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.*;


public class SolutionB {

    public static void main(String[] args) throws Exception {
        int tc = scan.nextInt();
        for (int i = 0; i < tc; i++) {
            solve();
        }
        out.close();
    }

    private static void solve() {
        int n = scan.nextInt();
        int m = scan.nextInt();
        int a = scan.nextInt();
        int b = scan.nextInt();
        int[] row = new int[n];
        int[] col = new int[m];
        int[][] board = new int[n][m];
        Queue<Integer> pq = new PriorityQueue<>(Comparator.comparingInt(v -> col[v]));
        for (int i = 0; i < m; i++) pq.add(i);
        for (int i = 0; i < n; i++) {
            Queue<Integer> temp = new LinkedList<>();
            for (int j = 0; j < a; j++) {
                Integer currCol = pq.poll();
                col[currCol]++;
                row[i]++;
                board[i][currCol] = 1;
                temp.add(currCol);
            }
            pq.addAll(temp);
        }
        for (int c : col) {
            if (c != b) {
                out.println("NO");
                return;
            }
        }
        for (int r : row) {
            if (r != a) {
                out.println("NO");
                return;
            }
        }
        out.println("YES");
        for (int[] bb : board) {
            for (int v : bb) {
                out.print(v);
            }
            out.println();
        }
    }

    private static int gcd(int a, int b) {
        if (a > b) return gcd(b, a);
        if (a == 0) return b;
        return gcd(b, b % a);
    }


    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    public static MyScanner scan = new MyScanner();

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
//--------------------------------------------------------

}