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.*;

public class CF1622E extends PrintWriter {
	CF1622E() { super(System.out); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1622E o = new CF1622E(); o.main(); o.flush();
	}

	void main() {
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int m = sc.nextInt();
			int[] xx = new int[n];
			for (int i = 0; i < n; i++)
				xx[i] = sc.nextInt();
			byte[][] ss = new byte[n][];
			for (int i = 0; i < n; i++)
				ss[i] = sc.next().getBytes();
			int[] kk = new int[m];
			int[] hh = new int[m];
			for (int h = 0; h < m; h++)
				hh[h] = h;
			long w_ = Long.MIN_VALUE;
			int[] hh_ = null;
			for (int b = 0; b < 1 << n; b++) {
				long w = 0;
				for (int i = 0; i < n; i++)
					if ((b & 1 << i) != 0)
						w -= xx[i];
					else
						w += xx[i];
				Arrays.fill(kk, 0);
				for (int h = 0; h < m; h++)
					for (int i = 0; i < n; i++) {
						if (ss[i][h] == '0')
							continue;
						if ((b & 1 << i) != 0)
							kk[h]++;
						else
							kk[h]--;
					}
				hh = Arrays.stream(hh).boxed().sorted((h1, h2) -> kk[h1] - kk[h2]).mapToInt($->$).toArray();
				for (int h = 0; h < m; h++)
					w += kk[hh[h]] * (h + 1);
				if (w_ < w) {
					w_ = w;
					hh_ = hh;
				}
			}
			int[] pp = new int[m];
			for (int h = 0; h < m; h++)
				pp[hh_[h]] = h + 1;
			for (int h = 0; h < m; h++)
				print(pp[h] + " ");
			println();
		}
	}
}
