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.Arrays;
import java.util.Scanner;

public class G {

	public static void main(String[] args) {
		Scanner file = new Scanner(System.in);
		int inputs = file.nextInt();
		while(inputs-->0) {
			int n = file.nextInt();
			int m = file.nextInt();
			int a = file.nextInt();
			int b = file.nextInt();
			if(a*n != b*m) {
				System.out.println("NO");
			}
			else {
				char[][] ans = new char[n][m];
				for(char[] c : ans)
					Arrays.fill(c, '0');
				int d = 1;
				while((d*n)%m!=0)
					d++;
				int offset = 0;
				for(int r = 0; r < n; r++) {
					for(int c = 0; c < a; c++) {
						ans[r][(c+offset)%m] = '1';
					}
					offset+=d;
				}
				System.out.println("YES");
				for(char[] c : ans)
					System.out.println(new String(c));
			}
		}
		file.close();
	}

}
