Hi,

I have seen the editorial of Div1B of the recent round and completely understood it. .

There is this recursion there that , f[i...j] = f[i...j-1] ^ f[i+1 ... j]

Now I get that some people noticed this via observation of patterns and some mentioned in comments that we can prove it through induction .

I want to ask people who solved this fastly in contest timings , how did you get to this solution?

If you made observations only , how did you make fast observations?

In case you actually "GOT" to the solution mathematically ( not proved through induction , but constructively ) , how did you do that?