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 
import java.io.*;
import java.util.*;

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////                                                                                                               /////////
////////                                                                                                               /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMMMM      MMMMMM      OOO      OOO        SSSS   SSS     EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEE           MMMM MMM  MMM MMMM    OOO          OOO    SSSS       SSS   EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM  MMMMMM  MMMM   OOO            OOO   SSSS             EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM  OOO              OOO   SSSSSSS         EEEEE          /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO      SSSSSS       EEEEEEEEEEE    /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO         SSSSSSS   EEEEEEEEEEE    /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM   OOO            OOO              SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM    OOO          OOO     SSS       SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM      OOO      OOO        SSS    SSSS    EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////                                                                                                               /////////
////////                                                                                                               /////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////


public class global18 {
    static char[][] all;
    static int[] a;
    static int n, m;


    static int solve(int msk) {
        int[] val = new int[n];
        int res = 0;
        for (int i = 0; i < n; i++) {
            if ((msk & 1 << i) != 0) {
                res += a[i];
                val[i] = -1;
            } else {
                res -= a[i];
                val[i] = 1;
            }
        }
        Integer[] vals = new Integer[m];
        for (int i = 0; i < m; i++)
            vals[i] = 0;
        for (int j = 0; j < n; j++) {
            for (int i = 0; i < m; i++) {
                if (all[j][i] == '1')
                    vals[i] += val[j];
            }
        }
        Arrays.sort(vals);

        for (int i = 0; i < m; i++)
            res += (i + 1) * vals[i];
        return res;
    }

    static int[] Gen(int msk) {
        int[] val = new int[n];
        for (int i = 0; i < n; i++) {
            if ((msk & 1 << i) != 0)
                val[i] = -1;
            else val[i] = 1;
        }
        Integer[] vals = new Integer[m];
        Integer[] ids = new Integer[m];
        for (int i = 0; i < m; i++) {
            vals[i] = 0;
            ids[i] = i;
        }
        for (int j = 0; j < n; j++) {
            for (int i = 0; i < m; i++) {
                if (all[j][i] == '1')
                    vals[i] += val[j];
            }
        }
        Arrays.sort(ids, (x, y) -> vals[x] - vals[y]);
        int[] res = new int[m];
        for (int i = 0; i < m; i++)
            res[ids[i]] = i + 1;
        return res;
    }


    public static void main(String[] args) throws IOException {

        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int t = sc.nextInt();
        while (t-- > 0) {
            n = sc.nextInt();
            m = sc.nextInt();
            a = sc.nextIntArr(n);
            int mAns = 0;
            int allans = 0;
            all = new char[n][];
            for (int i = 0; i < all.length; i++) {
                all[i] = sc.next().toCharArray();
            }
            for (int msk = 0; msk < 1 << n; msk++) {
                int here = solve(msk);
                if (here > allans) {
                    allans = here;
                    mAns = msk;
                }
            }

            int[] res = Gen(mAns);

            for (int x : res)
                pw.print(x + " ");
            pw.println();


        }

        pw.flush();

    }


    static class Scanner {
        BufferedReader br;
        StringTokenizer st;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader f) {
            br = new BufferedReader(f);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public int[] nextIntArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = Integer.parseInt(next());
            }
            return arr;
        }

    }

}