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.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.fill;

public class Main {

    static void run() throws IOException {
        file("", "");
        int t = nextInt();
        while (t-- > 0)
            solution();

        end();
    }

    static int[][] arr;

    static void solution() throws IOException {
        int n = nextInt();
        int m = nextInt();
        int a = nextInt();
        int b = nextInt();
        if (a * n != m * b) {
            out.println("NO");
            return;
        }
        arr = new int[n][m];
        out.println("YES");
        int point = 0;
        for (int i = 0; i < n; i++)
            for (int j = 0; j < a; j++)
                arr[i][point++ % m] = 1;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                out.print(arr[i][j]);
            }
            out.println();
        }
    }

    static mem create_mem(int from, int to, int val) {
        mem y = new mem();
        y.from = from;
        y.to = to;
        y.val = val;
        return y;
    }

    static class mem {
        int from, to, val;
    }

    /**
     * Z-function
     **/
    static int[] Z_function(char[] s) {
        int[] z = new int[s.length];
        for (int i = 1, l = 0, r = 0; i < s.length; i++) {
            if (i <= r)
                z[i] = min(r - i + 1, z[i - l]);
            while (z[i] + i < s.length && s[z[i] + i] == s[z[i]])
                ++z[i];
            if (i + z[i] - 1 > r) {
                l = i;
                r = i + z[i] - 1;
            }
        }
        return z;
    }

    /**
     * Pow
     **/
    static long Pow(long a, long b) {
        long h = 1;
        while (b > 0) {
            if (b % 2 != 0) {
                h *= a;
                b--;
            }
            b /= 2;
            a *= a;
        }
        return h;
    }

    /**
     * lcm
     **/
    static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    /**
     * gcd
     **/
    static long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    /**
     * end
     **/
    static void end() {
        out.flush();
        out.close();
        System.exit(0);
    }

    /**
     * files
     **/
    static BufferedReader br;
    static PrintWriter out;

    static void file(String input, String output) {
        if (input.equals("")) {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            try {
                br = new BufferedReader(new FileReader(input));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            try {
                out = new PrintWriter(output);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }
    }

    /**
     * inputs
     **/
    static StringTokenizer in = new StringTokenizer("");

    static String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            String s = br.readLine();
            if (s == null) return null;
            in = new StringTokenizer(s);
        }
        return in.nextToken();
    }


    static int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public static void main(String[] args) throws IOException {
        run();
    }
}