You are given $$Q$$ queries. Each input query contains three integers $$l$$, $$r$$, and $$k$$. Print the maximum bitwise AND value of a subset of size $$k$$ in the segment $$[l, r]$$.
Input format
Output format
Print the maximum bitwise AND value for each query in a new line.
Constraints
\(1 \le Q \le 2e5\\ 1 \le l \le r \le 1e18\\ 1 \le k \le r-l+1\)
For the first query, there is only 1 possible subset {8}.
For the third query, the maximum possible AND value is only possible for subset {4,5,6}.