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: /*
  stream Butter!
  eggyHide eggyVengeance
  I need U
  xiao rerun when
   */
  import static java.lang.Math.*;
  import java.util.*;
  import java.io.*;
  import java.math.*;
  
  public class x1622E
  {
      public static void main(String hi[]) throws Exception
      {
          int[] bc = new int[2000];
          for(int i=0; i < 2000; i++)
              bc[i] = Integer.bitCount(i);
          FastScanner infile = new FastScanner();
          int T = infile.nextInt();
          StringBuilder sb = new StringBuilder();
          while(T-->0)
          {
              int N = infile.nextInt();
              int M = infile.nextInt();
              int[] arr = infile.nextInts(N);
              int[][] grid = new int[N][M];
              for(int r=0; r < N; r++)
              {
                  char[] line = infile.nextLine().toCharArray();
                  for(int c=0; c < M; c++)
                      grid[r][c] = line[c]-'0';
              }
              int[] covers = new int[M];
              for(int i=0; i < M; i++)
                  for(int b=0; b < N; b++)
                      covers[i] |= grid[b][i]*(1<<b);
              int[] res = new int[M];
              long best = -1;
              for(int mask=0; mask < 1<<N; mask++)
              {
                  ArrayList<Unit> ls = new ArrayList<Unit>();
                  for(int i=0; i < M; i++)
                  {
                      int maximized = bc[mask&covers[i]];
                      int minimized = bc[covers[i]]-maximized;
                      ls.add(new Unit(i, maximized-minimized));
                  }
                  Collections.sort(ls);
                  int[] values = new int[M];
                  for(int i=0; i < M; i++)
                      values[ls.get(i).id] = i+1;
                  long temp = 0L;
                  for(int b=0; b < N; b++)
                  {
                      if((mask&(1<<b)) > 0)
                          temp -= arr[b];
                      else
                          temp += arr[b];
                  }
                  for(int i=0; i < M; i++)
                  {
                      Unit u = ls.get(i);
                      temp += values[u.id]*u.val;
                  }
                  if(best < temp)
                  {
                      best = temp;
                      res = values;
                  }
              }
              for(int x: res)
                  sb.append(x+" ");
              sb.append("\n");
          }
          System.out.print(sb);
      }
  }
  class Unit implements Comparable<Unit>
  {
      public int id;
      public int val;
  
      public Unit(int i, int v)
      {
          id = i;
          val = v;
      }
      public int compareTo(Unit oth)
      {
          return val-oth.val;
      }
  }
  class FastScanner
  {
      //I don't understand how this works lmao
      private int BS = 1 << 16;
      private char NC = (char) 0;
      private byte[] buf = new byte[BS];
      private int bId = 0, size = 0;
      private char c = NC;
      private double cnt = 1;
      private BufferedInputStream in;
  
      public FastScanner() {
          in = new BufferedInputStream(System.in, BS);
      }
  
      public FastScanner(String s) {
          try {
              in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
          } catch (Exception e) {
              in = new BufferedInputStream(System.in, BS);
          }
      }
  
      private char getChar() {
          while (bId == size) {
              try {
                  size = in.read(buf);
              } catch (Exception e) {
                  return NC;
              }
              if (size == -1) return NC;
              bId = 0;
          }
          return (char) buf[bId++];
      }
  
      public int nextInt() {
          return (int) nextLong();
      }
  
      public int[] nextInts(int N) {
          int[] res = new int[N];
          for (int i = 0; i < N; i++) {
              res[i] = (int) nextLong();
          }
          return res;
      }
  
      public long[] nextLongs(int N) {
          long[] res = new long[N];
          for (int i = 0; i < N; i++) {
              res[i] = nextLong();
          }
          return res;
      }
  
      public long nextLong() {
          cnt = 1;
          boolean neg = false;
          if (c == NC) c = getChar();
          for (; (c < '0' || c > '9'); c = getChar()) {
              if (c == '-') neg = true;
          }
          long res = 0;
          for (; c >= '0' && c <= '9'; c = getChar()) {
              res = (res << 3) + (res << 1) + c - '0';
              cnt *= 10;
          }
          return neg ? -res : res;
      }
  
      public double nextDouble() {
          double cur = nextLong();
          return c != '.' ? cur : cur + nextLong() / cnt;
      }
  
      public double[] nextDoubles(int N) {
          double[] res = new double[N];
          for (int i = 0; i < N; i++) {
              res[i] = nextDouble();
          }
          return res;
      }
  
      public String next() {
          StringBuilder res = new StringBuilder();
          while (c <= 32) c = getChar();
          while (c > 32) {
              res.append(c);
              c = getChar();
          }
          return res.toString();
      }
  
      public String nextLine() {
          StringBuilder res = new StringBuilder();
          while (c <= 32) c = getChar();
          while (c != '\n') {
              res.append(c);
              c = getChar();
          }
          return res.toString();
      }
  
      public boolean hasNext() {
          if (c > 32) return true;
          while (true) {
              c = getChar();
              if (c == NC) return false;
              else if (c > 32) return true;
          }
      }
  }