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.*;
import java.lang.*;

public class G {
    public static void main(String[] args) throws Exception {
        try {

            InputStreamReader isr = new InputStreamReader(System.in);
            BufferedReader br = new BufferedReader(isr);

            int test = Integer.parseInt(br.readLine());

            while (test-- > 0) {

                String str[] = br.readLine().split(" ");
                int n = Integer.parseInt(str[0]);
                int m = Integer.parseInt(str[1]);
                int a = Integer.parseInt(str[2]);
                int b = Integer.parseInt(str[3]);

                if (n * a == b * m) {
                    System.out.println("YES");
                    String s = "";
                    for (int i = 0; i < a; i++)
                        s+="1";

                    for (int i = a; i < m; i++)
                        s+="0";
                    System.out.println(s);
                    for (int i = 1; i < n; i++) {
                        s = s.substring(a) + s.substring(0,a);
                        System.out.println(s);
                    }

                } else {
                    System.out.println("NO");
                }


            }

        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}
