Going on Vacation

Katerina works a lot and urgently needs a vacation. She wants to take a trip to the islands and have as many consecutive days off as possible to relax, but she can only take one trip. Let the days be numbered from ~1~ to ~N~. Katerina has some obligations in her schedule (the total number of them being ~M~), which she has already committed to, corresponding to specific days: the ~i~-th obligation is scheduled for day ~D_i~.

Katerina is willing to cancel at most ~K~ of her obligations in order to take more days off. Help her find out how many consecutive vacation days she can take.

Problem

Develop a program in one of the IOI languages (Pascal, C, C++, Java) which will read the data and find the maximum number of consecutive vacation days that Katerina can take.

Input Files:

The input file named maketime.in is a text file where the first line contains three integers ~N~, ~M~, and ~K~, separated in pairs by a single space: the total number ~N~ of days, the number ~M~ of obligations scheduled by Katerina, and the maximum number ~K~ of obligations she is willing to cancel. The second line contains exactly ~M~ integers ~D_i~ (where ~1 \le i \le M~ and ~1 \le D_i \le N~): the days on which Katerina's ~M~ obligations are scheduled.

Output Files:

The output file named maketime.out is a text file consisting of a single line containing an integer: the maximum number of days Katerina can take off for vacation.

Examples of input - output files:

1st

STDIN (maketime.in)

10 5 2
6 9 3 2 7

STDOUT (maketime.out)

5

Explanation: Katerina can cancel the obligations scheduled for days ~2~ and ~3~. Thus, she can take a vacation from the ~1~st day to the ~5~th day, having a total of ~5~ vacation days.

2nd

STDIN (maketime.in)

12 4 1
4 10 4 8

STDOUT (maketime.out)

5

Explanation: In the second example, Katerina can cancel her obligation for day ~8~ and take a ~5~-day vacation (from the ~5~th day to the ~9~th day). Note that she has scheduled two obligations for the ~4~th day and is not willing to cancel both of them (~K = 1~).

3d

STDIN (maketime.in)

7 2 0
3 4

STDOUT (maketime.out)

3

In the third example, Katerina is not willing to cancel any obligation and can take a ~3~-day vacation, from the ~5~th day to the ~7~th day.

Constraints:

• For test cases worth 20%, of the total points, it will be:
  1 ~\le~ Ν ~\le~ 100, 1 ~\le~ Μ ~\le~ 100, 0 ~\le~ Κ ~\le~ Μ
• For test cases worth 50%, of the total points, it will be:
  1 ~\le~ Ν ~\le~ 10.000, 1 ~\le~ Μ ~\le~ 20.000, 0 ~\le~ Κ ~\le~ Μ

• For test cases worth 100%, of the total points, it will be:
  1 ~\le~ Ν ~\le~ 1.000.000, 1 ~\le~ Μ ~\le~ 2.000.000, 0 ~\le~ Κ ~\le~ Μ

• Formatting: In the output, each line terminates with a newline character.
  

• Maximum execution time: 1 sec.
  
• Maximum available memory: 64 MB.