Description

Help the cows by writing a tool that analyzes the records they wrote down in a file to find the truth. They are looking for the bit sequences of lengths between $A$ and $B$ (inclusive) that occur the top $n$ most times in the data file.

Occurrences may overlap, and every sequence that appears at least once should be counted.

Input Format

The first line contains three integers $A, B, n$, as defined in the description.

From the second line on is the string $s$, with at most $80$ characters per line. Concatenate all lines in order to obtain $s$.

Output Format

Output the $n$ most frequent sequences (in order from highest to lowest frequency). For sequences with the same frequency, order them by length from short to long; if the lengths are the same, order by binary value (ascending). If the number of distinct sequences is less than $n$, output all that exist.

For each frequency that occurs, first output a line containing only that frequency, then output the sequences with that frequency, separated by spaces. Print six sequences per line (unless fewer remain).

2 4 10
01010010010001000111101100001010011001111000010010011110010000000

23
00
15
01 10
12
100
11
11 000 001
10
010
8
0100
7
0010 1001
6
111 0000
5
011 110 1000
4
0001 0011 1100

Hint

Explanation for Sample 1

In the sample, the sequence $100$ appears $12$ times, while the sequence $1000$ appears $5$ times. The most frequent sequence is $00$, which appears $23$ times.

Constraints

For $100\%$ of the testdata, it is guaranteed that $1 \leq n \leq 50$, $1 \leq A \leq B \leq 12$, $s$ contains only the characters 0 and 1, and the length of $s$ is at most $2 \times 10^5$.

The problem translation is from NOCOW.

Translated by ChatGPT 5