CF1630A And Matching

You are given a set of $ n $ ( $ n $ is always a power of $ 2 $ ) elements containing all integers $ 0, 1, 2, \ldots, n-1 $ exactly once. Find $ \frac{n}{2} $ pairs of elements such that: - Each element in the set is in exactly one pair. - The sum over all pairs of the [bitwise AND](https://en.wikipedia.org/wiki/Bitwise_operation#AND) of its elements must be exactly equal to $ k $ . Formally, if $ a_i $ and $ b_i $ are the elements of the $ i $ -th pair, then the following must hold: $ $$$\sum_{i=1}^{n/2}{a_i \& b_i} = k, $ $ where $ \\& $ denotes the bitwise AND operation.

If there are many solutions, print any of them, if there is no solution, print $ -1$$$ instead.

The input consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 400 $ ) — the number of test cases. Description of the test cases follows. Each test case consists of a single line with two integers $ n $ and $ k $ ( $ 4 \leq n \leq 2^{16} $ , $ n $ is a power of $ 2 $ , $ 0 \leq k \leq n-1 $ ). The sum of $ n $ over all test cases does not exceed $ 2^{16} $ . All test cases in each individual input will be pairwise different.

For each test case, if there is no solution, print a single line with the integer $ -1 $ . Otherwise, print $ \frac{n}{2} $ lines, the $ i $ -th of them must contain $ a_i $ and $ b_i $ , the elements in the $ i $ -th pair. If there are many solutions, print any of them. Print the pairs and the elements in the pairs in any order.

In the first test, $ (0\&3)+(1\&2) = 0 $ . In the second test, $ (0\&2)+(1\&3) = 1 $ . In the third test, $ (0\&1)+(2\&3) = 2 $ . In the fourth test, there is no solution.