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 Main
{
    public static class AL<T> extends ArrayList<T> {};
    public static class HM<T,Integer> extends HashMap<T,T> {};
    public static class HS<T> extends HashSet<T> {};
    
    public static void main(String[] args) throws IOException 
	{
        FastReader fr=new FastReader();
        PrintWriter pr=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int t=fr.nxtInt();
        while(t-->0)
        {
            int n=fr.nxtInt(),m=fr.nxtInt(),a=fr.nxtInt(),b=fr.nxtInt();
            if(n*a==m*b)
            {
                pr.println("YES");
                String tmp=String.join("", Collections.nCopies(a, "1"))+String.join("0", Collections.nCopies(m-a+1, ""));
                int s=m-a;
                for(int i=0,j=0;i<n;i++,j=(j+s)%m)
                    pr.println(tmp.substring(m-j)+tmp.substring(0,m-j));
            }
            else pr.println("NO");
        }
		pr.flush();
		pr.close();
    }
    
    
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader(){br = new BufferedReader(new InputStreamReader(System.in));} 
  
        String nxt() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try{st=new StringTokenizer(br.readLine());} 
                catch (IOException  e){e.printStackTrace();} 
            } 
            return st.nextToken(); 
        } 
  
        int nxtInt(){return Integer.parseInt(nxt());} 
        long nxtLong(){return Long.parseLong(nxt());} 
        double nxtDoub(){return Double.parseDouble(nxt());} 
  
        String nxtLn() 
        { 
            String str = ""; 
            try{str = br.readLine();} 
            catch (IOException e){e.printStackTrace();} 
            return str; 
        } 
    }
}