Problem: Your friend Salem is Warawreh's brother and only loves math and geometry problems. He has solved plenty of such problems, but according to Warawreh, in order to graduate from university he has to solve more graph problems. Since Salem is not good with graphs he asked your help with the following problem.

<image>

You are given a complete directed graph with n vertices without self-loops. In other words, you have n vertices and each pair of vertices u and v (u ≠ v) has both directed edges (u, v) and (v, u).

Every directed edge of the graph is labeled with a single character: either 'a' or 'b' (edges (u, v) and (v, u) may have different labels).

You are also given an integer m > 0. You should find a path of length m such that the string obtained by writing out edges' labels when going along the path is a palindrome. The length of the path is the number of edges in it.

You can visit the same vertex and the same directed edge any number of times.

Input

The first line contains a single integer t (1 ≤ t ≤ 500) — the number of test cases.

The first line of each test case contains two integers n and m (2 ≤ n ≤ 1000; 1 ≤ m ≤ 10^{5}) — the number of vertices in the graph and desirable length of the palindrome.

Each of the next n lines contains n characters. The j-th character of the i-th line describes the character on the edge that is going from node i to node j.

Every character is either 'a' or 'b' if i ≠ j, or '*' if i = j, since the graph doesn't contain self-loops.

It's guaranteed that the sum of n over test cases doesn't exceed 1000 and the sum of m doesn't exceed 10^5.

Output

For each test case, if it is possible to find such path, print "YES" and the path itself as a sequence of m + 1 integers: indices of vertices in the path in the appropriate order. If there are several valid paths, print any of them.

Otherwise, (if there is no answer) print "NO".

Example

Input


5
3 1
*ba
b*b
ab*
3 3
*ba
b*b
ab*
3 4
*ba
b*b
ab*
4 6
*aaa
b*ba
ab*a
bba*
2 6
*a
b*


Output


YES
1 2
YES
2 1 3 2
YES
1 3 1 3 1
YES
1 2 1 3 4 1 4
NO

Note

The graph from the first three test cases is shown below:

<image>

In the first test case, the answer sequence is [1,2] which means that the path is:

$$$1 \xrightarrow{b} 2$$$

So the string that is obtained by the given path is b.

In the second test case, the answer sequence is [2,1,3,2] which means that the path is:

$$$2 \xrightarrow{b} 1 \xrightarrow{a} 3 \xrightarrow{b} 2$$$

So the string that is obtained by the given path is bab.

In the third test case, the answer sequence is [1,3,1,3,1] which means that the path is:

$$$1 \xrightarrow{a} 3 \xrightarrow{a} 1 \xrightarrow{a} 3 \xrightarrow{a} 1$$$

So the string that is obtained by the given path is aaaa.

The string obtained in the fourth test case is abaaba.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class EdE {
	static long[] mods = {1000000007, 998244353, 1000000009};
	static long mod = mods[0];
	public static MyScanner sc;
    public static PrintWriter out;
	public static void main(String[] omkar) throws Exception{
		// TODO Auto-generated method stub
 		sc = new MyScanner();
 		out = new PrintWriter(System.out);
 		int t = sc.nextInt();
 		for(int i = 0;i<t;i++){
//	 		String input1 = bf.readLine().trim();
//	 		String input2 = bf.readLine().trim();
//			COMPARING INTEGER OBJECTS U DO DOT EQUALS NOT ==
 			int n = sc.nextInt();
 			int m = sc.nextInt();
 			char[][] grid = new char[n+1][n+1];
 			for(int j = 0;j<n;j++){
 				String s = sc.next();
 				for(int k =0 ;k<n;k++){
 					grid[j+1][k+1] = s.charAt(k);
 				}
 			}
 			boolean found = false;
 			int index1 = -1;
 			int index2 = -1;
 			for(int j = 1;j<=n;j++){
 				for(int k = j+1;k<=n;k++){
 					if (grid[j][k] == grid[k][j]){
 						found = true;
 						index1 = j;
 						index2 = k;
 						break;
 					}
 				}
 				if (found)
 					break;
 			}
 			if (found){
 				out.println("YES");
 				for(int j = 0;j<=m;j++){
 					if (j%2 ==0)
 						out.print(index1 + " ");
 					else
 						out.print(index2 + " ");
 					
