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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int tt = sc.nextInt();
        StringBuffer sb = new StringBuffer();
        while (tt-- > 0) {
            int n = sc.nextInt();
            int m = sc.nextInt();
            int a = sc.nextInt();
            int b = sc.nextInt();
           
            if (n * a != m * b) {
                sb.append("NO\n");
            } else {
                int[][] mat = new int[n][m];
                for (int i = 0; i < n; ++i) {
                    for (int count = 0, j = (i * a) % m; count < a; j = (1 + j) % m, ++count){
                        mat[i][j] = 1;
                    }
                }
                //System.out.println("YES");
                sb.append("YES\n");
                print(mat, sb);
            }
        }

        System.out.println(sb.toString());
    }

    private static void print(int[][] mat, StringBuffer sb){
        for(int[] row : mat){
            for(int cell : row)
                sb.append(cell);
                //System.out.print(cell);
            sb.append("\n");
            //System.out.println();
        }
    }
    private static class FastReader {
        private BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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;
        }

        int[] readArray(int n){
            int[] arr = new int[n];
            for(int i = 0; i < n; ++i)
                arr[i] = nextInt();

            return arr;
        }
        long[] readLongArray(int n){
            long[] arr = new long[n];
            for(int i = 0; i < n; ++i)
                arr[i] = nextLong();

            return arr;
        }

        double[] readDoubleArray(int n){
            double[] arr = new double[n];
            for(int i = 0; i < n; ++i)
                arr[i] = nextDouble();
            return arr;
        }
    }
}
