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 File {
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }

            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
	
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		
		
		
		int T = sc.nextInt();
		
		for (int t = 1; t <= T; t++) {
			int m = sc.nextInt(); // Rows 
			int n = sc.nextInt(); // Columns
			int a = sc.nextInt(); // 1's per row
			int b = sc.nextInt(); // 1's per column
			
			// Not possible.
			if (a*m != b*n) {
				out.println("NO");
				continue;
			}			
			
			int[][] matrix = new int[m][n];
			
			
			/*
			1 1 0 0
			0 1 1 0
			0 0 1 1
			1 0 0 1 
			*/
			
			int ones = m*a;
			int row = 0;
			int col = 0;
			
			while (ones > 0) {
				matrix[row][col] = 1;
				
				row = (row + 1) % m;
				col = (col + 1) % n;
				
				ones--;
				
				if (row == 0 && matrix[row][col] == 1) {
				    col = (col + 1) % n;
				}
			}
			
			
			/*
			for (int r = 0; r < m; r++) {
			    out.println(Arrays.toString(matrix[r]));
			}
			*/
			
			boolean isPossible = true;
			
			for (int r = 0; r < m; r++) {
				int rowCount = 0;
				
				for (int c = 0; c < n; c++) {
					if (matrix[r][c] == 1) rowCount++;
				}
				
				if (rowCount != a) {
					isPossible = false;
				}
			}
			for (int c = 0; c < n; c++) {
				int colCount = 0;
				
				for (int r = 0; r < m; r++) {
					if (matrix[r][c] == 1) colCount++;
				}
				
				if (colCount != b) {
					isPossible = false;
				}
			}
			
			if (isPossible) {
				out.println("YES");
				
				for (int r = 0; r < m; r++) {
					for (int c = 0; c < n; c++) {
						out.print(matrix[r][c]);
					}
					
					out.println();
				}
			}
			else {
				out.println("NO");
			}
		}
		
		
		
		
		out.close();
	}
}