## MONODIG - Monodigital Representations

Let * K* be a decimal digit different from *0*. We say that an
arithmetic expression is a **K-representation of the integer X**
if a value
of this expression is X and if it contains only numbers composed of a
digit K.
(All the numbers are of course decimal). The following arithmetical
operations are allowed in the expression: addition, subtraction,
multiplication and division. Round brackets are
allowed too. Division may appear only when a dividend is a multiple of
a
divisor.

### Example

Each of the following expressions is the 5-representation of the number 12:

- 5+5+(5:5)+(5:5)
- (5+(5))+5:5+5:5
- 55:5+5:5
- (55+5):5

The** length** of the *K*-representation is the number of occurrences of
digit *K* in the expression. In the example above the first two representations have the length 6, the third - 5, and the forth - 4.

### Task

Write a program which:

- reads the digit
*K*and the series of numbers from the standard input, - verifies for each number from the series, whether it has a
*K*-representation of length at most 8, and if it does, then the program finds the minimal length of this representation, - writes results to the standard output.

### Input

The number of test cases t is in the first line of input, then t test cases follow separated by an empty line.
The first line of each test case contains digit *K*, * K* is en element of
{*1,...,9*}. The second line
contains number n, * 1<=n<=10*. In the following * n* lines there is the series of natural numbers
* a _{1},...,a_{n}*,

*1<=a*(for

_{i}<=32000*i=1,..,n*), one number in each line.

### Output

The output for each test case composes of * n* lines. The *i-*th line should
contain:

- exactly one number which is the minimal length of
*K*-representation of a_{i}, assuming that such a representation of length not grater then 8 exists, - one word NO, if the minimal length of the
*K*-representation of the number*a*_{i}is grater than 8.

### Example

Sample input:1 5 2 12 31168Sample output4 NO

Added by: | Piotr Łowiec |

Date: | 2004-09-13 |

Time limit: | 1.647s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All |

Resource: | 6th Polish Olympiad in Informatics, stage 1 |