E. Construct Matrix
constructive algorithms; math
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.