:51

use stl c++ or python sl

spa1ish: 2018-05-02 19:37:10

AC.. using two vectors and sorting

juancarlovieri: 2017-10-29 10:52:50

i've got wrong answer here :(

vincent_dj: 2017-09-23 10:15:23

The problem description is way too long and it would have been better if some unimportant details are deleted, or give highlights to the important details of the problem so that it is easier to spot them.

nadstratosfer: 2017-09-09 06:02:37

Spent far too much time on this one, but finally got to study some structures I used to disregard. Avoided using actual priority queue from Python's SL, but still kept all array changes and max() queries in O(1). Very satisfying.

No nasty WAs + learning = great problem.

saurav52: 2017-08-23 13:24:27

AC in ONE GO :)
Use 1 priority queue and 1 simple queue

up79: 2017-06-07 21:29:18

AC in one go . just one queue and one priority queue to maintain :)

lord_poseidon: 2017-02-21 09:12:40

AC in one go, simply use priority queue and a simple queue

ace_cocytus: 2016-09-27 12:43:26

Simulation of course. Create your own queue and proceed like the description says without worrying about optimum solution.

cnexans: 2016-08-03 07:09:52

What do you mean by bruteforce? 0.0s AC in the first attempt

Last edit: 2016-08-03 07:11:27

Added by:overwise
Date:2007-10-02
Time limit:0.285s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM ICPC NWERC 2006