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 i64 = long long;
  using u64 = unsigned long long;
  using u16 = unsigned short;
  using i16 = short;
  using u32 = unsigned int;
  using pii = std::pair<int, int>;
  using f64 = double;
  using f80 = long double;
  template <class T>
  using ve = std::vector<T>;
  template <class T>
  using fun = std::function<T>;
  template <class T1, class T2>
  using pr = std::pair<T1, T2>;
  template <class T>
  using pq = std::priority_queue<T>;
  template <class T>
  using lpq = std::priority_queue<T, std::vector<T>, std::greater<T>>;
  template <class T>
  using gpq = std::priority_queue<T, std::vector<T>, std::less<T>>;
  u32 def_cnt = 0;
  template <class T>
  void memset(int val, T& fir) {
    memset(fir, val, sizeof fir);
  }
  template <class T, class... args>
  void memset(int val, T& fir, args&... arg) {
    memset(fir, val, sizeof fir), memset(val, arg...);
  }
  template <class T>
  inline T read() {
    T x = 0;
    int f = 1;
    char ch = getchar();
    for (; !isdigit(ch); ch = getchar())
      if (ch == '-') f = -1;
    for (; isdigit(ch); ch = getchar()) x = x * 10 + ch - 48;
    return x * f;
  }
  template <class T>
  inline void read(T& x) {
    x = read<T>();
  }
  template <class T, class... Args>
  inline void read(T& fir, Args&... args) {
    read(fir), read(args...);
  }
  template <class T>
  inline void write(T x, char ch = '\n') {
    static int stk[32];
    if (x < 0) putchar('-'), x = -x;
    int top = 0;
    do stk[++top] = x % 10, x /= 10;
    while (x);
    while (top) putchar(stk[top--] + 48);
    putchar(ch);
  }
  template <class T, class... Args>
  inline void write(T fir, Args... args) {
    write(fir, ' '), write(args...);
  }
  inline void pre_work() { ; }
  inline void solv() {
    int n, m;
    read(n, m);
    ve<int> x(n);
    for (int i = 0; i < n; ++i) {
      x[i] = read<int>();
    }
    ve<std::string> s(n);
    for (int i = 0; i < n; ++i) {
      std::cin >> s[i];
    }
    ve<int> perm;
    int ret = -1;
    for (int mask = 0; mask < (1 << n); ++mask) {
      ve<int> c(m);
      int sum = 0;
      for (int i = 0; i < n; ++i) {
        if ((mask >> i) & 1) {
          sum += x[i];
          for (int j = 0; j < m; ++j) {
            if (s[i][j] == '1') --c[j];
          }
        } else {
          sum -= x[i];
          for (int j = 0; j < m; ++j) {
            if (s[i][j] == '1') ++c[j];
          }
        }
      }
      ve<int> ord(m);
      std::iota(ord.begin(), ord.end(), 0);
      std::sort(ord.begin(), ord.end(),
                [&](int x, int y) { return c[x] > c[y]; });
      ve<int> nper(m);
      for (int i = 0; i < m; ++i) {
        sum += (m - i) * c[ord[i]];
        nper[ord[i]] = m - i;
      }
      if (sum > ret) ret = sum, perm = nper;
    }
    for (auto it : perm) write(it, ' ');
    puts("");
  }
  signed main() {
    pre_work();
    int cza = read<int>();
    while (cza--) solv();
  }
  