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;
  template <class T>
  using vc = vector<T>;
  template <class T>
  using vvc = vc<vc<T>>;
  template <class T>
  void mkuni(vector<T> &v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
  }
  template <class T>
  void print(T x, long long suc = 1) {
    cout << x;
    if (suc == 1)
      cout << '\n';
    else
      cout << ' ';
  }
  template <class T>
  void print(const vector<T> &v, long long suc = 1) {
    for (long long i = 0; i < v.size(); i++)
      print(v[i], i == (long long)(v.size()) - 1 ? suc : 2);
  }
  long long x[20000];
  char s[20][10004];
  struct node {
    long long x, id;
    bool operator<(const node &b) const { return x < b.x; }
  } a[20000];
  long long anss[20000];
  signed main() {
    long long t;
    cin >> t;
    while (t--) {
      long long n, m;
      cin >> n >> m;
      for (long long i = 1; i <= n; ++i) cin >> x[i];
      for (long long i = 1; i <= n; ++i) {
        cin >> (s[i] + 1);
      }
      long long ans = -1;
      for (long long i = 0; i < 1 << n; ++i) {
        long long res = 0;
        for (long long j = 1; j <= m; ++j) a[j].x = 0, a[j].id = j;
        for (long long j = 0; j < n; ++j) {
          if (!(i >> j & 1)) {
            res += x[j + 1];
            for (long long k = 1; k <= m; ++k) {
              if (s[j + 1][k] == '1') a[k].x -= 1;
            }
          } else {
            res -= x[j + 1];
            for (long long k = 1; k <= m; ++k) {
              if (s[j + 1][k] == '1') a[k].x += 1;
            }
          }
        }
        sort(a + 1, a + 1 + m);
        for (long long j = 1; j <= m; ++j) {
          res += j * a[j].x;
        }
        if (ans < res) {
          ans = res;
          for (long long j = 1; j <= m; ++j) {
            anss[a[j].id] = j;
          }
        }
      }
      for (long long i = 1; i <= m; ++i) cout << anss[i] << " ";
      cout << endl;
    }
  }
  