#include <bits/stdc++.h>
using namespace std;
int n, m, a[10], c[10005];
char b[10][10005];
vector<int> g[10];
int id[10005];
bool cmp(int i1, int i2) { return c[i1] < c[i2]; }
int p[10005], p2[10005];
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; i++) {
      scanf("%d", &a[i]);
    }
    for (int i = 0; i < n; i++) {
      scanf("\n%s", b[i] + 1);
      g[i].clear();
      for (int j = 1; j <= m; j++) {
        if (b[i][j] == '1') {
          g[i].push_back(j);
        }
      }
    }
    long long ans = 0;
    for (int i = 1; i <= m; i++) id[i] = i;
    for (int i = 0; i < (1 << n); i++) {
      memset(c, 0, sizeof(c));
      for (int j = 0; j < n; j++) {
        for (int k : g[j]) {
          if (i & (1 << j))
            c[k]++;
          else
            c[k]--;
        }
      }
      sort(id + 1, id + 1 + m, cmp);
      for (int j = 1; j <= m; j++) {
        p[id[j]] = j;
      }
      long long sum = 0;
      for (int j = 0; j < n; j++) {
        int h = 0;
        for (int k : g[j]) {
          h += p[k];
        }
        sum += abs(a[j] - h);
      }
      if (sum >= ans) {
        ans = sum;
        for (int j = 1; j <= m; j++) {
          p2[j] = p[j];
        }
      }
    }
    for (int i = 1; i <= m; i++) {
      printf("%d ", p2[i]);
    }
    printf("\n");
  }
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
int n, m, a[10], c[10005];
char b[10][10005];
vector<int> g[10];
int id[10005];
bool cmp(int i1, int i2) { return c[i1] < c[i2]; }
int p[10005], p2[10005];
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; i++) {
      scanf("%d", &a[i]);
    }
    for (int i = 0; i < n; i++) {
      scanf("\n%s", b[i] + 1);
      g[i].clear();
      for (int j = 1; j <= m; j++) {
        if (b[i][j] == '1') {
          g[i].push_back(j);
        }
      }
    }
    long long ans = 0;
    for (int i = 1; i <= m; i++) id[i] = i;
    for (int i = 0; i < (1 << n); i++) {
      memset(c, 0, sizeof(c));
      for (int j = 0; j < n; j++) {
        for (int k : g[j]) {
          if (i & (1 << j))
            c[k]++;
          else
            c[k]--;
        }
      }
      sort(id + 1, id + 1 + m, cmp);
      for (int j = 1; j <= m; j++) {
        p[id[j]] = j;
      }
      long long sum = 0;
      for (int j = 0; j < n; j++) {
        int h = 0;
        for (int k : g[j]) {
          h += p[k];
        }
        sum += abs(a[j] - h);
      }
      if (sum >= ans) {
        ans = sum;
        for (int j = 1; j <= m; j++) {
          p2[j] = p[j];
        }
      }
    }
    for (int i = 1; i <= m; i++) {
      printf("%d ", p2[i]);
    }
    printf("\n");
  }
  return 0;
}

```