#include <bits/stdc++.h>
using namespace std;
void read(vector<int64_t> &a);
void read(vector<string> &a);
void read(vector<vector<int64_t>> &a);
void read(vector<pair<int64_t, int64_t>> &a);
void solve() {
  int64_t n, m;
  cin >> n >> m;
  vector<int64_t> exp(n);
  read(exp);
  vector<string> mat(n);
  read(mat);
  int64_t best = 0;
  vector<int64_t> ret;
  for (int64_t x = 0; x < (1 << n); x++) {
    string b = std::bitset<32>(x).to_string();
    reverse(b.begin(), b.end());
    vector<pair<int64_t, int64_t>> order(m);
    for (int64_t i = 0; i < m; i++) {
      int64_t temp = 0;
      for (int64_t j = 0; j < n; j++) {
        if (b[j] == '1')
          temp += (mat[j][i] - '0');
        else
          temp -= (mat[j][i] - '0');
      }
      order[i] = {temp, i};
    }
    sort(order.begin(), order.end());
    reverse(order.begin(), order.end());
    int64_t ans = 0;
    for (int64_t i = 0; i < n; i++) {
      if (b[i] == '0')
        ans += exp[i];
      else
        ans -= exp[i];
    }
    int64_t tog = m;
    vector<int64_t> haha(m);
    for (auto x : order) {
      ans += (x.first) * (tog);
      haha[x.second] = tog;
      tog--;
    }
    if (ans >= best) {
      best = ans;
      ret = haha;
    }
  }
  for (int64_t i : ret) cout << i << " ";
  cout << endl;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int64_t t = 1;
  cin >> t;
  for (int64_t tt = 1; tt <= t; tt++) {
    solve();
  }
  return 0;
}
void read(vector<int64_t> &a) {
  for (int64_t i = 0; i < a.size(); i++) cin >> a[i];
}
void read(vector<string> &a) {
  for (int64_t i = 0; i < a.size(); i++) cin >> a[i];
}
void read(vector<vector<int64_t>> &a) {
  for (int64_t i = 0; i < a.size(); i++)
    for (int64_t j = 0; j < a[i].size(); j++) cin >> a[i][j];
}
void read(vector<pair<int64_t, int64_t>> &a) {
  for (int64_t i = 0; i < a.size(); i++) cin >> a[i].first >> a[i].second;
}

### Prompt

Your task is to create 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>
using namespace std;
void read(vector<int64_t> &a);
void read(vector<string> &a);
void read(vector<vector<int64_t>> &a);
void read(vector<pair<int64_t, int64_t>> &a);
void solve() {
  int64_t n, m;
  cin >> n >> m;
  vector<int64_t> exp(n);
  read(exp);
  vector<string> mat(n);
  read(mat);
  int64_t best = 0;
  vector<int64_t> ret;
  for (int64_t x = 0; x < (1 << n); x++) {
    string b = std::bitset<32>(x).to_string();
    reverse(b.begin(), b.end());
    vector<pair<int64_t, int64_t>> order(m);
    for (int64_t i = 0; i < m; i++) {
      int64_t temp = 0;
      for (int64_t j = 0; j < n; j++) {
        if (b[j] == '1')
          temp += (mat[j][i] - '0');
        else
          temp -= (mat[j][i] - '0');
      }
      order[i] = {temp, i};
    }
    sort(order.begin(), order.end());
    reverse(order.begin(), order.end());
    int64_t ans = 0;
    for (int64_t i = 0; i < n; i++) {
      if (b[i] == '0')
        ans += exp[i];
      else
        ans -= exp[i];
    }
    int64_t tog = m;
    vector<int64_t> haha(m);
    for (auto x : order) {
      ans += (x.first) * (tog);
      haha[x.second] = tog;
      tog--;
    }
    if (ans >= best) {
      best = ans;
      ret = haha;
    }
  }
  for (int64_t i : ret) cout << i << " ";
  cout << endl;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int64_t t = 1;
  cin >> t;
  for (int64_t tt = 1; tt <= t; tt++) {
    solve();
  }
  return 0;
}
void read(vector<int64_t> &a) {
  for (int64_t i = 0; i < a.size(); i++) cin >> a[i];
}
void read(vector<string> &a) {
  for (int64_t i = 0; i < a.size(); i++) cin >> a[i];
}
void read(vector<vector<int64_t>> &a) {
  for (int64_t i = 0; i < a.size(); i++)
    for (int64_t j = 0; j < a[i].size(); j++) cin >> a[i][j];
}
void read(vector<pair<int64_t, int64_t>> &a) {
  for (int64_t i = 0; i < a.size(); i++) cin >> a[i].first >> a[i].second;
}

```