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 = 1e4 + 5;
  int T, n, m, x, y;
  int ans = 0, All[N], Xi[N], id[N], P[N], who[N];
  char s[11][N];
  int sgn(int t, int x) {
    if (t == 0)
      return (-1) * x;
    else
      return x;
  }
  bool cmp(int x, int y) { return Xi[x] < Xi[y]; }
  void rmain() {
    cin >> n >> m;
    for (int i = 1; i <= n; ++i) scanf("%d", &All[i]);
    for (int i = 1; i <= n; ++i) scanf("%s", s[i] + 1);
    ans = -1;
    for (int i = 0; i < (1 << n); ++i) {
      for (int j = 1; j <= m; ++j) Xi[j] = 0;
      int res = 0;
      for (int j = 1; j <= n; ++j) {
        res -= sgn(((i >> (j - 1)) & 1), All[j]);
        for (int k = 1; k <= m; ++k) {
          Xi[k] += sgn(((i >> (j - 1)) & 1), s[j][k] - '0');
          id[k] = k;
        }
      }
      sort(id + 1, id + m + 1, cmp);
      for (int j = 1; j <= m; ++j) {
        res += Xi[id[j]] * j;
        who[id[j]] = j;
      }
      if (res >= ans) {
        ans = res;
        for (int j = 1; j <= m; ++j) P[j] = who[j];
      }
    }
    for (int i = 1; i <= m; ++i) printf("%d ", P[i]);
    puts("");
  }
  int main() {
    for (cin >> T; T--;) rmain();
  }
  