2023
Description
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.
Input
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 $2023$.
Output
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.
7
2 2
5 2
3 1
7 17 7
4 2
1 289 1 1
3 1
7 17 17
1 1
289
1 1
2023
1 3
1
NO
NO
YES
7 1
YES
1
YES
7
YES
1
YES
7 17 17
Note
In third test case product is equal to $289 \cdot 7 = 2023$.
In fourth test case product is already equal to $2023$.
In seventh test case product is equal to $7 \cdot 17 \cdot 17 = 2023$.