#include <bits/stdc++.h>
using namespace std;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vc<vc<T>>;
template <class T>
void mkuni(vector<T> &v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
template <class T>
void print(T x, long long suc = 1) {
  cout << x;
  if (suc == 1)
    cout << '\n';
  else
    cout << ' ';
}
template <class T>
void print(const vector<T> &v, long long suc = 1) {
  for (long long i = 0; i < v.size(); i++)
    print(v[i], i == (long long)(v.size()) - 1 ? suc : 2);
}
long long x[20000];
char s[20][10004];
struct node {
  long long x, id;
  bool operator<(const node &b) const { return x < b.x; }
} a[20000];
long long anss[20000];
signed main() {
  long long t;
  cin >> t;
  while (t--) {
    long long n, m;
    cin >> n >> m;
    for (long long i = 1; i <= n; ++i) cin >> x[i];
    for (long long i = 1; i <= n; ++i) {
      cin >> (s[i] + 1);
    }
    long long ans = -1;
    for (long long i = 0; i < 1 << n; ++i) {
      long long res = 0;
      for (long long j = 1; j <= m; ++j) a[j].x = 0, a[j].id = j;
      for (long long j = 0; j < n; ++j) {
        if (!(i >> j & 1)) {
          res += x[j + 1];
          for (long long k = 1; k <= m; ++k) {
            if (s[j + 1][k] == '1') a[k].x -= 1;
          }
        } else {
          res -= x[j + 1];
          for (long long k = 1; k <= m; ++k) {
            if (s[j + 1][k] == '1') a[k].x += 1;
          }
        }
      }
      sort(a + 1, a + 1 + m);
      for (long long j = 1; j <= m; ++j) {
        res += j * a[j].x;
      }
      if (ans < res) {
        ans = res;
        for (long long j = 1; j <= m; ++j) {
          anss[a[j].id] = j;
        }
      }
    }
    for (long long i = 1; i <= m; ++i) cout << anss[i] << " ";
    cout << endl;
  }
}

### Prompt

Your task is to create 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;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vc<vc<T>>;
template <class T>
void mkuni(vector<T> &v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
template <class T>
void print(T x, long long suc = 1) {
  cout << x;
  if (suc == 1)
    cout << '\n';
  else
    cout << ' ';
}
template <class T>
void print(const vector<T> &v, long long suc = 1) {
  for (long long i = 0; i < v.size(); i++)
    print(v[i], i == (long long)(v.size()) - 1 ? suc : 2);
}
long long x[20000];
char s[20][10004];
struct node {
  long long x, id;
  bool operator<(const node &b) const { return x < b.x; }
} a[20000];
long long anss[20000];
signed main() {
  long long t;
  cin >> t;
  while (t--) {
    long long n, m;
    cin >> n >> m;
    for (long long i = 1; i <= n; ++i) cin >> x[i];
    for (long long i = 1; i <= n; ++i) {
      cin >> (s[i] + 1);
    }
    long long ans = -1;
    for (long long i = 0; i < 1 << n; ++i) {
      long long res = 0;
      for (long long j = 1; j <= m; ++j) a[j].x = 0, a[j].id = j;
      for (long long j = 0; j < n; ++j) {
        if (!(i >> j & 1)) {
          res += x[j + 1];
          for (long long k = 1; k <= m; ++k) {
            if (s[j + 1][k] == '1') a[k].x -= 1;
          }
        } else {
          res -= x[j + 1];
          for (long long k = 1; k <= m; ++k) {
            if (s[j + 1][k] == '1') a[k].x += 1;
          }
        }
      }
      sort(a + 1, a + 1 + m);
      for (long long j = 1; j <= m; ++j) {
        res += j * a[j].x;
      }
      if (ans < res) {
        ans = res;
        for (long long j = 1; j <= m; ++j) {
          anss[a[j].id] = j;
        }
      }
    }
    for (long long i = 1; i <= m; ++i) cout << anss[i] << " ";
    cout << endl;
  }
}

```