Penelope is part of the admin team of the newly built
supercomputer. Her job is to assign workstations to the
researchers who come here to run their computations at the
supercomputer.
Penelope is very lazy and hates unlocking machines for the
arriving researchers. She can unlock the machines remotely from
her desk, but does not feel that this menial task matches her
qualifications. Should she decide to ignore the security
guidelines she could simply ask the researchers not to lock
their workstations when they leave, and then assign new
researchers to workstations that are not used any more but that
are still unlocked. That way, she only needs to unlock each
workstation for the first researcher using it, which would be a
huge improvement for Penelope.
Unfortunately, unused workstations lock themselves
automatically if they are unused for more than $m$ minutes. After a workstation has
locked itself, Penelope has to unlock it again for the next
researcher using it. Given the exact schedule of arriving and
leaving researchers, can you tell Penelope how many unlockings
she may save by asking the researchers not to lock their
workstations when they leave and assigning arriving researchers
to workstations in an optimal way? You may assume that there
are always enough workstations available.
Input
The input consists of:

one line with two integers $n$ ($1 \leq n \leq 300\, 000$), the
number of researchers, and $m$ ($1 \leq m \leq 10^8$), the number
of minutes of inactivity after which a workstation locks
itself;

$n$ lines each with
two integers $a$ and
$s$ ($1 \leq a, s \leq 10^8$),
representing a researcher that arrives after $a$ minutes and stays for exactly
$s$ minutes.
Output
Output the maximum number of unlockings Penelope may save
herself.
Sample Input 1 
Sample Output 1 
3 5
1 5
6 3
14 6

2

Sample Input 2 
Sample Output 2 
5 10
2 6
1 2
17 7
3 9
15 6

3
