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 A
{
      public static void main(String ar[]) throws Exception
      {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            int t=Integer.parseInt(br.readLine());
            for(int r=0;r<t;r++)
            {
                  String s1[]=br.readLine().split(" ");
                  int n=Integer.parseInt(s1[0]);
                  int m=Integer.parseInt(s1[1]);
                  int a=Integer.parseInt(s1[2]);
                  int b=Integer.parseInt(s1[3]);
                  
                  if(n*a!=m*b)
                  {
                   System.out.println("NO");
                   continue;
                  }
                  else
                  {
                        int u=m/a;
                        StringBuffer sb=new StringBuffer();
                        sb.append("YES");
                        sb.append("\n");
                        int x[][]=new int[n][m];
                        for(int i=0;i<a;i++)
                         x[0][i]=1;
                        for(int i=0;i<n-1;i++)
                        {
                              for(int j=0;j<m;j++)
                              {
                                    if(x[i][j]==1)
                                     x[i+1][(j+a)%m]=1;
                              }
                        }
                        
                        for(int i=0;i<n;i++)
                        {
                          for(int j=0;j<m;j++)
                            sb.append(x[i][j]);
                          sb.append("\n");
                        }
                        System.out.print(sb);
                  }
            }
      }
}