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.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;
public class G644 {

	public static void main(String[] args) {
		FastScanner in = new FastScanner(System.in);
		int T = in.nextInt();
		StringBuilder sb = new StringBuilder();
		
		while(T --> 0) {
			int N = in.nextInt();
			int M = in.nextInt();
			int A = in.nextInt();
			int B = in.nextInt();
			
			if(N * A != M * B) {
				sb.append("NO\n");
				continue;
			}
			else {
				sb.append("YES\n");
			}
			
			int[][] arr = new int[N][M];
			
			for(int i = 0; i < N; i++) {
				int offset = A * i;
				for(int j = 0; j < A; j++) {
					arr[i][(offset + j) % M] = 1;
				}
			}
			
			//System.out.println("Arr = ");
			for(int i = 0; i < N; i++) {
				for(int j = 0; j < M; j++) {
					//System.out.print(arr[i][j] + " ");
					sb.append(arr[i][j]);
					if(j == M-1) {
						sb.append("\n");
					}
				}
				
			}
		}
		
		System.out.print(sb);
	}
	
	/**
	 * Source: Matt Fontaine
	 */
	static class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int chars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
		}

		int read() {
			if (chars == -1)
				throw new InputMismatchException();
			if (curChar >= chars) {
				curChar = 0;
				try {
					chars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (chars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

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

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

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}

}
/*
5
3 6 2 1
2 2 2 1
2 2 2 2
4 4 2 2
2 1 1 2
outputCopy
YES
010001
100100
001010
NO
YES
11
11
YES
1100
1100
0011
0011
YES
1
1
*/