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
// Don't place your source in a package
import java.util.*;
import java.lang.*;
import java.io.*;

// Please name your class Main
public class Main {
	public static void main (String[] args) throws java.lang.Exception {
	    Scanner in = new Scanner(System.in);
		int T =in.nextInt();
		for(int t=0;t<T;t++){
			int n=in.nextInt();int m=in.nextInt();
			int a=in.nextInt();int b=in.nextInt();
			Solution s=new Solution();
			s.solution(n,m,a,b);
		}
	}

}

class Solution{
	public void solution(int r,int c,int a,int b){
		if(r*a!=c*b){
			System.out.println("NO");
			return;
		}
		int grid[][]=new int[r][c];
		int d=0;
		for(int i=0;i<r;i++){
			for(int j=0;j<a;j++){
				grid[i][(d)%c]=1;d++;
				d%=c;
			}
		}
		System.out.println("YES");
		print(grid);
	}
	public void print(int grid[][]){
		for(int i=0;i<grid.length;i++){
			StringBuilder str=new StringBuilder();
			for(int j=0;j<grid[0].length;j++){
				str.append(""+grid[i][j]);
			}
			System.out.println(str.toString());
		}
	}
}