Codeforces Round 917 (Div. 2) |
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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:
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.
5 4 0 6 6 6 5 4 2 6 36
Yes 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Yes 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 No No Yes 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
In the first example, all conditions are satisfied:
In the third example, it can be shown that it's impossible to find a matrix satisfying all the problem's conditions.
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