Dr. Astro Insky works at a radiotelescope centre. Recently, she noticed a very curious microwave pulsing emission sent right from the centre of the galaxy. Is the emission transmitted by some extraterrestrial form of intelligent life? Or is it nothing but the usual heartbeat of the stars?


You must help Dr. Insky to find out the truth by providing a tool to analyse bit patterns in the files she records. Dr. Insky wants to find the patterns of length between (and including) A and B that repeat themselves most often in the data file of each day. In each case, the greatest N distinct frequencies (that is, number of occurrences) are sought. Pattern occurrences may overlap, and only patterns that occur at least once are taken into account.

Input Data

The file CONTACT.IN contains the data series, with the following format:

Sample Input

This asks for the top ten frequencies of patterns of length between two and four that occur in the bit pattern 01010010010001000111101100001010011001111000010010011110010000000
Note that the fourth line of the input file above appears split in order to fit herein. [Text has been changed to single column for HTML format] In this example, pattern 100 occurs 12 times, and pattern 1000 occurs 5 times. The most frequent pattern is 00.

Output Data

A report in file CONTACT.OUT with at most N lines, listing the at most N greatest frequencies and corresponding patterns. The listing must be produced in decreasing order of pattern frequency, and consists of lines formatted like frequency pattern pattern pattern where frequency is the number of occurrences of the patterns that follow. The patterns in each line must appear in decreasing order of length. Patterns of equal length must be listed in reverse numerical order. In case there are less than N distinct frequencies, the output listing will have less than N lines.

Sample Output

For the sample input above, the output must be
23 00
15 10 01
12 100
11 001 000 11
10 010
8 0100
7 1001 0010
6 0000 111
5 1000 110 011
4 1100 0011 0001


The input file may have up to 2 megabytes. The parameters A, B and N are constrained by:
0 < N <= 20
0 < A <= B <= 12