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
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringBuffer sb = new StringBuffer();
		int t = Integer.parseInt(br.readLine());
		while(t-- > 0){
		    String s[] = (br.readLine()).split(" ");
		    int n = Integer.parseInt(s[0]);
		    int m = Integer.parseInt(s[1]);
		    int a = Integer.parseInt(s[2]);
		    int b = Integer.parseInt(s[3]);
		    if(n * a == m * b){
		        sb.append("YES\n");
		        StringBuilder ss = new StringBuilder();
		        for(int i = 0; i < m; i++){
		            if(i < a) ss.append("1");
		            else ss.append("0");
		        }
		        String st = ss.toString();
		        sb.append(st+"\n");
		        for(int i = 0; i < n - 1; i++){
		            String t1 = st.substring(st.length() - a, st.length());
		            String t2 = st.substring(0, st.length() - a);
		            st = t1.concat(t2);
		            sb.append(st+"\n");
		        }
		    }
		    else sb.append("NO\n");
		}
		System.out.println(sb);
	}
}
