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 CodeForce {
 static ArrayList<Integer> inputarrlist(String[] str){
     ArrayList<Integer> arr=new ArrayList<>();
     for(int i=0;i<str.length;i++)
         arr.add(Integer.parseInt(str[i]));
     
     return arr;
 }
 static long[] inputarrlong(String[] str){
     long[] arr=new long[str.length];
     for(int i=0;i<str.length;i++)
         arr[i]=(Long.parseLong(str[i]));
     
     return arr;
 }
 
 static int[] inputarrint(String[] str){
     int[] arr=new int[str.length];
     for(int i=0;i<str.length;i++)
         arr[i]=Integer.parseInt(str[i]);
     
     return arr;
 }
 
 static long gcd(long a, long b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 
 
 static ArrayList<Long> allfactors(long n) 
    { 
        ArrayList<Long> a=new ArrayList<>();
        ArrayList<Long> b=new ArrayList<>();
        for (long i=1; i<=Math.sqrt(n); i++) 
        { 
            if (n%i==0) 
            { 
                
                if (n/i == i) 
                    a.add(i); 
       
                else 
                {
                    a.add(i);
                    b.add(n/i);
                }
            } 
        } 
        
        for(int i=b.size()-1;i>=0;i--){
            a.add(b.get(i));
        }
        
        return a;
    } 
 
    public static void main(String[] args) throws IOException {
        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t;
        //t=1;
        t=Integer.parseInt(br.readLine());
        while(t-->0){
           int[] arr=inputarrint(br.readLine().split(" "));
           
           int n=arr[0];
           int m=arr[1];
           int a=arr[2];
           int b=arr[3];
           
           if(n*a==b*m){
               System.out.println("YES");
               int[][] a1=new int[n][m];
               StringBuffer sb=new StringBuffer();
               for(int i=0;i<a;i++)
                   sb.append(1);
               
               for(int i=a;i<m;i++)
                   sb.append(0);
               StringBuffer temp;
               System.out.println(sb);
               for(int i=1;i<n;i++){
                   temp=new StringBuffer(sb.substring(m-a, m));
                           sb.delete(m-a, m);
                   //System.out.println(sb+" "+temp);
                  sb.insert(0,temp);
                   System.out.println(sb);
               }
           }
           else{
               System.out.println("NO");
           }
        }
}}