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 ld = long double;
  using ll = long long;
  using vi = vector<int>;
  using vvi = vector<vi>;
  using vll = vector<ll>;
  using vvll = vector<vll>;
  using vb = vector<bool>;
  using vvb = vector<vb>;
  using vd = vector<double>;
  using vs = vector<string>;
  using pii = pair<int, int>;
  using pll = pair<ll, ll>;
  using pdd = pair<double, double>;
  using vpii = vector<pii>;
  using vpll = vector<pll>;
  using vpdd = vector<pdd>;
  template <typename T>
  void ckmin(T &a, const T &b) {
    a = min(a, b);
  }
  template <typename T>
  void ckmax(T &a, const T &b) {
    a = max(a, b);
  }
  mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
  namespace __input {
  template <class T1, class T2>
  void re(pair<T1, T2> &p);
  template <class T>
  void re(vector<T> &a);
  template <class T, size_t SZ>
  void re(array<T, SZ> &a);
  template <class T>
  void re(T &x) {
    cin >> x;
  }
  void re(double &x) {
    string t;
    re(t);
    x = stod(t);
  }
  template <class Arg, class... Args>
  void re(Arg &first, Args &...rest) {
    re(first);
    re(rest...);
  }
  template <class T1, class T2>
  void re(pair<T1, T2> &p) {
    re(p.f, p.s);
  }
  template <class T>
  void re(vector<T> &a) {
    for (int i = 0; i < int((a).size()); i++) re(a[i]);
  }
  template <class T, size_t SZ>
  void re(array<T, SZ> &a) {
    for (int i = 0; i < SZ; i++) re(a[i]);
  }
  }  // namespace __input
  using namespace __input;
  namespace __output {
  template <typename T>
  struct is_outputtable {
    template <typename C>
    static constexpr decltype(declval<ostream &>() << declval<const C &>(),
                              bool())
    test(int) {
      return true;
    }
    template <typename C>
    static constexpr bool test(...) {
      return false;
    }
    static constexpr bool value = test<T>(int());
  };
  template <
      class T, typename V = decltype(declval<const T &>().begin()),
      typename second = typename enable_if<!is_outputtable<T>::value, bool>::type>
  void pr(const T &x);
  template <class T,
            typename V = decltype(declval<ostream &>() << declval<const T &>())>
  void pr(const T &x) {
    cout << x;
  }
  template <class T1, class T2>
  void pr(const pair<T1, T2> &x);
  template <class Arg, class... Args>
  void pr(const Arg &first, const Args &...rest) {
    pr(first);
    pr(rest...);
  }
  template <class T, bool pretty = true>
  void prContain(const T &x) {
    if (pretty) pr("{");
    bool fst = 1;
    for (const auto &a : x) pr(!fst ? pretty ? ", " : " " : "", a), fst = 0;
    if (pretty) pr("}");
  }
  template <class T>
  void pc(const T &x) {
    prContain<T, false>(x);
    pr("\n");
  }
  template <class T1, class T2>
  void pr(const pair<T1, T2> &x) {
    pr("{", x.f, ", ", x.s, "}");
  }
  template <class T, typename V, typename second>
  void pr(const T &x) {
    prContain(x);
  }
  void ps() { pr("\n"); }
  template <class Arg>
  void ps(const Arg &first) {
    pr(first);
    ps();
  }
  template <class Arg, class... Args>
  void ps(const Arg &first, const Args &...rest) {
    pr(first, " ");
    ps(rest...);
  }
  }  // namespace __output
  using namespace __output;
  namespace __algorithm {
  template <typename T>
  void dedup(vector<T> &v) {
    sort((v).begin(), (v).end());
    v.erase(unique((v).begin(), (v).end()), v.end());
  }
  template <typename T>
  typename vector<T>::const_iterator find(const vector<T> &v, const T &x) {
    auto it = lower_bound((v).begin(), (v).end(), x);
    return it != v.end() && *it == x ? it : v.end();
  }
  template <typename T>
  size_t index(const vector<T> &v, const T &x) {
    auto it = find(v, x);
    assert(it != v.end() && *it == x);
    return it - v.begin();
  }
  template <typename I>
  struct _reversed_struct {
    I &v_;
    explicit _reversed_struct(I &v) : v_{v} {}
    typename I::reverse_iterator begin() const { return v_.rbegin(); }
    typename I::reverse_iterator end() const { return v_.rend(); }
  };
  template <typename I>
  _reversed_struct<I> reversed(I &v) {
    return _reversed_struct<I>(v);
  }
  }  // namespace __algorithm
  using namespace __algorithm;
  namespace __io {
  void setIO() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout << setprecision(15);
  }
  }  // namespace __io
  using namespace __io;
  template <typename T_vector>
  void outvec(const T_vector &v, bool add_one = false, int start = -1,
              int end = -1) {
    if (start < 0) start = 0;
    if (end < 0) end = int(v.size());
    for (int i = start; i < end; i++)
      cout << v[i] + (add_one ? 1 : 0) << (i < end - 1 ? ' ' : '\n');
  }
  const ld pi = 3.14159265358979323846;
  const ll mod = 1000000007;
  const ll N = 7e5;
  ll n, m, k, l, r, x, y, z;
  const ll template_array_size = 1e6 + 1851;
  ll ar[template_array_size];
  ll br[template_array_size];
  ll cr[template_array_size];
  string s, t;
  void solve() {
    int n, m;
    cin >> n >> m;
    vi a(n);
    re(a);
    vector<string> s(n);
    vi ans(m);
    re(s);
    int best = -1e9;
    for (int i = 0; i < 1 << n; i++) {
      int current = 0;
      for (int j = 0; j < n; j++) {
        if (i & (1 << j))
          current -= a[j];
        else
          current += a[j];
      }
      vi bits(m);
      for (int j = 0; j < n; j++) {
        int x = ((i & (1 << j)) ? 1 : -1);
        for (int k = 0; k < m; k++) {
          if (s[j][k] == '1') bits[k] += x;
        }
      }
      vpii binds(m);
      for (int j = 0; j < m; j++) binds[j] = {bits[j], j};
      sort((binds).begin(), (binds).end());
      for (int j = 0; j < m; j++) current += binds[j].first * (j + 1);
      if (best < current) {
        best = current;
        for (int j = 0; j < m; j++) {
          ans[binds[j].second] = j + 1;
        }
      }
    }
    pc(ans);
  }
  int32_t main() {
    setIO();
    int t;
    cin >> t;
    for (int i = 0; i < t; i++) {
      solve();
    }
    return 0;
  }
  