 				}
 				out.println();
 			}
 			else if (n == 2 && m%2 == 0){
 				out.println("NO");
 			}
 			else if (n == 2){
 				out.println("YES");
 				for(int j = 0;j<=m;j++){
 					if (j%2 ==0)
 						out.print(1 + " ");
 					else
 						out.print(2 + " ");
 					
 				}
 				out.println();
 			}
 			else if (m%2 == 1){
 				out.println("YES");
 				for(int j = 0;j<=m;j++){
 					if (j%2 ==0)
 						out.print(1 + " ");
 					else
 						out.print(2 + " ");
 					
 				}
 				out.println();
 			}
 			else{
 				out.println("YES");
 				ArrayList<Integer> outa = new ArrayList<Integer>();
 				ArrayList<Integer> outb = new ArrayList<Integer>();
 				for(int j = 2;j<=n;j++){
 					if (grid[1][j] == 'a')
 						outa.add(j);
 					else
 						outb.add(j);
 				}
 				if (!outa.isEmpty() && !outb.isEmpty()){
 					int ver = 1;
 					int index3 = outa.get(0);
 					int index4 = outb.get(0);
 					run( ver,  index3,  index4,  m);
 				}
 				else if (outa.isEmpty()){
 					int v1 = outb.get(0);
 					int v2 = outb.get(1);
 					if (grid[v1][v2] == 'b'){
 						int index3 = 1;
 						int index4 = v2;
 						int ver = v1;
 						run( ver,  index3,  index4,  m);
 					}
 					else{
 						int index3 = 1;
 						int index4 = v1;
 						int ver = v2;
 						run( ver,  index3,  index4,  m);
 					}
 				}
 				else{
 					int v1 = outa.get(0);
 					int v2 = outa.get(1);
 					if (grid[v1][v2] == 'a'){
 						int index3 = v2; //ver--> index3 is 'a', ver--> index4 is 'b'
 						int index4 = 1;
 						int ver = v1;
 						run( ver,  index3,  index4,  m);
 					}
 					else{
 						int index3 = v1;
 						int index4 = 1;
 						int ver = v2;
 						run( ver,  index3,  index4,  m);
 					}
 				}
 			}
 		}
	 		
 		out.close();
 	}
	public static void run(int ver, int index3, int index4, int m){
		if (m%4 == 0){
			for(int j = 0;j<=m;j++){
				if (j%4 == 0 || j%4 == 2){
					out.print(ver + " ");
				}
				else if (j%4 == 1){
					out.print(index3 + " ");
				}
				else{
					out.print(index4 + " ");
				}
			}
		}
		else{
			for(int j = 0;j<=m;j++){
				if (j%4 == 1 || j%4 == 3){
					out.print(ver + " ");
				}
				else if (j%4 == 0){
					out.print(index3 + " ");
				}
				else{
					out.print(index4 + " ");
				}
			}
		}
		out.println();
	}
	public static void sort(int[] array){
		ArrayList<Integer> copy = new ArrayList<>();
		for (int i : array)
			copy.add(i);
		Collections.sort(copy);
		for(int i = 0;i<array.length;i++)
			array[i] = copy.get(i);
	}
	static String[] readArrayString(int n){
		String[] array = new String[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.next();
		return array;
	}
	static int[] readArrayInt(int n){
    	int[] array = new int[n];
    	for(int j = 0;j<n;j++)
    		array[j] = sc.nextInt();
    	return array;
    }
	static int[] readArrayInt1(int n){
		int[] array = new int[n+1];
		for(int j = 1;j<=n;j++){
			array[j] = sc.nextInt();
		}
		return array;
	}
	static long[] readArrayLong(int n){
		long[] array = new long[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextLong();
		return array;
	}
	static double[] readArrayDouble(int n){
		double[] array = new double[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextDouble();
		return array;
	}
	static int minIndex(int[] array){
		int minValue = Integer.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(long[] array){
		long minValue = Long.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(double[] array){
		double minValue = Double.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static long power(long x, long y){
		if (y == 0)
			return 1;
		if (y%2 == 1)
			return (x*power(x, y-1))%mod;
		return power((x*x)%mod, y/2)%mod;
	}
	static void verdict(boolean a){
        out.println(a ? "YES" : "NO");
    }
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } 
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String nextLine() {
            String str = "";
            try{
                str = br.readLine();
            } 
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        
    }	
}

//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is