ICPC 2006 · Problem E · Bit Compressor

Input File: bits.in

The aim of data compression is to reduce redundancy in stored or communicated data. This increases effective data density and speeds up data transfer rates. One possible method to compress any binary message is the following:

Replace any maximal sequence of n 1’s with the binary version of n whenever it shortens the length of the message.

For example, the compressed form of the data 11111111001001111111111111110011 becomes 10000010011110011. The original data is 32 bits long while the compressed data is only 17 bits long.

The drawback of this method is that sometimes the decompression process yields more than one result for the original message, making it impossible to obtain the original message. Write a program that determines if the original message can be obtained from the compressed data when the length of the original message (L), the number of 1’s in the original message (N) and the compressed data are given. The original message will be no longer than 16 Kbytes and the compressed data will be no longer than 40 bits.

Input

The input file contains several test cases. Each test case has two lines. The first line contains L and N and the second line contains the compressed data.

The last case is followed by a line containing two zeroes.

Output

For each test case, output a line containing the case number (starting with 1) and a message YES, NO or NOT UNIQUE. YES means that the original message can be obtained. NO means that the compressed data has been corrupted and the original message cannot be obtained. NOT UNIQUE means that more than one message could have been the original message. Follow the format shown in the sample output.

Sample Input

32 26
10000010011110011
9 7
1010101
14 14
111111
0 0

Sample Output

Case #1: YES
Case #2: NOT UNIQUE
Case #3: NO

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t consists of several trials, each described by one line of input. Each input line begins with an integer N

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he last trial is followed by a line containing a single zero.

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al, print a line containing the trial number, as shown in the sample output. If it is possible to construct a

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he lin starts with Minutes: followed by a plan that shows how the input shaft is connected

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he line for the hour hand starts with Hours: followed by a plan for connecting the input shaft to the hour shaft. Use the same format as the minute plan.