Consider

3 2
2 3
4 5
1 6

The correct anser is 3.

 The following greedy strategy works: consider intervals in the order
of ascending right endpoints, and whenever the next interval can be
taken, then take it.

 The problem is with checking the condition whether the next interval
can be taken.  The simple test right(Q[0]) <= left(A[i]) does not
quite work, since it is too restrictive.  Q[0] can finish before Q[1]
starts, and thus one could possibly squeeze A[i] as well, as Q[0] and
Q[1] do not add up in the capacity at any point.

 The only way I see how to fix it at the current moment is to
implement the checking condition on a counting tree / interval tree
with + updates on intervals and max queries on intervals (both in log
n time).  Implementation of such a tree is pretty hardcore, so if we
do not see any other solution, this increases the difficulty
significantly.