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;
  long long a[14][10004];
  long long n, m;
  long long x[15];
  long long cn[10004];
  long long recn[45];
  long long pval;
  vector<pair<long long, long long> > chist;
  long long bore[300005];
  signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    long long t;
    cin >> t;
    while (t--) {
      cin >> n >> m;
      for (long long i = 1; i <= m; i++) cn[i] = 0;
      pval = 0;
      for (long long i = 0; i <= 45; i++) recn[i] = 0;
      for (long long i = 0; i <= n - 1; i++) {
        cin >> x[i];
        pval -= x[i];
      }
      for (long long i = 0; i <= n - 1; i++)
        for (long long j = 1; j <= m; j++) {
          char c;
          cin >> c;
          long long vl = 0;
          if (c == '1') vl = 1;
          a[i][j] = vl;
          cn[j] += vl;
        }
      for (long long j = 1; j <= m; j++) {
        ++recn[cn[j] + 15];
      }
      long long ans = (long long)-1e18;
      long long old = 0;
      long long mask;
      for (long long dimw = 0; dimw <= (1 << n) - 1; dimw++) {
        long long vl = dimw ^ (dimw >> 1);
        for (long long i = 0; i <= n - 1; i++)
          if ((old ^ vl) & (1 << i)) {
            long long mval = ((old & (1 << i)) > 0);
            if (mval) {
              pval -= x[i] * 2;
            }
            if (mval == 0) {
              mval = -1;
              pval += x[i] * 2;
            }
            for (long long j = 1; j <= m; j++)
              if (a[i][j]) {
                --recn[cn[j] + 15];
                cn[j] += mval * 2;
                ++recn[cn[j] + 15];
              }
          }
        long long res = pval;
        long long mole = m;
        for (long long i = 44; i >= 0; i--)
          if (recn[i]) {
            long long fole = i - 15;
            long long bon = recn[i] * (mole * 2 - recn[i] + 1) / 2;
            mole -= recn[i];
            res += fole * bon;
          }
        old = vl;
        if (res >= ans) {
          ans = res;
          mask = vl;
        }
      }
      chist.clear();
      for (long long j = 1; j <= m; j++) cn[j] = 0;
      for (long long i = 0; i <= n - 1; i++) {
        bool bl = (mask & (1 << i)) > 0;
        for (long long j = 1; j <= m; j++)
          if (a[i][j]) {
            if (bl)
              --cn[j];
            else
              ++cn[j];
          }
      }
      for (long long j = 1; j <= m; j++)
        chist.push_back(pair<long long, long long>(cn[j], j));
      sort(chist.begin(), chist.end());
      long long cnt = 0;
      for (auto cl : chist) {
        bore[cl.second] = ++cnt;
      }
      for (long long i = 1; i <= m; i++) cout << bore[i] << " ";
      cout << "\n";
    }
  }
  