Given a number N, The problem asks you to find all such pairs u,v such that there exists another set of pairs a,b such that

1. a ^ b = u

2. a + b = v

where u , v <= N.

I finally concluded that basically we have to find a+b<=N, but how to proceed from here. Can we use counting principle to solve this problem, i mean count all a+b == N and a+b < N and to avoid repeatation we will considere a >= b.

Can anyone tell me the approach and intutition to solve it. Editorial is in japanese.