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;
  void solve() {
    int n, m;
    cin >> n >> m;
    vector<long long int> a(n);
    for (int i = 0; i < n; i++) cin >> a[i];
    vector<string> s(n);
    for (int i = 0; i < n; i++) cin >> s[i];
    long long int sur = 0;
    vector<int> ans;
    for (int mask = 0; mask < (1 << (n - 1)); mask++) {
      int lo = 1, hi = m;
      int lo2 = 1, hi2 = m;
      vector<int> cnt(m, 0);
      vector<bool> stat(n);
      for (int i = 0; i < n; i++) {
        if (mask & (1 << i))
          stat[i] = true;
        else
          stat[i] = false;
      }
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
          if (s[i][j] == '1') {
            cnt[j] += (stat[i] ? 1 : -1);
          }
        }
      }
      set<pair<int, int>> temp1, temp2;
      vector<int> tempAns(m, -1), tempAns2(m, -1);
      for (int i = 0; i < m; i++) {
        if (cnt[i] > 0)
          temp1.insert(make_pair(-cnt[i], i));
        else if (cnt[i] < 0)
          temp2.insert(make_pair(cnt[i], i));
      }
      for (auto it : temp1) {
        int index = it.second;
        tempAns[index] = hi--;
        tempAns2[index] = lo2++;
      }
      for (auto it : temp2) {
        int index = it.second;
        tempAns[index] = lo++;
        tempAns2[index] = hi2--;
      }
      for (int i = 0; i < m; i++) {
        if (tempAns[i] == -1) {
          tempAns[i] = lo++;
          tempAns2[i] = lo2++;
        }
      }
      long long int checkSur = 0, checkSur2 = 0;
      for (int i = 0; i < n; i++) {
        long long int score = 0;
        long long int score2 = 0;
        for (int j = 0; j < m; j++) {
          if (s[i][j] == '1') {
            score += tempAns[j];
            score2 += tempAns2[j];
          }
        }
        checkSur += abs(a[i] - score);
        checkSur2 += abs(a[i] - score2);
      }
      if (checkSur > sur || mask == 0) {
        sur = checkSur;
        ans = move(tempAns);
      }
      if (checkSur2 > sur) {
        sur = checkSur2;
        ans = move(tempAns2);
      }
    }
    for (int i = 0; i < m; i++) {
      cout << ans[i] << ' ';
    }
    cout << '\n';
  }
  int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int t = 1;
    cin >> t;
    while (t--) {
      solve();
    }
  }
  