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.io.*;
import java.util.*;

public class Main {
	public static void main(String[] args) {
		InputReader in = new InputReader();
		StringBuilder out = new StringBuilder();

		int T = in.nextInt();
		while (T-- > 0) {
			int N = in.nextInt();
			int M = in.nextInt();
			int A = in.nextInt();
			int B = in.nextInt();
			if (N * A != M * B) {
				out.append("NO\n");
				continue;
			}
			int[][] mat = new int[N][M];
			int[] rem = new int[M];
			Arrays.fill(rem, B);
			int last = 0;
			for (int i = 0; i < N; i++) {
				int a = A;
				for (; a > 0; last = (last + 1) % M) {
					if (rem[last] > 0) {
						mat[i][last] = 1;
						rem[last]--;
						a--;
					}
				}
				if (a > 0) {
					throw new RuntimeException();
				}
			}
			for (int i = 0; i < M; i++) {
				if (rem[i] > 0) {
					throw new RuntimeException();
				}
			}
			out.append("YES\n");
			for (int i = 0; i < N; i++) {
				for (int j = 0; j < M; j++) {
					out.append(mat[i][j]);
				}
				out.append('\n');
			}
		}

		System.out.print(out);
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer st;

		public InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(nextLine());
			}
			return st.nextToken();
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return null;
		}

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