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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.io.BufferedWriter;
import java.util.AbstractQueue;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.Objects;
import java.util.List;
import java.io.Writer;
import java.util.Optional;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author out_of_the_box
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        GABMatrix solver = new GABMatrix();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class GABMatrix {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            int a = in.nextInt();
            int b = in.nextInt();
            int[][] arr = new int[n][m];
            if ((a * n) == (b * m)) {
                PriorityQueue<Pair<Integer, Integer>> pq = new PriorityQueue<>(this::compare);
                for (int i = 0; i < m; i++) {
                    pq.add(Pair.of(i, 0));
                }

                for (int i = 0; i < n; i++) {
                    List<Pair<Integer, Integer>> cols = new ArrayList<>();
                    for (int j = 0; j < a; j++) {
                        Pair<Integer, Integer> pr = Optional.ofNullable(pq.poll())
                                .orElseThrow(() -> new RuntimeException("Unexpected"));
                        int col = pr.getLeft();
                        arr[i][col] = 1;
//                    pq.add(Pair.of(col, pr.getRight()+1));
                        cols.add(Pair.of(col, pr.getRight() + 1));
                    }
                    pq.addAll(cols);
                }
                out.println("YES");
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < m; j++) {
                        out.print(arr[i][j]);
                    }
                    out.println();
                }
            } else {
                out.println("NO");
            }
        }

        private int compare(Pair<Integer, Integer> a, Pair<Integer, Integer> b) {
            return a.getRight().compareTo(b.getRight());
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println() {
            writer.println();
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void print(int i) {
            writer.print(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

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

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

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

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

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

        public String next() {
            return nextString();
        }

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

        }

    }

    static class Pair<L, R> {
        private L left;
        private R right;

        private Pair(L left, R right) {
            this.left = left;
            this.right = right;
        }

        public L getLeft() {
            return left;
        }

        public R getRight() {
            return right;
        }

        public static <A, B> Pair<A, B> of(A a, B b) {
            return new Pair<>(a, b);
        }

        public String toString() {
            return "Pair{" +
                    "left=" + left +
                    ", right=" + right +
                    '}';
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair<?, ?> pair = (Pair<?, ?>) o;
            return Objects.equals(left, pair.left) &&
                    Objects.equals(right, pair.right);
        }

        public int hashCode() {
            return Objects.hash(left, right);
        }

    }
}

