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.util.ArrayDeque;
  import java.util.InputMismatchException;
  
  public class E {
      public static void main(String[] args) {
          FastIO io = new FastIO();
          int t = io.nextInt();
          while (t-- > 0) {
  
              int n = io.nextInt();
              int m = io.nextInt();
              int[] arr = new int[n];
              for (int i = 0; i < n; i++) arr[i] = io.nextInt();
              char[][] grid = new char[n][m];
              for (int i = 0; i < n; i++) grid[i] = io.next().toCharArray();
              long max = -1;
              int[] maxPer = new int[n];
              for (int i = 0; i < 1 << n; i++) {
                  int[] finalValue = new int[m];
                  Question[] count = new Question[m];
                  for (int j = 0; j < m; j++) {
                      count[j] = new Question(0, j);
                      for (int st = 0; st < n; st++) {
                          if (grid[st][j] == '1') {
                              if (((i >> st) & 1) == 0) {
                                  count[j].freq--;
                              } else count[j].freq++;
                          }
                      }
                  }
  
                  ArrayDeque<Question>[] questions = new ArrayDeque[21];
                  for (int j = 0; j < m; j++) {
                      if (questions[10 + count[j].freq] == null) questions[10 + count[j].freq] = new ArrayDeque<>();
                      questions[10 + count[j].freq].add(count[j]);
                  }
                  int score = 1;
                  for (int f = 0; f <= 20; f++) {
                      while (questions[f] != null && questions[f].size() > 0)
                          finalValue[questions[f].poll().ind] = score++;
                  }
  
  
                  long sum = 0;
                  for (int st = 0; st < n; st++) {
                      int localSum = 0;
                      for (int j = 0; j < m; j++) {
                          if (grid[st][j] == '1') localSum += finalValue[j];
                      }
                      sum += Math.abs(localSum - arr[st]);
                  }
                  if (sum > max) {
                      max = sum;
                      maxPer = finalValue;
                  }
  
              }
              for (int v : maxPer) {
                  io.print(v + " ");
              }
              io.println();
          }
  
          io.flush();
      }
  
  
      static class Question {
          int freq, ind;
  
          public Question(int freq, int ind) {
              this.freq = freq;
              this.ind = ind;
          }
      }
  
      private static class FastIO extends PrintWriter {
          private InputStream stream;
          private byte[] buf = new byte[1 << 16];
          private int curChar, numChars;
  
          // standard input
          public FastIO() {
              this(System.in, System.out);
          }
  
          public FastIO(InputStream i, OutputStream o) {
              super(o);
              stream = i;
          }
  
          // file input
          public FastIO(String i, String o) throws IOException {
              super(new FileWriter(o));
              stream = new FileInputStream(i);
          }
  
          // throws InputMismatchException() if previously detected end of file
          private int nextByte() {
              if (numChars == -1) throw new InputMismatchException();
              if (curChar >= numChars) {
                  curChar = 0;
                  try {
                      numChars = stream.read(buf);
                  } catch (IOException e) {
                      throw new InputMismatchException();
                  }
                  if (numChars == -1) return -1; // end of file
              }
              return buf[curChar++];
          }
  
          // to read in entire lines, replace c <= ' '
          // with a function that checks whether c is a line break
          public String next() {
              int c;
              do {
                  c = nextByte();
              } while (c <= ' ');
              StringBuilder res = new StringBuilder();
              do {
                  res.appendCodePoint(c);
                  c = nextByte();
              } while (c > ' ');
              return res.toString();
          }
  
          public int nextInt() { // nextLong() would be implemented similarly
              int c;
              do {
                  c = nextByte();
              } while (c <= ' ');
              int sgn = 1;
              if (c == '-') {
                  sgn = -1;
                  c = nextByte();
              }
              int res = 0;
              do {
                  if (c < '0' || c > '9')
                      throw new InputMismatchException();
                  res = 10 * res + c - '0';
                  c = nextByte();
              } while (c > ' ');
              return res * sgn;
          }
  
          public double nextDouble() {
              return Double.parseDouble(next());
          }
      }
  
  }
  