Crime at Piccadily Circus
Sherlock Holmes is carrying out an investigation into the crime at Piccadily Circus. Holmes is trying to determine the maximal and minimal number of people staying simultaneously at the crime scene at a moment when the crime could have been commited. Scotland Yard has already carried out a thorough investigation already, interrogated everyone seen at the crime scene and determined what time they appeared at the crime scene and what time they left. Doctor Watson offered his help to process the data gathered by Scotland Yard and find the numbers interesting Sherlock Holmes, but he has some difficulties. Help him!
Task
Write a program which
- reads from standard input the time interval during which the crime was commited and the data gathered by Scotland Yard,
- finds the minimal and the maximal number of people present simultaneously in the time interval when the crime could have been commited, (these numbers can be zero, though it would seem strange that noone was present at the crime scene when the crime was commited, but that's the type of crime Holmes and Watson have to deal with)
- writes the outcome to standard output.
Input
Ten test cases (given one under another, you have to process all!). The first line of each test case consists of two integer numbers p and k, 0<=p<=k<=100000000. These denote the first and the last moment when the crime could have been commited. The second line of each test case contains one integer n, 3<=n<=5000. This is the number of people interrogated by Scotland Yard. The next n lines consist of two integers - line i+2 contains numbers ai and bi separated by a single space, 0<=ai<=bi<=1000000000. These are the moments at which the i-th person apperared at and left the crime scene respectively. It means that the i-th person was at the crime scene for the whole time from moment ai until moment bi (inclusive).
Output
For every test case your program should write to the standard output only one line with two integers separated by a single space: the minimal and maximal number of people staying simultaneously at the crime scene, in the interval between moment p and k, (inclusive).
Example
Only one test case.
Input: 5 10 4 1 8 5 8 7 10 8 9 Output: 1 4