Flip the String

You are given two binary strings $A$ and $B$ with the same length. You may perform the following operation any number of times (including zero): pick a substring of $A$ with odd length and invert all the bits (change '0' to '1' or vice versa) at odd positions in this substring. For example, if we choose a substring "**0**1**0**1**1**", we can convert it to "**1**1**1**1**0**" (bits at odd posit