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.ArrayList;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {
	
	private static class Element implements Comparable<Element> {
		public int col;
		public int value;
		public Element(int col , int value) {
			this.col = col;
			this.value = value;
		}
		@Override
		public int compareTo(Element e) {
			return this.value - e.value;			
		}
	}
	
	private static boolean validate(int n , int m , int a , int b) {
		for (int i = 0;i < n;i ++) {
			int cnt = 0;
			for (int j = 0;j < m;j ++) {
				if (matrix[i][j] == '1') {
					cnt ++;
				}
			}
			if (cnt != a) {
				return false;
			}
		}
		for (int j = 0;j < m;j ++) {
			int cnt = 0;
			for (int i = 0;i < n;i ++) {
				if (matrix[i][j] == '1') {
					cnt ++;
				}
			}
			if (cnt != b) {
				return false;
			}
		}
		return true;
	}
	
	private static char[][] matrix = new char[100][100];
	
	public static void main(String[] args) {				
		
		Scanner scan = new Scanner(System.in);		
		int t = scan.nextInt() , i , j;
		while (t > 0) {
			int n = scan.nextInt() , m = scan.nextInt();
			int a = scan.nextInt() , b = scan.nextInt();
			PriorityQueue<Element> queue = new PriorityQueue<>();
			for (i = 0;i < 100;i ++) {
				for (j = 0;j < 100;j ++) {
					matrix[i][j] = '0';
				}
			}
			for (j = 0;j < m;j ++) {
				queue.add(new Element(j , 0));				
			}
			for (i = 0;i < n;i ++) {
				List<Element> nextList = new ArrayList<>();
				for (j = 0;j < a && !queue.isEmpty();j ++) {
					Element e = queue.poll();
					matrix[i][e.col] = '1';					
					e.value ++;					
					if (e.value + 1 <= b) {						
						nextList.add(e);						
					}
				}
				if (j < a) {					
					break;					
				}
				queue.addAll(nextList);
			}
			if (j == a && queue.isEmpty()) {
				if (validate(n , m , a , b)) {
					System.out.println("YES");					
					for (i = 0;i < n;i ++) {
						StringBuilder builder = new StringBuilder();
						for (j = 0;j < m;j ++) {
							builder.append(matrix[i][j]);
						}
						System.out.println(builder.toString());
					}
				} else {
					System.out.println("NO");
				}
			} else {
				System.out.println("NO");
			}
			t --;
		}
		
	}		
	
}
    





    
