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 maxn = 11;
  const int maxm = 1e4 + 1;
  int x[maxn];
  int s[maxn][maxm];
  pair<int, int> y[maxm];
  int an[maxm];
  int mx = 0;
  void gen(int n, int m, int id, string &t) {
    if (id == n) {
      for (int j = 0; j < m; ++j) {
        y[j].first = 0;
        y[j].second = j;
      }
      long long cst = 0;
      for (int i = 0; i < n; ++i) {
        if (t[i] == '+')
          cst += (long long)x[i];
        else
          cst -= (long long)x[i];
        for (int j = 0; j < m; ++j) {
          if (s[i][j] != 1) continue;
          if (t[i] == '+')
            y[j].first--;
          else
            y[j].first++;
        }
      }
      sort(y, y + m);
      int a[maxm];
      for (int i = 0; i < m; ++i) {
        int id = y[i].second;
        a[id] = i + 1;
        cst += (long long)(i + 1) * (long long)y[i].first;
      }
      for (int i = 0; i < n; ++i) {
        long long sm = 0;
        for (int j = 0; j < m; ++j) {
          if (s[i][j] == 1) sm += a[j];
        }
        if (t[i] == '+' && sm > x[i]) return;
        if (t[i] == '-' && sm < x[i]) return;
      }
      if (cst > mx) {
        mx = cst;
        swap(a, an);
      }
      return;
    }
    t += '+';
    gen(n, m, id + 1, t);
    t.pop_back();
    t += '-';
    gen(n, m, id + 1, t);
    t.pop_back();
    return;
  }
  void solve() {
    int n, m;
    cin >> n >> m;
    mx = 0;
    for (int i = 0; i < n; ++i) {
      cin >> x[i];
    }
    for (int i = 0; i < n; ++i) {
      string ss;
      cin >> ss;
      for (int j = 0; j < m; ++j) {
        s[i][j] = (ss[j] == '1');
        an[j] = j + 1;
      }
    }
    string tmp = "";
    gen(n, m, 0, tmp);
    for (int i = 0; i < m; ++i) cout << an[i] << " ";
    cout << "\n";
    return;
  }
  int main() {
    int T;
    cin >> T;
    while (T--) solve();
  }
  