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: import java.io.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.io.PrintWriter;
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.Collections;
  import java.util.Random;
  import java.util.StringTokenizer;
  
  /*
  
  
  e = expected, a = actual
  
  e_1 - a_1 
  a_2 - e_2
  e_3 - a_3
  
  
  ================
  
  -a_1 +a_2 -a_3 => maximize
  +e_1 -e_2 +e_3 => constant
  
  Each person is either + per question or - per question
  sort the question by their net score
  questionValue*timesCounted
  
  2^10 * 1024 * log
  
  
  1
  4 4
  6 2 0 10
  1001
  0010
  0110
  0101
  
  I say  4 3 1 2
  answer 2 3 4 1
  
  Expect: 6 2 0 10
  Me: Get 6 1 4 5
  Him:    3 4 7 4
   */
  public class E {
  
  	static boolean[][] personGotQuestion;
  	
  	public static void main(String[] args) {
  		FastScanner fs=new FastScanner();
  		PrintWriter out=new PrintWriter(System.out);
  		int T=fs.nextInt();
  		for (int tt=0; tt<T; tt++) {
  			int nPeople=fs.nextInt();
  			int nQuestions=fs.nextInt();
  			int[] expectedScores=fs.readArray(nPeople);
  			personGotQuestion=new boolean[nPeople][nQuestions];
  			for (int person=0; person<nPeople; person++) {
  				char[] line=fs.next().toCharArray();
  				for (int q=0; q<nQuestions; q++)
  					personGotQuestion[person][q]=line[q]=='1';
  			}
  			
  			ArrayList<Integer>[] count=new ArrayList[1<<nPeople];
  			for (int q=0; q<nQuestions; q++) {
  				int mask=0;
  				for (int p=0; p<nPeople; p++)
  					mask+=(1<<p)*(personGotQuestion[p][q]?1:0);
  				if (count[mask]==null) count[mask]=new ArrayList<>();
  				count[mask].add(q);
  			}
  			int nNonzero=0;
  			for (ArrayList<Integer> l:count) if (l!=null) nNonzero++;
  			Question[] questions=new Question[nNonzero];
  			nNonzero=0;
  			for (int mask=0; mask<1<<nPeople; mask++) {
  				if (count[mask]==null) continue;
  				questions[nNonzero++]=new Question(mask, count[mask]);
  			}
  			long best=0; int bestMask=0;
  			for (int mask=0; mask<1<<nPeople; mask++) {
  				//if this is a 1 bit, expected is positive
  				long constantToAdd=0;
  				for (int i=0; i<nPeople; i++) if ((mask&(1<<i))!=0) constantToAdd+=expectedScores[i]; else constantToAdd-=expectedScores[i];
  				
  				long bestOtherDist=bestOtherDist(mask, nQuestions, nPeople, questions, false);
  				if (bestOtherDist+constantToAdd>best) {
  					best=bestOtherDist+constantToAdd;
  					bestMask=mask;
  				}
  				
  //				System.out.println("For mask "+mask+" "+constantToAdd+" "+bestOtherDist);
  			}
  //			out.println(best+" "+bestMask);
  			finalAns=new int[nQuestions];
  			bestOtherDist(bestMask, nQuestions, nPeople, questions, true);
  			for (int i=0; i<nQuestions; i++) {
  				out.print(finalAns[i]+" ");
  			}
  			out.println();
  		}
  		out.close();
  	}
  
  	static int[] finalAns;
  	
  	static long bestOtherDist(int mask, int nQuestions, int nPeople, 
  			Question[] questions, boolean markAns) {
  		for (Question q:questions) {
  			q.netValue=0;
  			for (int i=0; i<nPeople; i++) {
  				if ((q.mask&(1<<i))!=0) {
  					if ((mask&(1<<i))!=0) {
  						q.netValue--;
  					}
  					else {
  						q.netValue++;
  					}
  				}
  			}
  		}
  		Arrays.sort(questions);
  		long ans=0;
  		int next=1;
  		for (Question qq:questions) {
  //			for (int i=0; i<qq.count; i++) {
  //				ans+=next*qq.netValue;
  //				next++;
  //			}
  			for (int i:qq.originalPositions) {
  				ans+=next*qq.netValue;
  				if (markAns) finalAns[i]=next;
  				next++;
  			}
  		}
  		return ans;
  	}
  	
  	static class Question implements Comparable<Question> {
  		int mask;
  		int netValue;
  		int count;
  		ArrayList<Integer> originalPositions;
  		
  		public Question(int mask, ArrayList<Integer> originalPositions) {
  			this.mask=mask;
  			this.count=originalPositions.size();
  			this.originalPositions=originalPositions;
  		}
  		
  		public int compareTo(Question o) {
  			return Integer.compare(netValue, o.netValue);
  		}
  	}
  	
  	static final Random random=new Random();
  	static final int mod=1_000_000_007;
  	
  	static void ruffleSort(int[] a) {
  		int n=a.length;//shuffle, then sort 
  		for (int i=0; i<n; i++) {
  			int oi=random.nextInt(n), temp=a[oi];
  			a[oi]=a[i]; a[i]=temp;
  		}
  		Arrays.sort(a);
  	}
  	static long add(long a, long b) {
  		return (a+b)%mod;
  	}
  	static long sub(long a, long b) {
  		return ((a-b)%mod+mod)%mod;
  	}
  	static long mul(long a, long b) {
  		return (a*b)%mod;
  	}
  	
  	static void sort(int[] a) {
  		ArrayList<Integer> l=new ArrayList<>();
  		for (int i:a) l.add(i);
  		Collections.sort(l);
  		for (int i=0; i<a.length; i++) a[i]=l.get(i);
  	}
  	
  	
  	static class FastScanner {
  		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
  		StringTokenizer st=new StringTokenizer("");
  		String next() {
  			while (!st.hasMoreTokens())
  				try {
  					st=new StringTokenizer(br.readLine());
  				} catch (IOException e) {
  					e.printStackTrace();
  				}
  			return st.nextToken();
  		}
  		
  		int nextInt() {
  			return Integer.parseInt(next());
  		}
  		int[] readArray(int n) {
  			int[] a=new int[n];
  			for (int i=0; i<n; i++) a[i]=nextInt();
  			return a;
  		}
  		long nextLong() {
  			return Long.parseLong(next());
  		}
  	}
  
  	
  }
  