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 N = 12;
  const int M = 10005;
  const int lim = 200000;
  const int inf = 1e9;
  int T;
  int n, m;
  int x[N];
  char s[N][M];
  int cnt[M];
  int b[M];
  int ans[M];
  bool cmp(int i, int j) { return cnt[i] < cnt[j]; }
  int main() {
    scanf("%d", &T);
    while (T--) {
      scanf("%d%d", &n, &m);
      for (int i = 0; i <= n - 1; ++i) scanf("%d", &x[i]);
      for (int i = 0; i <= n - 1; ++i) scanf("%s", s[i]);
      int ret = -inf;
      for (int mask = 0; mask <= (1 << n) - 1; ++mask) {
        for (int j = 0; j <= m - 1; ++j) cnt[j] = 0;
        for (int i = 0; i <= n - 1; ++i) {
          for (int j = 0; j <= m - 1; ++j) {
            if (s[i][j] == '1') {
              if (mask & (1 << i))
                ++cnt[j];
              else
                --cnt[j];
            }
          }
        }
        for (int j = 0; j <= m - 1; ++j) b[j] = j;
        sort(b, b + m, cmp);
        int tmp = 0;
        for (int i = 0; i <= n - 1; ++i) {
          int r = 0;
          for (int j = 0; j <= m - 1; ++j) {
            if (s[i][b[j]] == '1') {
              r += j + 1;
            }
          }
          if (mask & (1 << i))
            tmp += r - x[i];
          else
            tmp -= r - x[i];
        }
        if (tmp > ret) {
          ret = tmp;
          for (int j = 0; j <= m - 1; ++j) ans[b[j]] = j + 1;
        }
      }
      for (int j = 0; j <= m - 1; ++j) printf("%d ", ans[j]);
      printf("\n");
    }
    return 0;
  }
  