Find the missing number

An array A[1..n] contains all the integers from 0 to n except one. It
would be easy to determine the missing integer in O(n) time by using an
auxilary array B[0..n] to record which numbers appear in A. In this
problem however we cannot access an entire integer in A with a single
operation. The elements of A are represented in binary, the only
operation we can use to access them is " Fetch the jth bit of A[i] " ,
which takes constant time. Find the missing integer in O(n) time using
only that operation.

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