#include <bits/stdc++.h>
using namespace std;
const int maxn = 11;
const int maxm = 1e4 + 1;
int x[maxn];
int s[maxn][maxm];
pair<int, int> y[maxm];
int an[maxm];
int mx = 0;
void gen(int n, int m, int id, string &t) {
  if (id == n) {
    for (int j = 0; j < m; ++j) {
      y[j].first = 0;
      y[j].second = j;
    }
    long long cst = 0;
    for (int i = 0; i < n; ++i) {
      if (t[i] == '+')
        cst += (long long)x[i];
      else
        cst -= (long long)x[i];
      for (int j = 0; j < m; ++j) {
        if (s[i][j] != 1) continue;
        if (t[i] == '+')
          y[j].first--;
        else
          y[j].first++;
      }
    }
    sort(y, y + m);
    int a[maxm];
    for (int i = 0; i < m; ++i) {
      int id = y[i].second;
      a[id] = i + 1;
      cst += (long long)(i + 1) * (long long)y[i].first;
    }
    for (int i = 0; i < n; ++i) {
      long long sm = 0;
      for (int j = 0; j < m; ++j) {
        if (s[i][j] == 1) sm += a[j];
      }
      if (t[i] == '+' && sm > x[i]) return;
      if (t[i] == '-' && sm < x[i]) return;
    }
    if (cst > mx) {
      mx = cst;
      swap(a, an);
    }
    return;
  }
  t += '+';
  gen(n, m, id + 1, t);
  t.pop_back();
  t += '-';
  gen(n, m, id + 1, t);
  t.pop_back();
  return;
}
void solve() {
  int n, m;
  cin >> n >> m;
  mx = 0;
  for (int i = 0; i < n; ++i) {
    cin >> x[i];
  }
  for (int i = 0; i < n; ++i) {
    string ss;
    cin >> ss;
    for (int j = 0; j < m; ++j) {
      s[i][j] = (ss[j] == '1');
      an[j] = j + 1;
    }
  }
  string tmp = "";
  gen(n, m, 0, tmp);
  for (int i = 0; i < m; ++i) cout << an[i] << " ";
  cout << "\n";
  return;
}
int main() {
  int T;
  cin >> T;
  while (T--) solve();
}

### Prompt

Generate a CPP solution to 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 maxn = 11;
const int maxm = 1e4 + 1;
int x[maxn];
int s[maxn][maxm];
pair<int, int> y[maxm];
int an[maxm];
int mx = 0;
void gen(int n, int m, int id, string &t) {
  if (id == n) {
    for (int j = 0; j < m; ++j) {
      y[j].first = 0;
      y[j].second = j;
    }
    long long cst = 0;
    for (int i = 0; i < n; ++i) {
      if (t[i] == '+')
        cst += (long long)x[i];
      else
        cst -= (long long)x[i];
      for (int j = 0; j < m; ++j) {
        if (s[i][j] != 1) continue;
        if (t[i] == '+')
          y[j].first--;
        else
          y[j].first++;
      }
    }
    sort(y, y + m);
    int a[maxm];
    for (int i = 0; i < m; ++i) {
      int id = y[i].second;
      a[id] = i + 1;
      cst += (long long)(i + 1) * (long long)y[i].first;
    }
    for (int i = 0; i < n; ++i) {
      long long sm = 0;
      for (int j = 0; j < m; ++j) {
        if (s[i][j] == 1) sm += a[j];
      }
      if (t[i] == '+' && sm > x[i]) return;
      if (t[i] == '-' && sm < x[i]) return;
    }
    if (cst > mx) {
      mx = cst;
      swap(a, an);
    }
    return;
  }
  t += '+';
  gen(n, m, id + 1, t);
  t.pop_back();
  t += '-';
  gen(n, m, id + 1, t);
  t.pop_back();
  return;
}
void solve() {
  int n, m;
  cin >> n >> m;
  mx = 0;
  for (int i = 0; i < n; ++i) {
    cin >> x[i];
  }
  for (int i = 0; i < n; ++i) {
    string ss;
    cin >> ss;
    for (int j = 0; j < m; ++j) {
      s[i][j] = (ss[j] == '1');
      an[j] = j + 1;
    }
  }
  string tmp = "";
  gen(n, m, 0, tmp);
  for (int i = 0; i < m; ++i) cout << an[i] << " ";
  cout << "\n";
  return;
}
int main() {
  int T;
  cin >> T;
  while (T--) solve();
}

```