Contact

프로그램 명: ioi_contact

제한시간: 1 초

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?

Task

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

First line - The integer A indicating the minimum pattern length.
Second line - The integer B indicating the maximum pattern length.
Third line - The integer N indicating the number of distinct frequencies.
Fourth line - A sequence of 0 and 1 characters, terminated by a 2 character.

Sample Input


2

4

10

010100100100010001111011000010100110011110000100100111100100000002

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

Constraints

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

출처:IOI 98

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