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.lang.*;
import java.io.*;
import java.math.*;
public final class CF
{
    public static void main(String[]args)throws IOException
	{
		//int K=(int)Math.pow(10,9)+7;
          FastReader ob=new FastReader();
          StringBuffer sb=new StringBuffer();
          int t=ob.nextInt();
          while(t-->0)
          {
                int n=ob.nextInt();
                int m=ob.nextInt();
                int a=ob.nextInt();
                int b=ob.nextInt();
                int ans[][]=new int[n][m];
                int x=0,y=0,f=0;
               for(int i=0;i<n;i++)
               {
                    for(int j=0;j<a;j++)
                    {
                         ans[i][y]=1;
                         y=(y+1)%m;
                    }
               }
               for(int i=0;i<n;i++)
               {
                    int c=0;
                    for(int j=0;j<m;j++)
                    {
                         if(ans[i][j]==1)
                         ++c;
                    }
                    if(c!=a)
                    {f=1;break;}
               }
               for(int i=0;i<m;i++)
               {
                    int c=0;
                    for(int j=0;j<n;j++)
                    {
                         if(ans[j][i]==1)
                         ++c;
                    }
                    if(c!=b)
                    {f=1;break;}
               }
               if(f==1)
               {
                    sb.append("NO\n");
                    continue;
               }
               sb.append("YES\n");
               for (int i = 0; i < n; i++)
               {
                    for (int j = 0; j < m; j++)
                    sb.append(ans[i][j]);
                    sb.append("\n");     
               }
               
          }
          System.out.println(sb);
	}
}
class Pair
{
	int x,y;
	Pair(int x,int y)
	{
		this.x=x;
		this.y=y;
	}
}
class PairComparator implements Comparator<Pair>
{
	public int compare(Pair a,Pair b)
	{
		return a.x-b.x;
	}
}
class FastReader {
    BufferedReader br;
    StringTokenizer st;
    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e)  {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
    public String nextLine()
    {
        String s="";
        try {
        s=br.readLine();
        } catch (IOException e)  {
                e.printStackTrace();
            }
        return s;
    }
    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong() {
        return Long.parseLong(next());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
}