CF1360G 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.