B'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. The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The first line of each test case contains two integers n and m ( 1 <= n <= 10 ; 1 <= m <= 10^4 ) -- the number of students and the number of questions, respectively. The second line contains n integers x_1, x_2, ... , x_n ( 0 <= x_i <= 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 . 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. '...