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 $j$.

给你一个偶数 $n$ 和一个整数 $k$。你的任务是构造一个大小为 $n \times n$ 的、仅由数字 $0$ 和 $1$ 组成的矩阵，使其满足以下条件；若无法满足，则报告不可能：

• 矩阵中所有数字之和恰好为 $k$；
• 每行 $i$ 中所有数字的按位 $\texttt{XOR}$ 值均相同；
• 每列 $j$ 中所有数字的按位 $\texttt{XOR}$ 值均相同。

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 $2000$.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 130$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例由一行描述，该行包含两个整数 $n$ 和 $k$（$2 \leq n \leq 1000$，$n$ 为偶数，$0 \leq k \leq n^2$）。

保证所有测试用例中 $n$ 的总和不超过 $2000$。

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.

对于每个测试用例，如果能够构造出满足题目所有条件的矩阵，则输出 $\texttt{Yes}$；否则输出 $\texttt{No}$。

如果可以构造出这样的矩阵，则接下来的 $n$ 行中，第 $i$ 行应包含 $n$ 个整数，表示该矩阵第 $i$ 行的元素。

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.

在第一个例子中，所有条件均满足：

• 矩阵中所有数字的和恰好为 $0$；
• 对每个行 $i$，该行中所有数字的按位 $\texttt{XOR}$ 值为 $0$；
• 对每个列 $j$，该列中所有数字的按位 $\texttt{XOR}$ 值为 $0$。

在第三个例子中，可以证明不存在满足本题所有条件的矩阵。