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.InputStreamReader;
import java.util.Scanner;

public final class G {

    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        final int t = in.nextInt();
        for (int i = 0; i < t; i++) {
            final int n = in.nextInt();
            final int m = in.nextInt();
            final int a = in.nextInt();
            final int b = in.nextInt();
            if (n * a != m * b) {
                System.out.println("NO");
                continue;
            }
            System.out.println("YES");
            final int[][] matrix = new int[n][m];
            int x = 0;
            for (int y = 0; y < n; y++) {
                for (int wid = 0; wid < a; wid++) {
                    matrix[y][x] = 1;
                    x = (x + 1) % m;
                }
            }
            for (int j = 0; j < n; j++) {
                final StringBuilder sb = new StringBuilder();
                for (int k = 0; k < m; k++) {
                    sb.append(matrix[j][k]);
                }
                System.out.println(sb);
            }
        }
    }
}
