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.Arrays;
import java.util.InputMismatchException;

public class E {
    public static void main(String[] args) {
        FastIO io = new FastIO();
        int t = io.nextInt();
        while (t-- > 0) {

            int n = io.nextInt();
            int m = io.nextInt();
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) arr[i] = io.nextInt();
            char[][] grid = new char[n][m];
            for (int i = 0; i < n; i++) grid[i] = io.next().toCharArray();
            long max = 0;
            int[] maxPer = new int[n];
            for (int i = 0; i < 1 << n; i++) {
                int[] finalValue = new int[m];
                Question[] count = new Question[m];
                for (int j = 0; j < m; j++) {
                    count[j] = new Question(0, j);
                    for (int st = 0; st < n; st++) {
                        if (grid[st][j] == '1') {
                            if (((i >> st) & 1) == 0) {
                                count[j].freq--;
                            } else count[j].freq++;
                        }
                    }
                }
                Arrays.sort(count, (a, b) -> a.freq - b.freq);
                for (int j = 0; j < m; j++) {
                    finalValue[count[j].ind] = j + 1;
                }
                long sum = 0;
                for (int st = 0; st < n; st++) {
                    int localSum = 0;
                    for (int j = 0; j < m; j++) {
                        if (grid[st][j] == '1') localSum += finalValue[j];
                    }
                    sum += Math.abs(localSum - arr[st]);
                }
                if (sum > max) {
                    max = sum;
                    maxPer = finalValue;
                }

            }
            for (int v : maxPer) {
                io.print(v + " ");
            }
            io.println();
        }

        io.flush();
    }


    static class Question {
        int freq, ind;

        public Question(int freq, int ind) {
            this.freq = freq;
            this.ind = ind;
        }
    }

    private static class FastIO extends PrintWriter {
        private InputStream stream;
        private byte[] buf = new byte[1 << 16];
        private int curChar, numChars;

        // standard input
        public FastIO() {
            this(System.in, System.out);
        }

        public FastIO(InputStream i, OutputStream o) {
            super(o);
            stream = i;
        }

        // file input
        public FastIO(String i, String o) throws IOException {
            super(new FileWriter(o));
            stream = new FileInputStream(i);
        }

        // throws InputMismatchException() if previously detected end of file
        private int nextByte() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars == -1) return -1; // end of file
            }
            return buf[curChar++];
        }

        // to read in entire lines, replace c <= ' '
        // with a function that checks whether c is a line break
        public String next() {
            int c;
            do {
                c = nextByte();
            } while (c <= ' ');
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = nextByte();
            } while (c > ' ');
            return res.toString();
        }

        public int nextInt() { // nextLong() would be implemented similarly
            int c;
            do {
                c = nextByte();
            } while (c <= ' ');
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = nextByte();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = 10 * res + c - '0';
                c = nextByte();
            } while (c > ' ');
            return res * sgn;
        }

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

}
