G. A/B Matrix
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given four positive integers $$$n$$$, $$$m$$$, $$$a$$$, $$$b$$$ ($$$1 \le b \le n \le 50$$$; $$$1 \le a \le m \le 50$$$). Find any such rectangular matrix of size $$$n \times m$$$ 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 $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. Then $$$t$$$ test cases follow.

Each test case is described by four positive integers $$$n$$$, $$$m$$$, $$$a$$$, $$$b$$$ ($$$1 \le b \le n \le 50$$$; $$$1 \le a \le m \le 50$$$), 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 $$$n \times m$$$, 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