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.util.*;
import java.io.*;
public class Solution {
    public static void main(String args[] ) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int t=Integer.parseInt(br.readLine());
        while(t-->0)
        {
            String mystr[]=br.readLine().split(" ");
            int m=Integer.parseInt(mystr[1]);
           int n=Integer.parseInt(mystr[0]);
           int a=Integer.parseInt(mystr[2]);
           int b=Integer.parseInt(mystr[3]);
           if(n*a==m*b)
           {
               bw.write("YES\n");
               char ch[][]=new char[n][m];
               for(int x=0;x<n;x++)
               Arrays.fill(ch[x],'0');
               int i=0,j=0;
               while(j<m)
               {
                   for(int k=i;k<i+b;k++)
                   {
                       ch[k%n][j]='1';
                   }
                   i=i+b;
                   j++;
               }
               for(int x=0;x<n;x++)
               {
                   for(int y=0;y<m;y++)
                   {
                       bw.write(ch[x][y]+"");
                   }
                   bw.newLine();
               }
               
           }
           else
           {
               bw.write("NO\n");
           }
          
        }
         bw.close();
    }
}