Description

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.

3
4 3
5 1 2 2
110
100
101
100
4 4
6 2 0 10
1001
0010
0110
0101
3 6
20 3 15
010110
000101
111111

3 1 2 
2 3 4 1 
3 1 4 5 2 6