CF1916A.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.

在一个序列 $a$ 中，其所有元素的乘积等于 $2023$，从中移除了 $k$ 个数，得到一个长度为 $n$ 的序列 $b$。已知所得序列 $b$，请找出任意一个满足条件的原序列 $a$，并输出从 $a$ 中移除的 $k$ 个元素；若不存在这样的序列，则说明其不可能存在。

注意：不能保证这样的数组一定存在。

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 $2023$.

每个测试包含若干个测试用例。第一行包含一个整数 $t$（$1 \le t \le 100$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $k$（$1 \le n, k \le 5$），分别表示序列 $b$ 的长度以及从序列 $a$ 中移除的数字个数。

每个测试用例的第二行包含 $n$ 个整数 $b_1,b_2, \ldots,b_n$（$1 \leq b_i \leq 2023$），即剩余的序列。注意：$b_i$ 的值未必是 $2023$ 的因数。

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.

对于每个测试用例，如果序列 $a$ 存在，则输出 "YES"；并在下一行输出从序列 $a$ 中移除的 $k$ 个非负整数。如果序列 $a$ 不存在，则在单独一行中输出 "NO"。

你可以以任意大小写形式输出答案（大写或小写均可）。例如，字符串 "yEs"、"yes"、"Yes" 和 "YES" 均会被识别为肯定回答。

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 $7 \cdot 17 \cdot 17 = 2023$.

在第三个测试用例中，乘积等于 $289 \cdot 7 = 2023$。

在第四个测试用例中，乘积已经等于 $2023$。

在第七个测试用例中，乘积等于 $7 \cdot 17 \cdot 17 = 2023$。