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

// Imports
import java.util.*;
import java.io.*;

public class G1360 {

    /**
     * @param args the command line arguments
     * @throws IOException, FileNotFoundException 
     */
    public static void main(String[] args) throws IOException, FileNotFoundException {
        
        // TODO UNCOMMENT WHEN ALGORITHM CORRECT
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        
        /* BufferedReader f = new BufferedReader(new StringReader("5\n" +
"3 6 2 1\n" +
"2 2 2 1\n" +
"2 2 2 2\n" +
"4 4 2 2\n" +
"2 1 1 2")); */
        
        // TODO code application logic here
        int T = Integer.parseInt(f.readLine());
        
        for(int i = 0; i < T; i++) {
            StringTokenizer st = new StringTokenizer(f.readLine());
            int n = Integer.parseInt(st.nextToken());
            int m = Integer.parseInt(st.nextToken());
            int a = Integer.parseInt(st.nextToken());
            int b = Integer.parseInt(st.nextToken());
            
            if(n*a % m == 0 && n*a/m == b) {
                System.out.println("YES");
                
                int d = 1;
                while((n*d)%m != 0) {
                    d++;
                }
                
                for(int j = 0; j < n; j++) {
                    int[] arr = new int[m];
                    int rowcount = 0;
                    for(int k = j*d; k < j*d + m; k++) {
                        if(rowcount < a) {
                            arr[k%m] = 1;
                            rowcount++;
                        }
                        else {
                            arr[k%m] = 0;
                        }
                    }
                    
                    StringBuilder sb = new StringBuilder();
                    for(int k = 0; k < m; k++) {
                        sb.append(arr[k]);
                    }
                    System.out.println(sb);
                }
            }
            else {
                System.out.println("NO");
            }
        }
    }

}
