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.Arrays;
import java.util.Locale;
import java.util.StringTokenizer;

public class SolutionG {
    static BufferedReader input;
    static StringTokenizer _stk;

    static String readln() throws IOException {
        String l = input.readLine();
        if (l != null)
            _stk = new StringTokenizer(l, " ");
        return l;
    }

    static String next() {
        return _stk.nextToken();
    }

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

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

    static void dbg(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }

    static PrintWriter output = new PrintWriter(new BufferedWriter(
            new OutputStreamWriter(System.out)));

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        input = new BufferedReader(new InputStreamReader(System.in));
        readln();
        int t = nextInt();
        for (int testI = 0; testI < t; testI++) {
            readln();
            int n = nextInt();
            int m = nextInt();
            int a = nextInt();
            int b = nextInt();
            if (a * n != b * m) {
                output.println("NO");
                continue;
            }

            int[][] arr = new int[n][m];
            int d;
            for (d = 1; d < a; d++) {
                if (((d * n) % m) == 0) {
                    break;
                }
            }

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < a; j++) {
                    int y = (i * d + j) % m;
                    arr[i][y] = 1;
                }
            }

            output.println("YES");
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    output.print(arr[i][j]);
                }
                output.println();
            }
        }

        output.close();
    }
}