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 sun.awt.image.IntegerComponentRaster;

    import java.io.OutputStream;
    import java.io.IOException;
    import java.io.InputStream;
    import java.io.PrintWriter;
    import java.util.InputMismatchException;
    import java.util.*;
    /**
     * Built using CHelper plug-in
     * Actual solution is at the top
     *
     * @author Manan Patel
     */
    public class Main{
        public static void main(String[] args) {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            InputReader in = new InputReader(inputStream);
            PrintWriter w = new PrintWriter(outputStream);
            Solution solver = new Solution();
            int testCount = Integer.parseInt(in.next());
            for (int i = 1; i <= testCount; i++)
                solver.solve(1 , in, w);
            w.close();
        }

        static class Solution {
            public static long power(long x,int y){
                long res = 1;
                while (y > 0)
                {
                    if ((y & 1) == 1)
                        res = (res*x);
                    y = y >> 1;
                    x = x * x;
                }
                return res;
            }
            public void solve(int tc, InputReader sc, PrintWriter w) {
                int n = sc.nextInt(),
                m = sc.nextInt(),
                a = sc.nextInt(),
                b = sc.nextInt();
                if(n * a != m * b){
                    w.println("NO");
                    return;
                }
                w.println("YES");
                int cnt = 0 ;
                boolean vis[][] = new boolean[n][m];
                for(int i = 0 ; i < n ; i++){
                    for(int j = 0 ; j < a ; j++){
                        vis[i][cnt++] = true;
                        cnt %= m;
                    }
                }
                for(int i =  0 ; i < n ; i++){
                    for(int j = 0 ; j < m ; j++) {
                        w.print(vis[i][j] ? "1" : "0");
                        
                    }
                    w.println();
                }
            }
        }


        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 long nextLong() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                long 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 readString() {
                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 boolean isSpaceChar(int c) {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }

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

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

            }

        }

    }
