CF1582F2 Korney Korneevich and XOR (hard version)

This is a harder version of the problem with bigger constraints. Korney Korneevich dag up an array $ a $ of length $ n $ . Korney Korneevich has recently read about the operation [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR), so he wished to experiment with it. For this purpose, he decided to find all integers $ x \ge 0 $ such that there exists an increasing subsequence of the array $ a $ , in which the bitwise XOR of numbers is equal to $ x $ . It didn't take a long time for Korney Korneevich to find all such $ x $ , and he wants to check his result. That's why he asked you to solve this problem! A sequence $ s $ is a subsequence of a sequence $ b $ if $ s $ can be obtained from $ b $ by deletion of several (possibly, zero or all) elements. A sequence $ s_1, s_2, \ldots , s_m $ is called increasing if $ s_1 < s_2 < \ldots < s_m $ .

N/A

N/A

In the first test case: - To get value $ x = 0 $ it is possible to choose and empty subsequence - To get value $ x = 2 $ it is possible to choose a subsequence $ [2] $ - To get value $ x = 4 $ it is possible to choose a subsequence $ [4] $ - To get value $ x = 6 $ it is possible to choose a subsequence $ [2, 4] $