B. XOR Sequences

You are given two distinct non-negative integers 𝑥 and 𝑦. Consider two infinite sequences 𝑎1,𝑎2,𝑎3,… and 𝑏1,𝑏2,𝑏3,…, where

• 𝑎𝑛=𝑛⊕𝑥;
• 𝑏𝑛=𝑛⊕𝑦.

Here, 𝑥⊕𝑦 denotes the bitwise XOR operation of integers 𝑥 and 𝑦.

For example, with 𝑥=6, the first 8 elements of sequence 𝑎 will look as follows: [7,4,5,2,3,0,1,14,…]. Note that the indices of elements start with 1.

Your task is to find the length of the longest common subsegment † of sequences 𝑎 and 𝑏. In other words, find the maximum integer 𝑚 such that 𝑎𝑖=𝑏𝑗,𝑎𝑖+1=𝑏𝑗+1,…,𝑎𝑖+𝑚−1=𝑏𝑗+𝑚−1 for some 𝑖,𝑗≥1†A subsegment of sequence 𝑝 is a sequence 𝑝𝑙,𝑝𝑙+1,…,𝑝𝑟, where 1≤𝑙≤𝑟.