CF1622E.Math Test

Petya is a math teacher. $n$ of his students has written a test consisting of $m$ questions. For each student, it is known which questions he has answered correctly and which he has not.

If the student answers the $j$-th question correctly, he gets $p_j$ points (otherwise, he gets $0$ points). Moreover, the points for the questions are distributed in such a way that the array $p$ is a permutation of numbers from $1$ to $m$.

For the $i$-th student, Petya knows that he expects to get $x_i$ points for the test. Petya wonders how unexpected the results could be. Petya believes that the surprise value of the results for students is equal to $\sum\limits_{i=1}^{n} |x_i - r_i|$, where $r_i$ is the number of points that the $i$-th student has got for the test.

Your task is to help Petya find such a permutation $p$ for which the surprise value of the results is maximum possible. If there are multiple answers, print any of them.

佩佳是一名数学老师。他的 $n$ 名学生参加了一场包含 $m$ 道题的测验。对于每名学生，已知他哪些题目答对、哪些题目答错。

若某学生正确回答了第 $j$ 道题，则他获得 $p_j$ 分（否则得 $0$ 分）。此外，各题分值按如下方式分配：数组 $p$ 是 $1$ 到 $m$ 这些整数的一个排列。

对于第 $i$ 名学生，佩佳知道他预期在本次测验中获得 $x_i$ 分。佩佳想知道实际结果可能有多“出人意料”。佩佳定义学生们的“意外值”为 $\sum\limits_{i=1}^{n} |x_i - r_i|$，其中 $r_i$ 表示第 $i$ 名学生实际获得的分数。

你的任务是帮助佩佳找出一个排列 $p$，使得结果的意外值尽可能大。如有多个满足条件的答案，输出任意一个即可。

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains two integers $n$ and $m$ ($1 \le n \le 10$; $1 \le m \le 10^4$) — the number of students and the number of questions, respectively.

The second line contains $n$ integers $x_1, x_2, \dots, x_n$ ($0 \le x_i \le \frac{m(m+1)}{2}$), where $x_i$ is the number of points that the $i$-th student expects to get.

This is followed by $n$ lines, the $i$-th line contains the string $s_i$ ($|s_i| = m; s_{i, j} \in {0, 1}$), where $s_{i, j}$ is $1$ if the $i$-th student has answered the $j$-th question correctly, and $0$ otherwise.

The sum of $m$ for all test cases does not exceed $10^4$.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

每个测试用例的第一行包含两个整数 $n$ 和 $m$（$1 \le n \le 10$；$1 \le m \le 10^4$）—— 分别表示学生人数和题目数量。

第二行包含 $n$ 个整数 $x_1, x_2, \dots, x_n$（$0 \le x_i \le \frac{m(m+1)}{2}$），其中 $x_i$ 表示第 $i$ 个学生预期获得的分数。

接下来是 $n$ 行，第 $i$ 行包含一个字符串 $s_i$（$|s_i| = m$；$s_{i, j} \in \{0, 1\}$），其中 $s_{i, j}$ 为 $1$ 表示第 $i$ 个学生正确回答了第 $j$ 道题，为 $0$ 则表示回答错误。

所有测试用例的 $m$ 值之和不超过 $10^4$。

For each test case, print $m$ integers — a permutation $p$ for which the surprise value of the results is maximum possible. If there are multiple answers, print any of them.

对于每个测试用例，输出 $m$ 个整数——一个使得结果的“惊喜值”达到最大可能值的排列 $p$。如果存在多个答案，输出其中任意一个即可。