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;
  using LL = long long;
  mt19937_64 rng(time(0));
  int random(int l, int r) { return uniform_int_distribution<int>(l, r)(rng); }
  const int maxn = 1000100;
  void solve(int tc) {
    int n, m;
    cin >> n >> m;
    vector<int> tab(n);
    for (int i = (0); i < (n); ++i) cin >> tab[i];
    vector<string> correct(n);
    for (int i = (0); i < (n); ++i) cin >> correct[i];
    int all = (1 << n);
    long long best = -1;
    vector<int> odpowiedz;
    for (int mask = (0); mask < (all); ++mask) {
      vector<bool> bit(n);
      vector<long long> q_score(m, 0);
      for (int i = (0); i < (n); ++i) {
        if (mask & (1 << i))
          bit[i] = 1;
        else
          bit[i] = 0;
      }
      for (int i = (0); i < (n); ++i) {
        for (int q = (0); q < (m); ++q) {
          if (correct[i][q] == '1') {
            if (bit[i])
              q_score[q]++;
            else
              q_score[q]--;
          }
        }
      }
      vector<pair<int, int> > qs(m);
      for (int i = (0); i < (m); ++i) qs[i] = {q_score[i], i};
      sort(begin(qs), end(qs));
      vector<long long> policzone(n, 0);
      vector<int> tmp(m);
      for (int i = (0); i < (m); ++i) {
        int score = i + 1;
        int pytanie = qs[i].second;
        tmp[pytanie] = score;
        for (int student = (0); student < (n); ++student) {
          if (correct[student][pytanie] == '1') policzone[student] += score;
        }
      }
      long long opt = 0;
      for (int student = (0); student < (n); ++student)
        opt += abs(policzone[student] - tab[student]);
      if (opt > best) {
        best = opt;
        odpowiedz = tmp;
      }
    }
    0 && cerr;
    for (int i = (0); i < (m); ++i) cout << odpowiedz[i] << ' ';
    cout << "\n";
  }
  int main() {
    {
      ios_base::sync_with_stdio(false);
      cin.tie(0);
      cout.tie(0);
    };
    int tests;
    cin >> tests;
    for (int test = (1); test <= (tests); ++test) {
      solve(test);
    }
  }
  