A13539 | A/B Matrix

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:

$$$$ \begin{vmatrix} 0 & 1 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \end{vmatrix} $$$$

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.

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.