Description:
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 $$$j$$$.
Input Format:
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 $$$2000$$$.
Output Format:
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.
Note:
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.