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>
  template <class T>
  inline bool chmax(T& a, T b) {
    if (a < b) {
      a = b;
      return 1;
    }
    return 0;
  }
  template <class T>
  inline bool chmin(T& a, T b) {
    if (a > b) {
      a = b;
      return 1;
    }
    return 0;
  }
  using namespace std;
  template <typename T>
  vector<vector<T>> vec2d(int n, int m, T v) {
    return vector<vector<T>>(n, vector<T>(m, v));
  }
  template <typename T>
  vector<vector<vector<T>>> vec3d(int n, int m, int k, T v) {
    return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
  }
  template <typename T>
  void print_vector(vector<T> v, char delimiter = ' ') {
    if (v.empty()) {
      cout << "\n";
      return;
    }
    for (int i = 0; i + 1 < v.size(); i++) cout << v[i] << delimiter;
    cout << v.back() << "\n";
  }
  using P = pair<int, int>;
  using T = tuple<int, int, int>;
  void solve() {
    int n, m;
    cin >> n >> m;
    vector<int> x(n);
    for (int i = 0; i < n; i++) cin >> x[i];
    vector<string> s(n);
    for (int i = 0; i < n; i++) cin >> s[i];
    vector<int> pcnt(1 << n);
    for (int i = 0; i < (1 << n); i++) {
      for (int j = 0; j < n; j++) {
        if (i & (1 << j)) pcnt[i]++;
      }
    }
    vector<int> cnt(1 << n);
    vector<int> tt(m);
    for (int i = 0; i < m; i++) {
      int t = 0;
      for (int j = 0; j < n; j++) {
        if (s[j][i] == '1') {
          t += 1 << j;
        }
      }
      tt[i] = t;
      cnt[t]++;
    }
    long long ans = -1;
    vector<int> ans_v(m);
    int all_student = (1 << n) - 1;
    for (int s = 0; s < (1 << n); s++) {
      int others = all_student - s;
      vector<P> vp;
      long long tmp = 0;
      for (int i = 0; i < n; i++) {
        if (s & (1 << i))
          tmp -= x[i];
        else
          tmp += x[i];
      }
      for (int i = 0; i < m; i++) {
        int t = tt[i];
        int correct_pos = pcnt[s & t];
        int correct_neg = pcnt[others & t];
        vp.push_back(P(correct_pos - correct_neg, i));
      }
      sort(vp.begin(), vp.end(), greater<P>());
      int cur = m;
      for (auto [cnt_pos, _] : vp) {
        tmp += cur * cnt_pos;
        cur -= 1;
      }
      if (chmax(ans, tmp)) {
        int cur = m;
        for (auto [cnt_pos, i] : vp) {
          ans_v[i] = cur;
          cur--;
        }
      }
      assert(cur == 0);
    }
    print_vector(ans_v);
  }
  int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    int t;
    cin >> t;
    while (t--) solve();
  }
  