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 ABMatrix {

	// https://codeforces.com/contest/1360/problem/G
	
	// TLE idk why
	public static void main(String[] args) throws IOException, FileNotFoundException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		//BufferedReader in = new BufferedReader(new FileReader("ABMatrix"));

		StringBuilder s = new StringBuilder();
		int t = Integer.parseInt(in.readLine()); 
		for (int j=0; j<t; j++) {
			StringTokenizer st = new StringTokenizer(in.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 > m || b > n) {
				s.append("NO\n");
			}
			else if (a*n != b*m) {
				s.append("NO\n");
			}
			else {
				int cur_index=0;
				int[][] arr = new int[n][m];
				for (int i=0; i<n; i++) {
					for (int k=0; k<a; k++) {
						arr[i][cur_index] = 1;
						cur_index++;
						if (cur_index == m) cur_index = 0;
					}
				}
				s.append("YES\n");
				for (int i=0; i<n; i++) {
					for (int c=0; c<m; c++) {
						s.append(arr[i][c]);
					}
					s.append("\n");
				}
			}
		}
		System.out.print(s);
	}
}
/*

			int cur_row_count = 0;
			boolean works = true;
			
			int[] col_count = new int[m];
			for (int i=0; i<n; i++) {
				for (int c=0; c<m; c++) {
					if (col_count[c] == b) continue;
					else {
						arr[i][c] = 1;
						cur_row_count++;
						col_count[c]++;
						if (cur_row_count == a) break;
					}
				}
				if (cur_row_count != a) {
					works = false;
					break;
				}
				else {
					cur_row_count = 0;
				}
			}
			for (int i=0; i<m; i++) {
				if (col_count[i] != b) works = false;
			}
			if (works) {
				System.out.println("YES");
				for (int i=0; i<n; i++) {
					for (int c=0; c<m; c++) {
						System.out.print(arr[i][c]);
					}
					System.out.println();
				}
			}
			else System.out.println("NO");
*/
