SUPERCOMPUTER ARIS

The Ministry of Education announced that starting this year, the supercomputer ARIS~^1~ installed in a dedicated space of the ministry is made available to the scientific and research community. During a ~24~-hour period, its computing power will be allocated to at most M research teams (numbered from ~1~ to ~M~), each of which will use it to run a data processing program.

To ensure fair distribution of computing power during the ~24~-hour period, the program of each team can only run continuously for a short time, referred to as an "execution window." Then, the program execution is paused, if it has not completed, to be resumed at a later time after the programs of other teams have been executed. Each ~24~-hour period is divided into N execution windows of equal-duration, and the order in which the programs of the teams are executed is recorded in a daily log file.

Problem

Develop a program in one of the IOI languages (Pascal, C, C++, Java) that, after reading the program execution log file, will calculate:

• the number of programs executed
• the number of execution windows allocated to the program that required the least computing power, and
• the number of execution windows allocated to the program that required the most computing power.

Input Files:

The input files with the name aris.in are text files with the following structure: They consist of exactly two lines. The first line contains two integers N ~(1 \le N \le 1.000.000)~ and M ~(1 \le M \le 1.000.000)~, separated by a space: the number of execution windows and the number of research groups. The second line contains exactly ~N~ integers S~\mathbf{_i}~, separated between them by a space (1 ~\le~ S~\mathbf{_i}~ ~\le~ ~M~, where 1 ~\le~ i ~\le~ N). The integer S~\mathbf{_i}~ is the number of the group whose program was executed in the ~i~-th execution window.

Output Files:

The output files with the name aris.out are text files with the following structure: They have exactly one line containing three integers K, X, Y, separated between them by a space.

• ~K~: the number of groups whose programs were executed during the ~24~ hours ~(K \le M)~. Note that ~K~ can be less than ~M~ if the programs of some groups are not executed at all during the ~24~ hours.
• ~X~: the total number of execution windows for the program that was executed the fewest times ~(X \le N)~.
• ~Y~: the total number of execution windows for the program that was executed the most times ~(Y \le N)~.

Examples of Input - Output Files:

1st

STDIN (aris.in)

10 5
1 2 3 4 1 5 1 5 2 1

STDOUT (aris.out)

5 1 4

Explanation: The programs of a total of ~5~ groups were executed (with numbers ~1~, ~2~, ~3~, ~4~, ~5~). The programs of groups ~3~ and ~4~ were given the least total time (~1~ execution window each), while the program of group ~1~ was given the most (~4~ execution windows).

2nd

STDIN (aris.in)

12 6
3 5 5 1 2 3 1 5 3 5 3 2

STDOUT (aris.out)

4 2 4

Explanation: The programs of a total of ~4~ groups were executed (with numbers ~1~, ~2~, ~3~, ~5~). Note that the programs of groups ~4~ and ~6~ were not executed at all during the ~24~ hours. The programs of groups ~1~ and ~2~ were given the least total time (~2~ execution windows each), while those of groups ~3~ and ~5~ were given the most (~4~ execution windows each).

Note: It has officially been included in the top ~500~ most powerful supercomputers in the world, with processing power of ~180~ teraflops (~180 \times 10^{12}~ floating-point operations per second) and a main memory capacity of ~1~ Petabyte (~1 \times 2^{50}~ bytes). See http://hpc.grnet.gr.