#include <bits/stdc++.h>
std::mt19937 rng(
    (unsigned int)std::chrono::steady_clock::now().time_since_epoch().count());
using namespace std;
void solve(int ttt) {
  long long int n, m;
  cin >> n >> m;
  vector<long long int> x(n);
  for (long long int i = 0; i < n; i++) cin >> x[i];
  vector<vector<int> > a(n, vector<int>(m));
  for (long long int i = 0; i < n; i++) {
    string s;
    cin >> s;
    for (long long int j = 0; j < m; j++) {
      if (s[j] == '1')
        a[i][j] = 1;
      else
        a[i][j] = 0;
    }
  }
  long long int res = LLONG_MIN;
  vector<long long int> perm;
  for (int msk = 0; msk < (1 << n); msk++) {
    vector<int> coeff(m, 0);
    long long int curVal = 0;
    for (long long int i = 0; i < n; i++) {
      if (msk & (1 << i)) {
        curVal += x[i];
        for (long long int j = 0; j < m; j++) {
          if (a[i][j]) coeff[j]--;
        }
      } else {
        curVal -= x[i];
        for (long long int j = 0; j < m; j++) {
          if (a[i][j]) coeff[j]++;
        }
      }
    }
    vector<int> ind(m);
    iota(ind.begin(), ind.end(), 0);
    sort(ind.begin(), ind.end(),
         [&](int i, int j) { return coeff[i] < coeff[j]; });
    long long int c = 1;
    for (auto i : ind) {
      curVal += c * coeff[i];
      c++;
    }
    if (res < curVal) {
      res = curVal;
      vector<long long int> tmp(m);
      for (long long int i = 0; i < m; i++) {
        tmp[ind[i]] = i + 1;
      }
      swap(perm, tmp);
    }
  }
  for (long long int i = 0; i < m; i++) {
    cout << perm[i] << " ";
  }
  cout << "\n";
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int ttt;
  ttt = 1;
  cin >> ttt;
  for (long long int i = 0; i < ttt; i++) solve(i);
}

### Prompt

Generate a cpp solution to the following problem:

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 

### Response

```cpp
#include <bits/stdc++.h>
std::mt19937 rng(
    (unsigned int)std::chrono::steady_clock::now().time_since_epoch().count());
using namespace std;
void solve(int ttt) {
  long long int n, m;
  cin >> n >> m;
  vector<long long int> x(n);
  for (long long int i = 0; i < n; i++) cin >> x[i];
  vector<vector<int> > a(n, vector<int>(m));
  for (long long int i = 0; i < n; i++) {
    string s;
    cin >> s;
    for (long long int j = 0; j < m; j++) {
      if (s[j] == '1')
        a[i][j] = 1;
      else
        a[i][j] = 0;
    }
  }
  long long int res = LLONG_MIN;
  vector<long long int> perm;
  for (int msk = 0; msk < (1 << n); msk++) {
    vector<int> coeff(m, 0);
    long long int curVal = 0;
    for (long long int i = 0; i < n; i++) {
      if (msk & (1 << i)) {
        curVal += x[i];
        for (long long int j = 0; j < m; j++) {
          if (a[i][j]) coeff[j]--;
        }
      } else {
        curVal -= x[i];
        for (long long int j = 0; j < m; j++) {
          if (a[i][j]) coeff[j]++;
        }
      }
    }
    vector<int> ind(m);
    iota(ind.begin(), ind.end(), 0);
    sort(ind.begin(), ind.end(),
         [&](int i, int j) { return coeff[i] < coeff[j]; });
    long long int c = 1;
    for (auto i : ind) {
      curVal += c * coeff[i];
      c++;
    }
    if (res < curVal) {
      res = curVal;
      vector<long long int> tmp(m);
      for (long long int i = 0; i < m; i++) {
        tmp[ind[i]] = i + 1;
      }
      swap(perm, tmp);
    }
  }
  for (long long int i = 0; i < m; i++) {
    cout << perm[i] << " ";
  }
  cout << "\n";
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int ttt;
  ttt = 1;
  cin >> ttt;
  for (long long int i = 0; i < ttt; i++) solve(i);
}

```