E. Math Testtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputPetya 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.InputThe 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.OutputFor 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.ExampleInput
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
Output
3 1 2 
2 3 4 1 
3 1 4 5 2 6 

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  
['bitmasks', 'brute force', 'greedy', '*2200']