#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    int n, m;
    cin >> n >> m;
    long long exp[n];
    long long score[n];
    int tempscore[m];
    for (int i = 0; i < n; i++) {
      cin >> exp[i];
      score[i] = 0;
    }
    string answers[n];
    for (int i = 0; i < n; i++) {
      cin >> answers[i];
    }
    long long currVal = -1;
    long long bestVal = -1;
    int currPerm[m];
    int bestPerm[m];
    int maxmask = 1 << n;
    for (int mask = 0; mask < maxmask; mask++) {
      memset(tempscore, 0, sizeof(tempscore));
      for (int i = 0; i < n; i++) score[i] = 0;
      currVal = 0;
      for (int i = 0; i < n; i++) {
        if ((mask >> i) & 1) {
          for (int j = 0; j < m; j++) {
            tempscore[j] += answers[i][j] == '1';
          }
        } else {
          for (int j = 0; j < m; j++) {
            tempscore[j] -= answers[i][j] == '1';
          }
        }
      }
      vector<pair<int, int> > myVec;
      for (int j = 0; j < m; j++) {
        myVec.push_back({tempscore[j], j});
      }
      sort(myVec.begin(), myVec.end());
      for (int j = 0; j < m; j++) {
        currPerm[myVec[j].second] = j + 1;
        for (int i = 0; i < n; i++) {
          score[i] += (answers[i][myVec[j].second] == '1') * (j + 1);
        }
      }
      for (int i = 0; i < n; i++) {
        currVal += abs(score[i] - exp[i]);
      }
      if (currVal > bestVal) {
        bestVal = currVal;
        for (int j = 0; j < m; j++) {
          bestPerm[j] = currPerm[j];
        }
      }
    }
    for (int j = 0; j < m; j++) {
      cout << bestPerm[j] << " ";
    }
    cout << "\n";
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

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>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    int n, m;
    cin >> n >> m;
    long long exp[n];
    long long score[n];
    int tempscore[m];
    for (int i = 0; i < n; i++) {
      cin >> exp[i];
      score[i] = 0;
    }
    string answers[n];
    for (int i = 0; i < n; i++) {
      cin >> answers[i];
    }
    long long currVal = -1;
    long long bestVal = -1;
    int currPerm[m];
    int bestPerm[m];
    int maxmask = 1 << n;
    for (int mask = 0; mask < maxmask; mask++) {
      memset(tempscore, 0, sizeof(tempscore));
      for (int i = 0; i < n; i++) score[i] = 0;
      currVal = 0;
      for (int i = 0; i < n; i++) {
        if ((mask >> i) & 1) {
          for (int j = 0; j < m; j++) {
            tempscore[j] += answers[i][j] == '1';
          }
        } else {
          for (int j = 0; j < m; j++) {
            tempscore[j] -= answers[i][j] == '1';
          }
        }
      }
      vector<pair<int, int> > myVec;
      for (int j = 0; j < m; j++) {
        myVec.push_back({tempscore[j], j});
      }
      sort(myVec.begin(), myVec.end());
      for (int j = 0; j < m; j++) {
        currPerm[myVec[j].second] = j + 1;
        for (int i = 0; i < n; i++) {
          score[i] += (answers[i][myVec[j].second] == '1') * (j + 1);
        }
      }
      for (int i = 0; i < n; i++) {
        currVal += abs(score[i] - exp[i]);
      }
      if (currVal > bestVal) {
        bestVal = currVal;
        for (int j = 0; j < m; j++) {
          bestPerm[j] = currPerm[j];
        }
      }
    }
    for (int j = 0; j < m; j++) {
      cout << bestPerm[j] << " ";
    }
    cout << "\n";
  }
}

```