CF842D Vitya and Strange Lesson

Today at the lesson Vitya learned a very interesting function — mex. Mex of a sequence of numbers is the minimum non-negative number that is not present in the sequence as element. For example, $ mex([4,33,0,1,1,5])=2 $ and $ mex([1,2,3])=0 $ . Vitya quickly understood all tasks of the teacher, but can you do the same? You are given an array consisting of $ n $ non-negative integers, and $ m $ queries. Each query is characterized by one number $ x $ and consists of the following consecutive steps: - Perform the bitwise addition operation modulo $ 2 $ (xor) of each array element with the number $ x $ . - Find mex of the resulting array. Note that after each query the array changes.

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