Problem D
Intervals

A new streaming service, My Stream, has launched and wants to analyze user activity patterns. Each time a user logs on, the service records the hour they started streaming and the hour they finished.

For example, if a user started streaming at 3 a.m. and ended at 2 p.m., this interval would be recorded as starting at time 3 and ending at time 14, for a total duration of 11 hours.

Given $n$ user intervals, each represented as a pair of integers $[a_i, b_i]$ where $0 \le a_i < b_i \le 24$, and an integer $k$, determine how many hours during the day had at least $k$ users streaming simultaneously.

Input

• The first line contains two integers $n$ and $k$ ($1 \le n \le 1000$, $1 \le k \le n$) — the number of user intervals and the minimum number of users to count.

• Each of the next $n$ lines contains two integers $a_i$ and $b_i$ ($0 \le a_i < b_i \le 24$), representing the start and end time of the $i$-th user interval.

Output

Print a single integer — the number of hours during which at least $k$ users were streaming.

4 2
12 18
1 13
17 20
18 22

4

7 3
8 17
2 5
3 12
11 23
14 19
10 20
9 13

10