#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tt;
  cin >> tt;
  while (tt--) {
    int n, m;
    cin >> n >> m;
    vector<int> x(n);
    for (int i = 0; i < n; i++) {
      cin >> x[i];
    }
    vector<vector<int>> a(n, vector<int>(m));
    for (int i = 0; i < n; i++) {
      string s;
      cin >> s;
      for (int j = 0; j < m; j++) {
        a[i][j] = (s[j] == '1');
      }
    }
    const long long inf = (long long)2e18L;
    long long res = -inf, msk = 0;
    for (int i = 0; i < (1 << n); i++) {
      long long z = 0;
      for (int j = 0; j < n; j++) {
        if ((1 << j) & i) {
          z -= x[j];
        } else {
          z += x[j];
        }
      }
      long long ans = z;
      vector<int> cnt(m, 0);
      for (int j = 0; j < n; j++) {
        if ((1 << j) & i) {
          for (int k = 0; k < m; k++) {
            if (a[j][k]) {
              cnt[k] += 1;
            }
          }
        } else {
          for (int k = 0; k < m; k++) {
            if (a[j][k]) {
              cnt[k] -= 1;
            }
          }
        }
      }
      sort(cnt.begin(), cnt.end());
      for (int j = 0; j < m; j++) {
        ans += cnt[j] * 1LL * (j + 1);
      }
      if (ans > res) {
        res = ans;
        msk = i;
      }
    }
    {
      vector<pair<int, int>> cnt(m);
      for (int i = 0; i < m; i++) {
        cnt[i].first = 0;
        cnt[i].second = i;
      }
      for (int j = 0; j < n; j++) {
        if ((1 << j) & msk) {
          for (int k = 0; k < m; k++) {
            if (a[j][k]) {
              cnt[k].first += 1;
            }
          }
        } else {
          for (int k = 0; k < m; k++) {
            if (a[j][k]) {
              cnt[k].first -= 1;
            }
          }
        }
      }
      sort(cnt.begin(), cnt.end());
      vector<int> p(m);
      for (int j = 0; j < m; j++) {
        p[cnt[j].second] = j + 1;
      }
      for (const auto& xx : p) {
        cout << xx << " ";
      }
      cout << '\n';
    }
  }
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tt;
  cin >> tt;
  while (tt--) {
    int n, m;
    cin >> n >> m;
    vector<int> x(n);
    for (int i = 0; i < n; i++) {
      cin >> x[i];
    }
    vector<vector<int>> a(n, vector<int>(m));
    for (int i = 0; i < n; i++) {
      string s;
      cin >> s;
      for (int j = 0; j < m; j++) {
        a[i][j] = (s[j] == '1');
      }
    }
    const long long inf = (long long)2e18L;
    long long res = -inf, msk = 0;
    for (int i = 0; i < (1 << n); i++) {
      long long z = 0;
      for (int j = 0; j < n; j++) {
        if ((1 << j) & i) {
          z -= x[j];
        } else {
          z += x[j];
        }
      }
      long long ans = z;
      vector<int> cnt(m, 0);
      for (int j = 0; j < n; j++) {
        if ((1 << j) & i) {
          for (int k = 0; k < m; k++) {
            if (a[j][k]) {
              cnt[k] += 1;
            }
          }
        } else {
          for (int k = 0; k < m; k++) {
            if (a[j][k]) {
              cnt[k] -= 1;
            }
          }
        }
      }
      sort(cnt.begin(), cnt.end());
      for (int j = 0; j < m; j++) {
        ans += cnt[j] * 1LL * (j + 1);
      }
      if (ans > res) {
        res = ans;
        msk = i;
      }
    }
    {
      vector<pair<int, int>> cnt(m);
      for (int i = 0; i < m; i++) {
        cnt[i].first = 0;
        cnt[i].second = i;
      }
      for (int j = 0; j < n; j++) {
        if ((1 << j) & msk) {
          for (int k = 0; k < m; k++) {
            if (a[j][k]) {
              cnt[k].first += 1;
            }
          }
        } else {
          for (int k = 0; k < m; k++) {
            if (a[j][k]) {
              cnt[k].first -= 1;
            }
          }
        }
      }
      sort(cnt.begin(), cnt.end());
      vector<int> p(m);
      for (int j = 0; j < m; j++) {
        p[cnt[j].second] = j + 1;
      }
      for (const auto& xx : p) {
        cout << xx << " ";
      }
      cout << '\n';
    }
  }
  return 0;
}

```