ertain programming tasks require determining the optimal (or best) solution from many possible solutions. Usually this kind of task can be illustrated and described with graphs—mathematical structures that help model relations between objects in a set. This article demonstrates a practical approach to some optimization tasks. As an example, it uses a problem from the ACM International Collegiate Programming Contest (ACM-ICPC) 2006 Finals.

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.

*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.

```
Sample Input Output for the Sample Input
------------------------------------------------------------------------
32 26 Case #1: YES
10000010011110011
9 7 Case #2: NOT UNIQUE
1010101
14 14 Case #3: NO
111111
```