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.

Input

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 $$$10^4$$$.

Output

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.

Math Test

Examples