AT_arc213_b [ARC213B] Hamming Distance is not 1

You are given non-negative integers $ q,L,R\;(q \in \{ 0,1\}, \; L \leq R) $ . Consider a set $ S $ that satisfies all of the following conditions. - $ S $ consists of distinct integers between $ L $ and $ R $ , inclusive. - If $ a \in S, \; b \in S, \; a \neq b $ , then $ a $ and $ b $ differ in at least two digits in binary representation. More formally, there exist at least two non-negative integers $ i $ such that $ \left\lfloor\frac{a}{2^i}\right\rfloor $ and $ \left\lfloor\frac{b}{2^i}\right\rfloor $ have different parities. - Among those satisfying the above two conditions, the number of elements is maximum. If $ q=0 $ , find the number of elements in such a set $ S $ . If $ q=1 $ , construct one such set $ S $ . For each input file, solve $ T $ test cases.

The input is given from Standard Input in the following format: > $ T $ $ case_1 $ $ case_2 $ $ \vdots $ $ case_T $ Each case is given in the following format: > $ q $ $ L $ $ R $

Output the answers in a total of $ T $ lines. The $ t $ -th line should contain the answer for the $ t $ -th test case. For each test case, if $ q=0 $ , print the number of elements in a set $ S $ that satisfies the conditions. If $ q=1 $ , for a set $ S $ that satisfies the conditions, let $ B_i=\begin{cases} 1 \; (S \text{ contains } i) \\ 0 \; (S \text{ does not contain } i) \end{cases} $ and output it in the following format: > $ B_L $ $ B_{L+1} $ $ \dots $ $ B_R $ If there are multiple sets $ S $ that satisfy the conditions, you may print any of them.

### Sample Explanation 1 In the first test case, $ S=\{0,3\} $ satisfies the conditions. $ S=\{1,2\} $ also satisfies the conditions, so it is correct as well. In the second test case, the only $ S $ that satisfies the conditions is $ \{1,2\} $ , whose number of elements is $ 2 $ . ### Constraints - $ 1 \leq T \leq 2 \times 10^5 $ - $ 0 \leq q \leq 1 $ - $ 0 \leq L \leq R \leq 10^{18} $ - The sum of $ q(R-L) $ over all test cases is at most $ 5\times 10^6 $ . - All input values are integers.