CF1917E Construct Matrix

You are given an even integer $ n $ and an integer $ k $ . Your task is to construct a matrix of size $ n \times n $ consisting of numbers $ 0 $ and $ 1 $ in such a way that the following conditions are true, or report that it is impossible: - the sum of all the numbers in the matrix is exactly $ k $ ; - the bitwise $ \texttt{XOR} $ of all the numbers in the row $ i $ is the same for each $ i $ ; - the bitwise $ \texttt{XOR} $ of all the numbers in the column $ j $ is the same for each $ j $ .

Each test consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 130 $ ) — the number of test cases. The description of the test cases follows. Each test case is described by a single line, which contains two integers $ n $ and $ k $ ( $ 2 \leq n \leq 1000 $ , $ n $ is even, $ 0 \leq k \leq n^2 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2000 $ .

For each test case, output $ \texttt{Yes} $ if it's possible to construct a matrix that satisfies all of the problem's conditions, and $ \texttt{No} $ otherwise. If it is possible to construct a matrix, the $ i $ -th of the next $ n $ lines should contain $ n $ integers representing the elements in the $ i $ -th row of the matrix.

In the first example, all conditions are satisfied: - the sum of all the numbers in the matrix is exactly $ 0 $ ; - the bitwise $ \texttt{XOR} $ of all the numbers in the row $ i $ is $ 0 $ for each $ i $ ; - the bitwise $ \texttt{XOR} $ of all the numbers in the column $ j $ is $ 0 $ for each $ j $ . In the third example, it can be shown that it's impossible to find a matrix satisfying all the problem's conditions.