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
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
	
	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
	int t=Integer.parseInt(bf.readLine());
	StringBuilder sb=new StringBuilder();
	while(t-->0)
	{
	    String []s=bf.readLine().split(" ");
	    int n=Integer.parseInt(s[0]);
	    int m=Integer.parseInt(s[1]);
	    int a=Integer.parseInt(s[2]);
	    int b=Integer.parseInt(s[3]);
	    int p=0;
	    if(n*a==m*b)
	    {
	        sb.append("YES\n");
	        int f[][]=new int[n][m];
	        for(int i=0;i<n;i++)
	        {
	            int count=0;
	            for(int j=0;j<a;j++)
	            {
	                count++;
	                f[i][p]=1;
	                p++;
	                if(p>=m)
	                {
	                    p=0;
	                }
	               // if(count==a)
	               // {
	               //     break;
	               // }
	            }
	        }
	        for(int i=0;i<n;i++)
	        {
	            for(int j=0;j<m;j++)
	            {
	                sb.append(f[i][j]);
	            }
	            sb.append("\n");
	        }
	    }
	    else
	    {
	        sb.append("NO\n");
	    }
	}
	System.out.println(sb);
	}
}