description: 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 ∑_{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 ≤ 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 ≤ (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} ∈ \{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.
  
  Example
  
  Input
  
  
  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 
solution: I=lambda:[*map(int,input().split())]
  r=range;s=sum
  for _ in[0]*I()[0]:
  	n,m=I();e=I();M=[[*map(int,[*input().strip()])]for i in r(n)];o=[bin(i).count('1')for i in r(1<<n)];q=[s(1<<i for i in r(n)if M[i][j])for j in r(m)];b=-1
  	for i in r(1<<n):
  		c=[0]*(n+1);v=[0]*m;d=c[:];P=v[:]
  		for j in r(m):v[j]=o[i^q[j]];c[v[j]]+=1
  		for j in r(n):d[j+1]=d[j]+c[j]
  		for j in r(m):d[v[j]]+=1;P[j]=d[v[j]]
  		T=2*s(e[j]for j in r(n) if(i>>j)&1)-s(e)+s((o[q[j]]-2*o[i&q[j]])*P[j]for j in r(m))
  		if T>b:b,p=T,P
  	print(*p)