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.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scn= new Scanner(System.in);
		int t =scn.nextInt();
		while(t-->0){
			int n=scn.nextInt();
			int m =scn.nextInt();
			int a =scn.nextInt();
			int b =scn.nextInt();
			int val2 =gcd(a,b);
			int val1 =gcd(n,m);
			if(m/val1==a/val2 && n/val1==b/val2){
				System.out.println("YES");
				int [][]arr =new int[n][m];
				int cnt=0;
				for(int i=0;i<n;i++){
					for(int j=0;j<a;j++){
							arr[i][cnt%m]=1;
						  cnt++;
						  cnt=cnt%m;
						
					}
				}
				StringBuilder sb1 =new StringBuilder();
				for(int i=0;i<n;i++){
					for(int j=0;j<m;j++){
						sb1.append(arr[i][j]);
					}
					if(i!=n-1)
					sb1.append('\n');
					
				}
				System.out.println(sb1);
			}else{
				System.out.println("NO");
			}
		}
//			if(((m/val2)*(b/val1))%((n/val2)*(a/val1))==0){
//				System.out.println("YES");
//				int [][] arr =new int[n][m];
//				
//				int gap = m/a;
//				
//				for(int i=0;i<n;i++){
//					int cnt=0;
//					for(int j=i%gap;j<m&&cnt<a;j+=gap){
//						arr[i][j]=1;
//						cnt++;
//					}
//				}
//				StringBuilder sb1 =new StringBuilder();
//				for(int i=0;i<n;i++){
//					for(int j=0;j<m;j++){
//						sb1.append(arr[i][j]);
//					}
//					if(i!=n-1)
//					sb1.append('\n');
//					
//				}
//				System.out.println(sb1);
//			}else{
//				System.out.println("NO");
//			}
//		}

	}
	
	public static int gcd(int a ,int b){
		if(b==0){
			return a;
		}
		
		return gcd(b,a%b);
	}

}