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
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */



import java.util.Scanner;

/**
 *
 * @author Pieter
 */
public class F {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        StringBuilder sb = new StringBuilder("");

        int tests = sc.nextInt();

        for(int t = 0; t < tests; t++) {
            int n = sc.nextInt();
            int m = sc.nextInt();
            int a = sc.nextInt();
            int b = sc.nextInt();
            
            int[][] matrix = new int[n][m];
            
            if(m*b == n*a && b <= n && a <= m) {
                sb.append("YES\n");
                int startIndex = 0;
                
                for(int i = 0; i < n; i++) {
                    
                    int[] arr = new int[m];
                    
                    for(int j = 0; j < a; j++) {
                        int index = startIndex + j;
                        if(index >= m) index -= m;
                        arr[index] = 1;
                    }
                    
                    
                    for(int j : arr) {
                        sb.append(j);
                    }
                    sb.append("\n");
                    
                    startIndex = startIndex += a;
                    startIndex = startIndex % m;
                    if(startIndex < 0) startIndex += m;
                }
                
                
            } else {
                sb.append("NO\n");
            }
        }

        System.out.println(sb);
    }
}
