CF2249D Xor Permutation Matrix

You are given two integers $ n $ and $ x $ ( $ 0 \le x \le n-1 $ ). Construct a matrix $ A $ of size $ n\times n $ satisfying all of the following conditions: - For every $ 1 \le i, j \le n $ , $ 0 \le A_{i,j}\le n-1 $ ; - Every row in $ A $ forms a permutation of $ 0, 1, \ldots, n-1 $ ; - Every column in $ A $ forms a permutation of $ 0, 1, \ldots, n-1 $ ; - For every $ 1 \le i, j\le n-1 $ , $ A_{i,j} \oplus A_{i+1,j} \oplus A_{i,j+1} \oplus A_{i+1,j+1} = x. $Here, $ \oplus $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Or determine that no such matrix exists.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 180 $ ). The description of the test cases follows. The only line of each test case contains two integers $ n $ and $ x $ ( $ 2\le n\le 2500 $ , $ 0\le x \lt n $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2500 $ .

For each test case, output $ -1 $ if no such matrix exists. Otherwise, output any valid $ n $ lines of the matrix. If several valid matrices exist, you may output any of them.

In the first test case, the displayed matrix has both rows and columns equal to permutations of $ 0,1 $ , and its only adjacent $ 2\times2 $ submatrix has XOR $ 0 $ . The second and third test cases are impossible. In the last two test cases, every adjacent $ 2\times2 $ submatrix has XOR, respectively, $ 1 $ and $ 0 $ .