## Editorial for TLE '16 Contest 7 P3 - NOR

Remember to use this editorial

**only**when stuck, and**not to copy-paste code from it**. Please be respectful to the problem author and editorialist.**Submitting an official solution before solving the problem yourself is a bannable offence.**Author:

It is not necessary to use a segment tree or a sparse table to solve this problem. These approaches are overkill and run quite slowly. Binary search is also not necessary, and it increases execution time.

The first observation is that , where can be any expression. In particular, if , then the answer to the query is **always** .

To solve a query, it is only necessary to get the largest that satisfies both and . In case are all `0`

's, let . This information can be preprocessed and stored in an array in time (linear time). Now there are cases to consider:

- : In this case, all integers are equal to .
- : In this case, only the first integer is equal to . The rest are equal to .
- : In this case, , because and .

A query can be solved in (constant time). Make sure to print the correct answer for each case.

**Time Complexity:**

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