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 MAX = 1e4 + 10;
  const int MOD = 998244353;
  int x[11], p[MAX], q[MAX], ret[MAX];
  char s[11][MAX];
  int main() {
    int T;
    cin >> T;
    while (T--) {
      int n, m;
      scanf("%d%d", &n, &m);
      for (int i = 0; i < n; i++) scanf("%d", x + i);
      for (int i = 0; i < n; i++) scanf("%s", s[i] + 1);
      long long ans = 0;
      for (int i = 0; i < (1 << n); i++) {
        for (int j = 1; j <= m; j++) p[j] = 0;
        for (int j = 1; j <= m; j++) q[j] = j;
        long long sum = 0;
        for (int j = 0; j < n; j++) {
          int tag = ((1 << j) & i) ? 1 : -1;
          sum -= tag * x[j];
          for (int k = 1; k <= m; k++) {
            if (s[j][k] == '0') continue;
            p[k] += tag;
          }
        }
        sort(q + 1, q + m + 1, [](int x, int y) { return p[x] < p[y]; });
        for (int j = 1; j <= m; j++) sum += p[q[j]] * j;
        if (sum >= ans) {
          ans = sum;
          for (int j = 1; j <= m; j++) ret[q[j]] = j;
        }
      }
      for (int i = 1; i <= m; i++) printf("%d ", ret[i]);
      cout << endl;
    }
    return 0;
  }
  