You are given four positive integers n, m, a, b (1 ≤ b ≤ n ≤ 50; 1 ≤ a ≤ m ≤ 50). Find any such rectangular matrix of size n × m that satisfies all of the following conditions:

  * each row of the matrix contains exactly a ones; 
  * each column of the matrix contains exactly b ones; 
  * all other elements are zeros. 



If the desired matrix does not exist, indicate this.

For example, for n=3, m=6, a=2, b=1, there exists a matrix satisfying the conditions above:

$$$ \begin{vmatrix} 0 & 1 & 0 & 0 & 0 & 1 \\\ 1 & 0 & 0 & 1 & 0 & 0 \\\ 0 & 0 & 1 & 0 & 1 & 0 \end{vmatrix} $$$

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t test cases follow.

Each test case is described by four positive integers n, m, a, b (1 ≤ b ≤ n ≤ 50; 1 ≤ a ≤ m ≤ 50), where n and m are the sizes of the matrix, and a and b are the number of ones for rows and columns, respectively.

Output

For each test case print:

  * "YES" (without quotes) and the required matrix (if there are several answers, print any) if it exists, or 
  * "NO" (without quotes) if it does not exist. 



To print the matrix n × m, print n rows, each of which consists of m numbers 0 or 1 describing a row of the matrix. Numbers must be printed without spaces.

Example

Input


5
3 6 2 1
2 2 2 1
2 2 2 2
4 4 2 2
2 1 1 2


Output


YES
010001
100100
001010
NO
YES
11
11
YES
1100
1100
0011
0011
YES
1
1
import java.io.*;
import java.util.*;

public class g {
	
	static PrintWriter out = new PrintWriter(System.out);

	static int n, m, a, b;
	static int[][] ans;
	
	public static void main(String[] args) throws IOException {
		FastScanner stdin = new FastScanner(System.in);
		
		int t = stdin.nextInt();
		
		for (int z = 1; z <= t; z++)
		{
			n = stdin.nextInt();
			m = stdin.nextInt();
			a = stdin.nextInt();
			b = stdin.nextInt();
			
			ans = new int[n][m];
			
			if (n*a != m*b)
				out.println("no");
			else
			{
				out.println("yes");
				for (int i = 0; i < n; i ++)
				{
					int section = (i*a)%m;
					for (int j = 0; j < a; j ++)
						ans[i][(section+j)%m] = 1;
					for (int j = 0; j < m; j ++)
						out.print(ans[i][j]);
					out.println();
				}
			}
		}
		
		out.flush();
	}
	
	static class FastScanner {
	    BufferedReader br;
	    StringTokenizer st;
		
	    public FastScanner(InputStream i) {
	        br = new BufferedReader(new InputStreamReader(i));
	        st = new StringTokenizer("");
	    }
				
	    public String next() throws IOException {
	        if(st.hasMoreTokens())
	            return st.nextToken();
	        else
	            st = new StringTokenizer(br.readLine());
	        return next();
	    }

	    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());
	    }
	 }
}
