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.io.PrintWriter;
import java.util.ArrayList;
import java.util.InputMismatchException;

public class E {

	public static void main(String[] args) throws Exception {
		// TODO Auto-generated method stub
		InputReader s = new InputReader(System.in);
		PrintWriter p = new PrintWriter(System.out);
		int t = s.nextInt();
		while (t-- > 0) {
			int n = s.nextInt();
			int m = s.nextInt();
			int a = s.nextInt();
			int b = s.nextInt();
			int[][] arr = new int[n][m];
			int temp = 0;
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < b; j++) {
					arr[temp % n][i] = 1;
					temp++;
				}
			}
			int flag = 0;
			for (int i = 0; i < n; i++) {
				temp = 0;
				for (int j = 0; j < m; j++) {
					if (arr[i][j] == 1)
						temp++;
				}
				if (temp != a) {
					p.println("NO");
					flag = 1;
					break;
				}
			}
//			p.println("YES");
//			for (int i = 0; i < n; i++) {
//				for (int j = 0; j < m; j++) {
//					p.print(arr[i][j] + " ");
//				}
//				p.println();
//			}
			if (flag == 0) {
				p.println("YES");
				for (int i = 0; i < n; i++) {
					for (int j = 0; j < m; j++) {
						p.print(arr[i][j]);
					}
					p.println();
				}

			}
		}
		p.flush();
		p.close();
	}

	public static boolean prime(long n) {
		if (n == 1) {
			return false;
		}
		if (n == 2) {
			return true;
		}
		for (long i = 2; i <= (long) Math.sqrt(n); i++) {
			if (n % i == 0)
				return false;
		}
		return true;
	}

	public static ArrayList Divisors(long n) {
		ArrayList<Long> div = new ArrayList<>();

		for (long i = 1; i <= Math.sqrt(n); i++) {
			if (n % i == 0) {
				div.add(i);

				if (n / i != i)
					div.add(n / i);
			}
		}
		return div;
	}

	public static int BinarySearch(long[] a, long k) {
		int n = a.length;
		int i = 0, j = n - 1;
		int mid = 0;

		if (k < a[0])
			return 0;
		else if (k >= a[n - 1])
			return n;
		else {
			while (j - i > 1) {
				mid = (i + j) / 2;

				if (k >= a[mid])
					i = mid;
				else
					j = mid;
			}
		}

		return i + 1;
	}

	public static long GCD(long a, long b) {
		if (b == 0)
			return a;
		else
			return GCD(b, a % b);
	}

	public static long LCM(long a, long b) {
		return (a * b) / GCD(a, b);
	}

	static class pair implements Comparable<pair> {
		Integer x, y;

		pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(pair o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);

			return result;
		}

		public String toString() {
			return x + " " + y;
		}

		public boolean equals(Object o) {
			if (o instanceof pair) {
				pair p = (pair) o;
				return p.x - x == 0 && p.y - y == 0;
			}
			return false;
		}

		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode();
		}
	}

	static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

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

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

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

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

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

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

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

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}

	static class CodeX {
		public static void sort(long arr[]) {
			merge_sort(arr, 0, arr.length - 1);
		}

		private static void merge_sort(long A[], long start, long end) {
			if (start < end) {
				long mid = (start + end) / 2;
				merge_sort(A, start, mid);
				merge_sort(A, mid + 1, end);
				merge(A, start, mid, end);
			}

		}

		private static void merge(long A[], long start, long mid, long end) {
			long p = start, q = mid + 1;
			long Arr[] = new long[(int) (end - start + 1)];
			long k = 0;

			for (int i = (int) start; i <= end; i++) {
				if (p > mid)
					Arr[(int) k++] = A[(int) q++];

				else if (q > end)
					Arr[(int) k++] = A[(int) p++];

				else if (A[(int) p] < A[(int) q])
					Arr[(int) k++] = A[(int) p++];

				else
					Arr[(int) k++] = A[(int) q++];
			}
			for (int i = 0; i < k; i++) {
				A[(int) start++] = Arr[i];
			}

		}

	}

}