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_case();
  signed main() {
    cin.tie(0), cout.tie(0)->sync_with_stdio(0);
    int test;
    cin >> test;
    while (test--) {
      solve_case();
    }
  }
  const int N = 15, M = 1e4 + 5;
  int n, m, a[N], delta[M], p[M], res[M];
  vector<int> vec[N * 2];
  long long ans;
  string s[N];
  void solve_case() {
    cin >> n >> m;
    ans = -1;
    for (int i = 0; i < n; i++) cin >> a[i];
    for (int i = 0; i < n; i++) cin >> s[i];
    for (int mask = 0; mask < 1 << n; mask++) {
      fill(delta, delta + m, 0);
      long long cur = 0;
      for (int i = 0; i < n; i++) {
        int f = mask >> i & 1 ? 1 : -1;
        cur -= f * a[i];
        for (int j = 0; j < m; j++)
          if (s[i][j] == '1') delta[j] += f;
      }
      for (int i = 0; i < m; i++) vec[delta[i] + N].push_back(i);
      for (int i = 0, f = 1; i < N * 2; i++) {
        for (auto v : vec[i]) {
          cur += f * delta[v];
          p[v] = f++;
        }
        vec[i].clear();
      }
      if (cur > ans) {
        ans = cur;
        for (int i = 0; i < m; i++) res[i] = p[i];
      }
    }
    for (int i = 0; i < m; i++) cout << res[i] << ' ';
    cout << '\n';
  }
  