#include <bits/stdc++.h>
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
using namespace std;
template <typename T>
vector<vector<T>> vec2d(int n, int m, T v) {
  return vector<vector<T>>(n, vector<T>(m, v));
}
template <typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v) {
  return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}
template <typename T>
void print_vector(vector<T> v, char delimiter = ' ') {
  if (v.empty()) {
    cout << "\n";
    return;
  }
  for (int i = 0; i + 1 < v.size(); i++) cout << v[i] << delimiter;
  cout << v.back() << "\n";
}
using P = pair<int, int>;
using T = tuple<int, int, int>;
void solve() {
  int n, m;
  cin >> n >> m;
  vector<int> x(n);
  for (int i = 0; i < n; i++) cin >> x[i];
  vector<string> s(n);
  for (int i = 0; i < n; i++) cin >> s[i];
  vector<int> pcnt(1 << n);
  for (int i = 0; i < (1 << n); i++) {
    for (int j = 0; j < n; j++) {
      if (i & (1 << j)) pcnt[i]++;
    }
  }
  vector<int> cnt(1 << n);
  vector<int> tt(m);
  for (int i = 0; i < m; i++) {
    int t = 0;
    for (int j = 0; j < n; j++) {
      if (s[j][i] == '1') {
        t += 1 << j;
      }
    }
    tt[i] = t;
    cnt[t]++;
  }
  long long ans = -1;
  vector<int> ans_v(m);
  int all_student = (1 << n) - 1;
  for (int s = 0; s < (1 << n); s++) {
    int others = all_student - s;
    vector<P> vp;
    long long tmp = 0;
    for (int i = 0; i < n; i++) {
      if (s & (1 << i))
        tmp -= x[i];
      else
        tmp += x[i];
    }
    for (int i = 0; i < m; i++) {
      int t = tt[i];
      int correct_pos = pcnt[s & t];
      int correct_neg = pcnt[others & t];
      vp.push_back(P(correct_pos - correct_neg, i));
    }
    sort(vp.begin(), vp.end(), greater<P>());
    int cur = m;
    for (auto [cnt_pos, _] : vp) {
      tmp += cur * cnt_pos;
      cur -= 1;
    }
    if (chmax(ans, tmp)) {
      int cur = m;
      for (auto [cnt_pos, i] : vp) {
        ans_v[i] = cur;
        cur--;
      }
    }
    assert(cur == 0);
  }
  print_vector(ans_v);
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << setprecision(10) << fixed;
  int t;
  cin >> t;
  while (t--) solve();
}

### 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>
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
using namespace std;
template <typename T>
vector<vector<T>> vec2d(int n, int m, T v) {
  return vector<vector<T>>(n, vector<T>(m, v));
}
template <typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v) {
  return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}
template <typename T>
void print_vector(vector<T> v, char delimiter = ' ') {
  if (v.empty()) {
    cout << "\n";
    return;
  }
  for (int i = 0; i + 1 < v.size(); i++) cout << v[i] << delimiter;
  cout << v.back() << "\n";
}
using P = pair<int, int>;
using T = tuple<int, int, int>;
void solve() {
  int n, m;
  cin >> n >> m;
  vector<int> x(n);
  for (int i = 0; i < n; i++) cin >> x[i];
  vector<string> s(n);
  for (int i = 0; i < n; i++) cin >> s[i];
  vector<int> pcnt(1 << n);
  for (int i = 0; i < (1 << n); i++) {
    for (int j = 0; j < n; j++) {
      if (i & (1 << j)) pcnt[i]++;
    }
  }
  vector<int> cnt(1 << n);
  vector<int> tt(m);
  for (int i = 0; i < m; i++) {
    int t = 0;
    for (int j = 0; j < n; j++) {
      if (s[j][i] == '1') {
        t += 1 << j;
      }
    }
    tt[i] = t;
    cnt[t]++;
  }
  long long ans = -1;
  vector<int> ans_v(m);
  int all_student = (1 << n) - 1;
  for (int s = 0; s < (1 << n); s++) {
    int others = all_student - s;
    vector<P> vp;
    long long tmp = 0;
    for (int i = 0; i < n; i++) {
      if (s & (1 << i))
        tmp -= x[i];
      else
        tmp += x[i];
    }
    for (int i = 0; i < m; i++) {
      int t = tt[i];
      int correct_pos = pcnt[s & t];
      int correct_neg = pcnt[others & t];
      vp.push_back(P(correct_pos - correct_neg, i));
    }
    sort(vp.begin(), vp.end(), greater<P>());
    int cur = m;
    for (auto [cnt_pos, _] : vp) {
      tmp += cur * cnt_pos;
      cur -= 1;
    }
    if (chmax(ans, tmp)) {
      int cur = m;
      for (auto [cnt_pos, i] : vp) {
        ans_v[i] = cur;
        cur--;
      }
    }
    assert(cur == 0);
  }
  print_vector(ans_v);
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << setprecision(10) << fixed;
  int t;
  cin >> t;
  while (t--) solve();
}

```