#include <bits/stdc++.h>
using namespace std;
constexpr long long int MOD = 998244353;
constexpr double EPS = 1e-8;
long long int N, M, K, T, H, W, L, R;
void Solve() {
  cin >> N >> M;
  vector<int> v(N);
  for (int i = 0; i < N; i++) {
    cin >> v[i];
  }
  vector<string> s(N);
  for (auto& i : s) cin >> i;
  int score = -1;
  vector<int> ans(M);
  for (int i = 0; i < 1 << N; i++) {
    vector<int> sum(N);
    vector<int> point(M);
    int csum = 0;
    vector<pair<int, int>> vp;
    for (int j = 0; j < M; j++) {
      int n = 0;
      for (int k = 0; k < N; k++) {
        if (s[k][j] == '1') {
          if (i >> k & 1) {
            n++;
          } else {
            n--;
          }
        }
      }
      vp.push_back({n, j});
    }
    sort(vp.begin(), vp.end());
    for (int j = 0; j < vp.size(); j++) {
      point[vp[j].second] = j + 1;
    }
    for (int j = 0; j < N; j++) {
      for (int k = 0; k < M; k++) {
        if (s[j][k] == '1') {
          sum[j] += point[k];
        }
      }
    }
    for (int j = 0; j < N; j++) {
      csum += abs(v[j] - sum[j]);
    }
    if (csum > score) {
      score = csum;
      ans = point;
    }
  }
  for (auto i : ans) cout << i << " ";
  cout << endl;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  T = 1;
  cin >> T;
  while (T--) {
    Solve();
  }
}

### Prompt

Create a solution in Cpp for 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;
constexpr long long int MOD = 998244353;
constexpr double EPS = 1e-8;
long long int N, M, K, T, H, W, L, R;
void Solve() {
  cin >> N >> M;
  vector<int> v(N);
  for (int i = 0; i < N; i++) {
    cin >> v[i];
  }
  vector<string> s(N);
  for (auto& i : s) cin >> i;
  int score = -1;
  vector<int> ans(M);
  for (int i = 0; i < 1 << N; i++) {
    vector<int> sum(N);
    vector<int> point(M);
    int csum = 0;
    vector<pair<int, int>> vp;
    for (int j = 0; j < M; j++) {
      int n = 0;
      for (int k = 0; k < N; k++) {
        if (s[k][j] == '1') {
          if (i >> k & 1) {
            n++;
          } else {
            n--;
          }
        }
      }
      vp.push_back({n, j});
    }
    sort(vp.begin(), vp.end());
    for (int j = 0; j < vp.size(); j++) {
      point[vp[j].second] = j + 1;
    }
    for (int j = 0; j < N; j++) {
      for (int k = 0; k < M; k++) {
        if (s[j][k] == '1') {
          sum[j] += point[k];
        }
      }
    }
    for (int j = 0; j < N; j++) {
      csum += abs(v[j] - sum[j]);
    }
    if (csum > score) {
      score = csum;
      ans = point;
    }
  }
  for (auto i : ans) cout << i << " ";
  cout << endl;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  T = 1;
  cin >> T;
  while (T--) {
    Solve();
  }
}

```