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 G1360 {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	static StringTokenizer st;
	public static void main(String[]args)throws IOException {
		int t = readInt();
		while(t--!=0) {
			int n = readInt(); int m = readInt(); int a = readInt(); int b = readInt();
			if(n*a==m*b) {
				boolean works = true;
				int[][]array = new int[n][m];
				int mod = m;
				int rem = a;
				for(int i = 2; i<=49; i++) {
					while(true) {
						if(mod%i==0&rem%i==0) {
							mod/=i;
							rem/=i;
						}
						else {
							break;
						}
					}
				}
				for(int i = 0; i<n; i++) {
					for(int j = 0; j<m; j++) {
						if((i+j)%mod<rem) {
							array[i][j] = 1;
						}
					}
				}
				for(int i = 0; i<n; i++) {
					int count = 0;
					for(int j = 0; j<m; j++) {
						count+=array[i][j];
					}
					if(count!=a)works = false;
				}
				for(int j = 0; j<m; j++){
					int count = 0;
					for(int i = 0; i<n; i++) {
						count+=array[i][j];
					}
					if(count!=b)works = false;
				}
				if(works) {
					pr.println("YES");
					for(int i = 0; i<n; i++) {
						for(int j = 0; j<m; j++) {
							pr.print(array[i][j]);
						}
						pr.println();
					}
				}
				else {
					pr.println("NO");
				}
			}
			else {
				pr.println("NO");
			}
		}
		pr.close();
	}
	static String next () throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine().trim());
		return st.nextToken();
	}
	static long readLong () throws IOException {
		return Long.parseLong(next());
	}
	static int readInt () throws IOException {
		return Integer.parseInt(next());
	}
	static double readDouble () throws IOException {
		return Double.parseDouble(next());
	}
	static char readCharacter () throws IOException {
		return next().charAt(0);
	}
	static String readLine () throws IOException {
		return br.readLine().trim();
	}
}
