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

public class Question4 {

	static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public int[] readArray(int n) throws IOException {
        	int[] temp =new int[n];
        	for(int i = 0;i < n;i++) {
        		temp[i] = nextInt();
        	}
        	return temp;
        	
        }
        
        public ArrayList<Integer> readList(int n) throws IOException {
        	ArrayList<Integer> list = new ArrayList<>();
        	for(int i = 0;i < n;i++)list.add(nextInt());
        	return list;
        }
        
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
	

	static Scanner sc = new Scanner(System.in);
	static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	
	static boolean bool = false;
	public static void main(String[] args) throws IOException {
		int t = sc.nextInt();
		for(int p = 0;p < t;p++) {
			solve(p);
		}
		bw.flush();
		bw.close();
		
	}
	
	public static void solve(int t) throws IOException {
		
		int n = sc.nextInt();
		int k = sc.nextInt();
		//for the get method
		ArrayList<Integer> alist[], blist[];
		alist =new ArrayList[n];
		blist = new ArrayList[n];
		
		for(int i = 0;i < n;i++) {
			alist[i] = new ArrayList<>();
			blist[i] = new ArrayList<>();
			
		}
		
		char[][] arr = new char[n][n];
		for(int i =0;i < n;i++)
			arr[i] = sc.next().toCharArray();
		//forming alist and blist for get
		for(int i = 0;i < n;i++) {
			for(int j = 0;j < n;j++) {
				if(i == j)continue;
				if(arr[i][j] == 'a')alist[i].add(j);
				else if(arr[i][j] == 'b')blist[i].add(j);
			}
		}
		
		for(int i = 0;i < n;i++) {
			for(int j = 0;j < n;j++) {
				if(j == i)continue;
				if(arr[i][j] == arr[j][i]) {
					printAns(new int[]{i, j}, k);
					return;
				}
			}
		}
		
		//if odd
		if(k % 2 == 1) {
			
			int i = 1;
			bw.write("YES\n");
			while(i <= k + 1) {
				bw.write(String.valueOf((i % 2)+ 1) + " ");
				i++;
			}
			bw.write("\n");
			return;
		}
		
		//k is even.. no two are the same.
		//4, 8, 12, etc..
		
		if( k % 4 == 0) {
			//bw.write("here\n");
			for(int i = 0;i < n;i++) {
				if(alist[i].isEmpty() || blist[i].isEmpty())continue;
				int p1 = 0, p2 = 0;
				for(Integer ix : alist[i]) {p1 = ix;break;}
				for(Integer ix : blist[i]) {p2 = ix;break;}
				printAns(new int[] {i, p1, i, p2}, k);
				return;
			}
			bw.write("NO\n");
			return;
		}
		
		//2, 6, 10. etc
		
		for(int i = 0;i < n;i++) {
			for(int j =0;j < n;j++) {
				if(i == j)continue;
				
				//for p
				int p = -1;
				char c = arr[i][j];
				if(c == 'a')p = get(j,alist);
				else p = get(j, blist);
				
				
				if(p != -1) {
					printAns(new int[]{i, j, p, j}, k);
					return;
				}
			}
		}

		bw.write("NO\n");
		return;
		
	}
	
	public static void printAns(int[] arr, int k) throws IOException{
		k++;
		bw.write("YES\n");
		for(int i = 0;i < k;i++)bw.write(String.valueOf(arr[i % arr.length] + 1) + " ");
		bw.write("\n");
	}
	
	public static int get(int i, ArrayList<Integer> list[]) {
			
		for(Integer ix : list[i])return ix;
		return -1;
	}
	
}