Shake Hands With Your Opponent?

A and B are the only two participants of a race. The rules of this race are very different from the normal rules, but are very simple.

(1) A has to run with a constant speed "u"

(2)B will stand "x" meters ahead of A, and will begin from rest moving with a constant acceleration "a"

(3)Whenever A and B meet each other on the track they need to shake hands.

If 'm' is the maximum number of times A and B can shake hands on the track, then find m + 1.


they never waste time or slow down to shake hands. they do it in an instant.

assume that the race track is of infinite length


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