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.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedOutputStream;
import java.io.UncheckedIOException;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        GABMatrix solver = new GABMatrix();
        solver.solve(1, in, out);
        out.close();
    }

    static class GABMatrix {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            int testCases = in.ints();
            for (int testCase = 1; testCase <= testCases; testCase++) {
                int n = in.ints(), m = in.ints(), a = in.ints(), b = in.ints();
                char[][] ans = new char[n][m];
                ArrayUtil.fill(ans, '0');
                int col = 0;
                int[] sum = new int[m];
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < a; j++) {
                        sum[col]++;
                        ans[i][col] = '1';
                        if (++col == m) col = 0;
                    }
                }
                boolean ok = true;
                for (int i = 0; i < m; i++) {
                    if (sum[i] != b) {
                        ok = false;
                        break;
                    }
                }
                out.ans(ok).ln();
                if (ok) {
                    for (int i = 0; i < n; i++) out.ans(String.valueOf(ans[i])).ln();
                }
            }
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;
        private LightWriter.BoolLabel boolLabel = LightWriter.BoolLabel.YES_NO_FIRST_UP;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new OutputStreamWriter(new BufferedOutputStream(out), Charset.defaultCharset()));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(boolean b) {
            return ans(boolLabel.transfer(b));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

        public enum BoolLabel {
            YES_NO_FIRST_UP("Yes", "No"),
            YES_NO_ALL_UP("YES", "NO"),
            YES_NO_ALL_DOWN("yes", "no"),
            Y_N_ALL_UP("Y", "N"),
            POSSIBLE_IMPOSSIBLE_FIRST_UP("Possible", "Impossible"),
            POSSIBLE_IMPOSSIBLE_ALL_UP("POSSIBLE", "IMPOSSIBLE"),
            POSSIBLE_IMPOSSIBLE_ALL_DOWN("possible", "impossible"),
            FIRST_SECOND_FIRST_UP("First", "Second"),
            FIRST_SECOND_ALL_UP("FIRST", "SECOND"),
            FIRST_SECOND_ALL_DOWN("first", "second"),
            ALICE_BOB_FIRST_UP("Alice", "Bob"),
            ALICE_BOB_ALL_UP("ALICE", "BOB"),
            ALICE_BOB_ALL_DOWN("alice", "bob"),
            ;
            private final String positive;
            private final String negative;

            BoolLabel(String positive, String negative) {
                this.positive = positive;
                this.negative = negative;
            }

            private String transfer(boolean f) {
                return f ? positive : negative;
            }

        }

    }

    static final class ArrayUtil {
        private ArrayUtil() {
        }

        public static void fill(char[] a, char v) {
            Arrays.fill(a, v);
        }

        public static void fill(char[][] a, char v) {
            for (int i = 0; i < a.length; i++) {
                fill(a[i], v);
            }
        }

    }

    static class LightScanner implements AutoCloseable {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public void close() {
            try {
                this.reader.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }
}

