A16414 | 2023

In a sequence $a$ , whose product was equal to $2023$ , $k$ numbers were removed, leaving a sequence $b$ of length $n$ . Given the resulting sequence $b$ , find any suitable sequence $a$ and output which $k$ elements were removed from it, or state that such a sequence could not have existed.

Notice that you are not guaranteed that such array exists.

Each test consists of several test cases. The first line contains a single integer $t$ ( $1 \le t \le 100$ ) — the number of test cases. This is followed by a description of the test cases.

The first line of each test case contains two integers $n$ ( $1 \le n, k \le 5$ ) — the size of sequence $b$ and the number of numbers removed from sequence $a$ .

The second line contains $n$ integers $b_1,b_2, \ldots,b_n$ ( $1 \leq b_i \leq 2023$ ) — the remaining sequence. The values of $b_i$ might not be divisors of $2023$ .

For each test case, output "YES" if the sequence $a$ exists, and in the following line output $k$ non-negative integers that were removed from the sequence $a$ . If the sequence $a$ does not exist, output "NO" in a single line.

You can output the answer in any case (uppercase or lowercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive answers.