CF2057C Trip to the Olympiad

In the upcoming year, there will be many team olympiads, so the teachers of "T-generation" need to assemble a team of three pupils to participate in them. Any three pupils will show a worthy result in any team olympiad. But winning the olympiad is only half the battle; first, you need to get there... Each pupil has an independence level, expressed as an integer. In "T-generation", there is exactly one student with each independence levels from $ l $ to $ r $ , inclusive. For a team of three pupils with independence levels $ a $ , $ b $ , and $ c $ , the value of their team independence is equal to $ (a \oplus b) + (b \oplus c) + (a \oplus c) $ , where $ \oplus $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Your task is to choose any trio of students with the maximum possible team independence.

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The description of the test cases follows. The first line of each test case set contains two integers $ l $ and $ r $ ( $ 0 \le l, r < 2^{30} $ , $ r - l > 1 $ ) — the minimum and maximum independence levels of the students.

For each test case set, output three pairwise distinct integers $ a, b $ , and $ c $ , such that $ l \le a, b, c \le r $ and the value of the expression $ (a \oplus b) + (b \oplus c) + (a \oplus c) $ is maximized. If there are multiple triples with the maximum value, any of them can be output.

In the first test case, the only suitable triplet of numbers ( $ a, b, c $ ) (up to permutation) is ( $ 0, 1, 2 $ ). In the second test case, one of the suitable triplets is ( $ 8, 7, 1 $ ), where $ (8 \oplus 7) + (7 \oplus 1) + (8 \oplus 1) = 15 + 6 + 9 = 30 $ . It can be shown that $ 30 $ is the maximum possible value of $ (a \oplus b) + (b \oplus c) + (a \oplus c) $ for $ 0 \le a, b, c \le 8 $ .