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: #include <bits/stdc++.h>
  using namespace std;
  const int N = 10, M = 1e4 + 10;
  int n, m, first[N], s[M][N], coef[M], ord[M], res[M];
  void solve() {
    cin >> n >> m;
    for (int i = 0; i < n; i++) cin >> first[i];
    for (int i = 0; i < n; i++) {
      string b;
      cin >> b;
      for (int j = 0; j < m; j++) s[j + 1][i] = b[j] - '0';
    }
    int ans = -1;
    for (int i = 0; i < 1 << n; i++) {
      int sum = 0;
      for (int j = 0; j < n; j++) {
        if (i >> j & 1)
          sum += first[j];
        else
          sum -= first[j];
      }
      for (int j = 1; j <= m; j++) {
        coef[j] = 0;
        for (int k = 0; k < n; k++) {
          if (s[j][k]) coef[j] += (i >> k & 1) ? -1 : 1;
        }
        ord[j] = j;
      }
      sort(ord + 1, ord + m + 1,
           [&](int first, int second) { return coef[first] < coef[second]; });
      for (int j = 1; j <= m; j++) sum += j * coef[ord[j]];
      if (ans < sum) {
        for (int j = 1; j <= m; j++) res[ord[j]] = j;
        ans = sum;
      }
    }
    for (int i = 1; i <= m; i++) cout << res[i] << " ";
    cout << endl;
    return;
  }
  int main() {
    int t;
    for (cin >> t; t--; solve())
      ;
    return 0;
  }
  