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.*;
public class R644D3A {
 
	public static void main(String[] args) throws Exception{
 
		// TODO Auto-generated method stub
//		BufferedReader bf = new BufferedReader(new FileReader("input.txt"));
		
		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
// 		PrintWriter out = new PrintWriter("output.txt");
 		PrintWriter out = new PrintWriter(System.out);
 		
 		int t = Integer.parseInt(bf.readLine());
 		for(int i =0 ;i<t;i++){
 			StringTokenizer st = new StringTokenizer(bf.readLine());
 			
 			int n = Integer.parseInt(st.nextToken());
 			int m = Integer.parseInt(st.nextToken());
 			int a = Integer.parseInt(st.nextToken());
 			int b = Integer.parseInt(st.nextToken());
 			
 			if (a*n != m*b)
 				out.println("NO");
 			else{
 				out.println("YES");
 				int startindex = 0;
 				for(int j = 0;j<n;j++){
 					for(int k = 0;k<m;k++){
	 					if (startindex+a <=m){
		 					if (k >= startindex && k <startindex+a)
		 						out.print(1);
		 					else
		 						out.print(0);
	 					}
	 					else{
	 						if (k >= startindex || k < (startindex+a)%m)
	 							out.print(1);
	 						else
	 							out.print(0);
	 					}
 					}
 					out.println();
 	 				startindex+=a;
 	 				startindex = startindex%m;
 				}
 				
 			}
 			
 		}
 		
 		
 		
 		out.close();
 		
 		
 		
 		
	}
 
 }
	
 	
// 
////StringJoiner sj = new StringJoiner(" "); 
////sj.add(strings)
////sj.toString() gives string of those stuff w spaces or whatever that sequence is
//class BinaryIndexedTree 
//{  
//    // Max tree size 
//    final static int MAX = 1000005;      
//  
//    static int BITree[] = new int[MAX];     
//    /* n --> No. of elements present in input array.  
//    BITree[0..n] --> Array that represents Binary  
//                    Indexed Tree. 
//    arr[0..n-1] --> Input array for which prefix sum  
//                    is evaluated. */
//  
//    // Returns sum of arr[0..index]. This function  
//    // assumes that the array is preprocessed and  
//    // partial sums of array elements are stored  
//    // in BITree[]. 
//    int getSum(int index){ 
//        int sum = 0;
//        index = index + 1; 
//        while(index>0){ 
//            sum += BITree[index]; 
//            index -= index & (-index); 
//        } 
//        return sum; 
//    } 
//    public static void updateBIT(int n, int index, int val){ 
//        index = index + 1; 
//        while(index <= n){ 
//	        BITree[index] += val; 
//	        index += index & (-index); 
//        } 
//    } 
//    void constructBITree(int arr[], int n){ 
//        for(int i=1; i<=n; i++) 
//            BITree[i] = 0; 
//        for(int i = 0; i < n; i++) 
//            updateBIT(n, i, arr[i]); 
//    } 
//}
 	