A question from moed B 2014

In this question the output of the circuit should be 1
iff k distinct strings were inputs of the circuit
(in different clock cycles)
I didn’t understand the functionality of
the marked part of the circuit-
If I understand correctly- the output of the OR-TREE
will be 1 if and only if k distinct strings were inputs.
So why isn’t it enough that the output of the circuit will
be the output of the OR-TREE?

Notice that the output should remain 1 forever after the first k distinct strings. The marked part takes care of clock cycles after the first time we saw k distinct strings, by always outputting 1.