#include <bits/stdc++.h>
using namespace std;
void solve() {
  int n, m;
  cin >> n >> m;
  vector<long long int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  vector<string> s(n);
  for (int i = 0; i < n; i++) cin >> s[i];
  long long int sur = 0;
  vector<int> ans;
  for (int mask = 0; mask < (1 << (n - 1)); mask++) {
    int lo = 1, hi = m;
    int lo2 = 1, hi2 = m;
    vector<int> cnt(m, 0);
    vector<bool> stat(n);
    for (int i = 0; i < n; i++) {
      if (mask & (1 << i))
        stat[i] = true;
      else
        stat[i] = false;
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        if (s[i][j] == '1') {
          cnt[j] += (stat[i] ? 1 : -1);
        }
      }
    }
    set<pair<int, int>> temp1, temp2;
    vector<int> tempAns(m, -1), tempAns2(m, -1);
    for (int i = 0; i < m; i++) {
      if (cnt[i] > 0)
        temp1.insert(make_pair(-cnt[i], i));
      else if (cnt[i] < 0)
        temp2.insert(make_pair(cnt[i], i));
    }
    for (auto it : temp1) {
      int index = it.second;
      tempAns[index] = hi--;
      tempAns2[index] = lo2++;
    }
    for (auto it : temp2) {
      int index = it.second;
      tempAns[index] = lo++;
      tempAns2[index] = hi2--;
    }
    for (int i = 0; i < m; i++) {
      if (tempAns[i] == -1) {
        tempAns[i] = lo++;
        tempAns2[i] = lo2++;
      }
    }
    long long int checkSur = 0, checkSur2 = 0;
    for (int i = 0; i < n; i++) {
      long long int score = 0;
      long long int score2 = 0;
      for (int j = 0; j < m; j++) {
        if (s[i][j] == '1') {
          score += tempAns[j];
          score2 += tempAns2[j];
        }
      }
      checkSur += abs(a[i] - score);
      checkSur2 += abs(a[i] - score2);
    }
    if (checkSur > sur || mask == 0) {
      sur = checkSur;
      ans = move(tempAns);
    }
    if (checkSur2 > sur) {
      sur = checkSur2;
      ans = move(tempAns2);
    }
  }
  for (int i = 0; i < m; i++) {
    cout << ans[i] << ' ';
  }
  cout << '\n';
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}

### Prompt

Your challenge is to write 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 solve() {
  int n, m;
  cin >> n >> m;
  vector<long long int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  vector<string> s(n);
  for (int i = 0; i < n; i++) cin >> s[i];
  long long int sur = 0;
  vector<int> ans;
  for (int mask = 0; mask < (1 << (n - 1)); mask++) {
    int lo = 1, hi = m;
    int lo2 = 1, hi2 = m;
    vector<int> cnt(m, 0);
    vector<bool> stat(n);
    for (int i = 0; i < n; i++) {
      if (mask & (1 << i))
        stat[i] = true;
      else
        stat[i] = false;
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        if (s[i][j] == '1') {
          cnt[j] += (stat[i] ? 1 : -1);
        }
      }
    }
    set<pair<int, int>> temp1, temp2;
    vector<int> tempAns(m, -1), tempAns2(m, -1);
    for (int i = 0; i < m; i++) {
      if (cnt[i] > 0)
        temp1.insert(make_pair(-cnt[i], i));
      else if (cnt[i] < 0)
        temp2.insert(make_pair(cnt[i], i));
    }
    for (auto it : temp1) {
      int index = it.second;
      tempAns[index] = hi--;
      tempAns2[index] = lo2++;
    }
    for (auto it : temp2) {
      int index = it.second;
      tempAns[index] = lo++;
      tempAns2[index] = hi2--;
    }
    for (int i = 0; i < m; i++) {
      if (tempAns[i] == -1) {
        tempAns[i] = lo++;
        tempAns2[i] = lo2++;
      }
    }
    long long int checkSur = 0, checkSur2 = 0;
    for (int i = 0; i < n; i++) {
      long long int score = 0;
      long long int score2 = 0;
      for (int j = 0; j < m; j++) {
        if (s[i][j] == '1') {
          score += tempAns[j];
          score2 += tempAns2[j];
        }
      }
      checkSur += abs(a[i] - score);
      checkSur2 += abs(a[i] - score2);
    }
    if (checkSur > sur || mask == 0) {
      sur = checkSur;
      ans = move(tempAns);
    }
    if (checkSur2 > sur) {
      sur = checkSur2;
      ans = move(tempAns2);
    }
  }
  for (int i = 0; i < m; i++) {
    cout << ans[i] << ' ';
  }
  cout << '\n';
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}

```