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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.Set;
import java.util.SortedSet;
import java.util.TreeSet;

public class CF {

	private static List<Map<Long, Boolean>> dp;
	private static char[][] dpc[][][][];

	public static void main(String args[]) {
		Scanner input = new Scanner(System.in);
		int T = input.nextInt();
		Map<In, List<String>> map = new HashMap<>();
		for (int i = 1; i <= T; i++) {
			int n = input.nextInt();
			int m = input.nextInt();
			int a = input.nextInt();
			int b = input.nextInt();
			if (n * a != m * b) {
				System.out.println("NO");
				continue;
			}
			In in = new In(n, m, a, b);
			if (map.get(in) != null) {
				System.out.println("YES");
				for (int ii = 0; ii < n; ii++) {
					System.out.println(map.get(in).get(ii));
				}
				continue;
			}
			Map<Integer, Integer> col = new HashMap<>();
			for (int ii = 0; ii < m; ii++) {
				col.put(ii, b);
			}
			char[][] c = new char[n][m];
			int nextStart = 0;
			for (int ii = 0; ii < n; ii++) {
				int pom = a;
				int last = 0;
				for (int iii = 0; iii < m; iii++) {
					if (pom > 0 && col.get((iii + nextStart) % m) > 0) {
						c[ii][(iii + nextStart) % m] = '1';
						pom--;
						col.put((iii + nextStart) % m, col.get((iii + nextStart) % m) - 1);
						last = (iii + nextStart) % m;
					} else {
						c[ii][(iii + nextStart) % m] = '0';
					}
				}
				nextStart = (last + 1) % m;
			}
			List<String> res = new ArrayList<>();
			for (int ii = 0; ii < n; ii++) {
				StringBuilder sb = new StringBuilder();
				for (int iii = 0; iii < m; iii++) {
					sb.append(c[ii][iii]);
				}
				res.add(sb.toString());
			}
			map.put(in, res);

			System.out.println("YES");
			for (int ii = 0; ii < n; ii++) {
				System.out.println(map.get(in).get(ii));
			}
		}
	}

	private static class In {
		int n;
		int m;
		int a;
		int b;

		public In(int n, int m, int a, int b) {
			this.n = n;
			this.m = m;
			this.a = a;
			this.b = b;
		}

		@Override
		public boolean equals(Object o) {
			if (this == o) {
				return true;
			}
			if (o == null || getClass() != o.getClass()) {
				return false;
			}
			In in = (In) o;
			return n == in.n &&
					m == in.m &&
					a == in.a &&
					b == in.b;
		}

		@Override
		public int hashCode() {
			return Objects.hash(n, m, a, b);
		}
	}

}