After we convert the problem to the binary array version, I somehow came up with another conclusion to determine whether it is possible for min(a1,b1) to be 1. The conclusion is: min(a1,b1) is able to reach 1 is equivalent to ''there exists 2 pairs (ai,bi),(aj,bj) which are both (1,1) AND there exists no (0,0) pairs between them.''

I am uncertain about its validity since it differs from the tutorial. It would be awesome if anyone could prove it or come up with a counterexample.

Thanks a lot!

UPD1: I didn't clarify my conclusion well... Now I'm wondering if the sufficient&necessary constraint for min(a1,b1)=1 is that, the number of (1,1) pairs is greater than the number of (0,0) pairs. It seems to be right...? Still, any counterexamples? QwQ