A16401 | 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.