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.*;
  import java.math.BigInteger;
  import java.util.*;
  
  public class Main {
      static int MOD = 1000000007;
  
      // After writing solution, quick scan for:
      //   array out of bounds
      //   special cases e.g. n=1?
      //   npe, particularly in maps
      //
      // Big numbers arithmetic bugs:
      //   int overflow
      //   sorting, or taking max, after MOD
      void solve() throws IOException {
          int T = ri();
          for (int Ti = 0; Ti < T; Ti++) {
              int[] nm = ril(2);
              int n = nm[0];  // tiny
              int m = nm[1];
              int[] x = ril(n);
  
              char[][] results = new char[n][];
              for (int i = 0; i < n; i++) results[i] = rs();
  
              // Find a permutation of the m=10^4 questions.
              // There are few students
  
              // We can't take any question individually, since we only think about the sum
              // of points for each student...
  
              // What about for an individual student?
              // Let's say his score was x[i]. We would be surprised if the sum of his points
              // was super low or super high...
              //
              // There is sacrifice: if we make i's score super high, then we may inadvertantly
              // make other students' scores not surprising at all.
              // We must link the students somehow. In a graph?
  
              // Connect two students with an edge j if they both do question j.
              // Multi edges are clearly allowed.
  
              // 2^10 = 1024. Can we brute force on which students should be low vs high?
              // 0 means low, 1 means high
              // Give the lowest scores to the problems that the "bad kids" solve.
              // Among them, the lowest score should be given to the problem that a lot of the
              // bad kids solve.
  
              long maxSurprise = -1;
              int[] bestAssignment = null;
  
              List<Integer> order = new ArrayList<>(m);
              for (int i = 0; i < m; i++) order.add(i);
  
              for (int mask = 0; mask < (1 << n); mask++) {
                  int[] badkidsolves = new int[m];
                  for (int i = 0; i < n; i++) {
                      if (((1 << i) & mask) > 0) continue;
                      for (int j = 0; j < m; j++) {
                          if (results[i][j] == '1') badkidsolves[j]++;
                      }
                  }
  
                  int[] goodkidsolves = new int[m];
                  for (int i = 0; i < n; i++) {
                      if (((1 << i) & mask) == 0) continue;
                      for (int j = 0; j < m; j++) {
                          if (results[i][j] == '1') goodkidsolves[j]++;
                      }
                  }
  
                  int[] solvesPoints = new int[m];
                  for (int i = 0; i < m; i++) {
                      // It's "bad" if the bad kids get points at all
                      solvesPoints[i] = goodkidsolves[i] - badkidsolves[i];
                  }
  
                  Collections.sort(order, (i1, i2) -> -Integer.compare(solvesPoints[i1], solvesPoints[i2]));
  
                  int[] assignment = new int[m];
                  int pts = m;
                  for (int z : order) {
                      assignment[z] = pts--;
                  }
  
                  long surprise = 0;
                  for (int i = 0; i < n; i++) {
                      long score = 0;
                      for (int j = 0; j < m; j++) if (results[i][j] == '1') score += assignment[j];
                      surprise += Math.abs(score - x[i]);
                  }
  
                  if (surprise > maxSurprise) {
                      maxSurprise = surprise;
                      bestAssignment = assignment;
                  }
              }
  
              for (int z : bestAssignment) {
                  pw.print(z + " ");
              }
              pw.println();
          }
      }
      // IMPORTANT
      // DID YOU CHECK THE COMMON MISTAKES ABOVE?
  
      // Template code below
  
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      PrintWriter pw = new PrintWriter(System.out);
  
      public static void main(String[] args) throws IOException {
          Main m = new Main();
          m.solve();
          m.close();
      }
  
      void close() throws IOException {
          pw.flush();
          pw.close();
          br.close();
      }
  
      int ri() throws IOException {
          return Integer.parseInt(br.readLine().trim());
      }
  
      long rl() throws IOException {
          return Long.parseLong(br.readLine().trim());
      }
  
      int[] ril(int n) throws IOException {
          int[] nums = new int[n];
          int c = 0;
          for (int i = 0; i < n; i++) {
              int sign = 1;
              c = br.read();
              int x = 0;
              if (c == '-') {
                  sign = -1;
                  c = br.read();
              }
              while (c >= '0' && c <= '9') {
                  x = x * 10 + c - '0';
                  c = br.read();
              }
              nums[i] = x * sign;
          }
          while (c != '\n' && c != -1) c = br.read();
          return nums;
      }
  
      long[] rll(int n) throws IOException {
          long[] nums = new long[n];
          int c = 0;
          for (int i = 0; i < n; i++) {
              int sign = 1;
              c = br.read();
              long x = 0;
              if (c == '-') {
                  sign = -1;
                  c = br.read();
              }
              while (c >= '0' && c <= '9') {
                  x = x * 10 + c - '0';
                  c = br.read();
              }
              nums[i] = x * sign;
          }
          while (c != '\n' && c != -1) c = br.read();
          return nums;
      }
  
      int[] rkil() throws IOException {
          int sign = 1;
          int c = br.read();
          int x = 0;
          if (c == '-') {
              sign = -1;
              c = br.read();
          }
          while (c >= '0' && c <= '9') {
              x = x * 10 + c - '0';
              c = br.read();
          }
          return ril(x);
      }
  
      long[] rkll() throws IOException {
          int sign = 1;
          int c = br.read();
          int x = 0;
          if (c == '-') {
              sign = -1;
              c = br.read();
          }
          while (c >= '0' && c <= '9') {
              x = x * 10 + c - '0';
              c = br.read();
          }
          return rll(x);
      }
  
      char[] rs() throws IOException {
          return br.readLine().toCharArray();
      }
  
      void sort(int[] A) {
          Random r = new Random();
          for (int i = A.length-1; i > 0; i--) {
              int j = r.nextInt(i+1);
              int temp = A[i];
              A[i] = A[j];
              A[j] = temp;
          }
          Arrays.sort(A);
      }
  
      void printDouble(double d) {
          pw.printf("%.16f", d);
      }
  }