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 = 5e4 + 43;
  int facts[MAXN];
  int bfacts[MAXN];
  const int mod = 998244353;
  int ml(int a, int b) { return (a * 1ll * b) % mod; }
  int cNr(int n, int r) {
    if (n < r) return 0;
    return ml(facts[n], ml(bfacts[r], bfacts[n - r]));
  }
  int b_p(int b, int p) {
    if (p == 0) return 1;
    if (p & 1) return ml(b, b_p(b, p - 1));
    int v = b_p(b, p >> 1);
    return ml(v, v);
  }
  int add(int a, int b) {
    int res = a + b;
    if (res >= mod) res -= mod;
    return res;
  }
  int sub(int a, int b) { return add(a, mod - b); }
  void solve() {
    int t;
    cin >> t;
    while (t--) {
      int n, m;
      cin >> n >> m;
      vector<int> xi;
      for (int i = 0; i < n; ++i) {
        int x;
        cin >> x;
        xi.push_back(x);
      }
      vector<string> tst;
      for (int i = 0; i < n; ++i) {
        string s;
        cin >> s;
        tst.push_back(s);
      }
      vector<int> answr(m, 0);
      for (int i = 0; i < m; ++i) {
        answr[i] = i + 1;
      }
      int mx = -1;
      for (int mask = 0; mask < (1 << n); ++mask) {
        int cr = 0;
        vector<int> coef(m, 0);
        for (int j = 0; j < n; ++j) {
          if ((1 << j) & mask) {
            cr -= xi[j];
            for (int k = 0; k < m; ++k) {
              if (tst[j][k] == '1') {
                coef[k]++;
              }
            }
          } else {
            cr += xi[j];
            for (int k = 0; k < m; ++k) {
              if (tst[j][k] == '1') {
                coef[k]--;
              }
            }
          }
        }
        vector<pair<int, int>> vp;
        for (int i = 0; i < m; ++i) {
          vp.push_back({coef[i], i});
        }
        sort(vp.begin(), vp.end());
        vector<int> cur_a(m, 0);
        for (int j = m; j >= 1; --j) {
          cur_a[vp[j - 1].second] = j;
          cr += vp[j - 1].first * j;
        }
        if (cr > mx) {
          mx = cr;
          answr = cur_a;
        }
      }
      for (auto e : answr) {
        cout << e << " ";
      }
      cout << "\n";
    }
  }
  signed main() {
    cin.tie(0);
    cout.tie(0);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    solve();
  }
  