Hi all, I have been doing some dynamic programming problems and I stumbled around a Never seen before type of problem

Ofcourse the problem is new to me maybe because I am not much experienced but I still feel like the problem uses a unconventional style of DP and I am NOT able to understand it,

If some people have not tried DP , or want to try new problem on DP, attempt the problem,its a good one ( when doing with DP) : Problem : 276D - Девочка и максимальный XOR || Author's DP solution

Please help me understand the DP state and the transition,I tried understanding with editorial but was not able to after my best efforts,

Thankyou,looking forward to your help.