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 {
    static PrintWriter out=new PrintWriter(System.out);
    
	public static void main (String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		String[] input=br.readLine().trim().split(" ");
		int numTestCases=Integer.parseInt(input[0]);
		while(numTestCases-->0){
		    input=br.readLine().trim().split(" ");
    	    int n=Integer.parseInt(input[0]);
    	    int m=Integer.parseInt(input[1]);
    	    int a=Integer.parseInt(input[2]);
    	    int b=Integer.parseInt(input[3]);
    	    printMatrix(n,m,a,b);
		}
		out.flush();
		out.close();
	}
	public static void printMatrix(int n,int m,int a,int b)
	{
	    if(n*a!=m*b)
	    {
	        out.println("NO");
	        return;
	    }
	    out.println("YES");
	    int[][] arr=new int[n][m];
	    int col=0;
	    for(int i=0;i<n;i++){
	        for(int j=0;j<a;j++){
	            arr[i][col]=1;
	            col=(col+1)%m;
	        }
	    }
	    for(int i=0;i<n;i++){
	        for(int j=0;j<m;j++){
	            out.print(arr[i][j]);
	        }
	        out.println();
	    }
	}
}