#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353;
const int N = 1e5 + 10;
const long long INF = 1e15 + 7;
void solve() {
  long long n, m;
  cin >> n >> m;
  vector<long long> v(n);
  for (auto& x : v) cin >> x;
  vector<string> s(n);
  for (auto& x : s) cin >> x;
  long long nax = 0;
  vector<long long> ans(m, 0);
  for (int i = 0; i < (1 << n); i++) {
    vector<long long> cnt(m, 0);
    vector<long long> res(m, 0);
    vector<int> flag(n, -1);
    for (int j = 0; j < n; j++) {
      if (i & (1 << j)) flag[j] = 1;
    }
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < m; k++) {
        if (s[j][k] == '1') cnt[k] += flag[j];
      }
    }
    vector<pair<long long, long long> > temp;
    for (int j = 0; j < m; j++) temp.push_back({cnt[j], j});
    sort(temp.begin(), temp.end());
    long long num = 1;
    for (auto j : temp) {
      res[j.second] = num;
      num++;
    }
    long long curr = 0;
    for (int j = 0; j < n; j++) {
      long long now = 0;
      for (int k = 0; k < m; k++) {
        if (s[j][k] == '1') now += res[k];
      }
      curr += abs(now - v[j]);
    }
    if (curr >= nax) {
      nax = curr;
      ans = res;
    }
  }
  for (auto i : ans) cout << i << " ";
  cout << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tests = 1;
  cin >> tests;
  while (tests--) {
    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;
const int mod = 998244353;
const int N = 1e5 + 10;
const long long INF = 1e15 + 7;
void solve() {
  long long n, m;
  cin >> n >> m;
  vector<long long> v(n);
  for (auto& x : v) cin >> x;
  vector<string> s(n);
  for (auto& x : s) cin >> x;
  long long nax = 0;
  vector<long long> ans(m, 0);
  for (int i = 0; i < (1 << n); i++) {
    vector<long long> cnt(m, 0);
    vector<long long> res(m, 0);
    vector<int> flag(n, -1);
    for (int j = 0; j < n; j++) {
      if (i & (1 << j)) flag[j] = 1;
    }
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < m; k++) {
        if (s[j][k] == '1') cnt[k] += flag[j];
      }
    }
    vector<pair<long long, long long> > temp;
    for (int j = 0; j < m; j++) temp.push_back({cnt[j], j});
    sort(temp.begin(), temp.end());
    long long num = 1;
    for (auto j : temp) {
      res[j.second] = num;
      num++;
    }
    long long curr = 0;
    for (int j = 0; j < n; j++) {
      long long now = 0;
      for (int k = 0; k < m; k++) {
        if (s[j][k] == '1') now += res[k];
      }
      curr += abs(now - v[j]);
    }
    if (curr >= nax) {
      nax = curr;
      ans = res;
    }
  }
  for (auto i : ans) cout << i << " ";
  cout << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tests = 1;
  cin >> tests;
  while (tests--) {
    solve();
  }
}

```