|시간 제한||메모리 제한||제출||정답||맞은 사람||정답 비율|
|3 초||512 MB||3||3||3||100.000%|
The Japanese government plans to increase the number of inbound tourists to forty million in the year 2020, and sixty million in 2030. Not only increasing touristic appeal but also developing tourism infrastructure further is indispensable to accomplish such numbers.
One possible enhancement on transport is providing cars extremely long and/or wide, carrying many passengers at a time. Too large a car, however, may require too long to evacuate all passengers in an emergency. You are requested to help estimating the time required.
The car is assumed to have the following seat arrangement.
A rough estimation requested is based on a simple step-wise model. All passengers are initially on a distinct seat, and they can make one of the following moves in each step.
The seat or the aisle position to move to must be empty; either no other passenger is there before the step, or the passenger there empties the seat by moving to another position in the same step. When two or more passengers satisfy the condition for the same position, only one of them can move, keeping the others wait in their original positions.
The leftmost figure of Figure C.1 depicts the seat arrangement of a small car given in Sample Input 1. The car have five rows of seats, two seats each on both sides of the aisle, totaling twenty. The initial positions of seven passengers on board are also shown.
The two other figures of Figure C.1 show possible positions of passengers after the first and the second steps. Passenger movements are indicated by fat arrows. Note that, two of the passengers in the front seat had to wait for a vacancy in the first step, and one in the second row had to wait in the next step.
Your task is to write a program that gives the smallest possible number of steps for all the passengers to get off the car, given the seat arrangement and passengers’ initial positions.
Figure C.1. Simple Model
The input consists of a single test case of the following format.
r s p i1 j1 . . . ip jp
Here, r is the number of passenger seat rows, s is the number of seats on each side of the aisle, and p is the number of passengers. They are integers satisfying 1 ≤ r ≤ 500, 1 ≤ s ≤ 500, and 1 ≤ p ≤ 2rs.
The following p lines give initial seat positions of the passengers. The k-th line with ik and jk means that the k-th passenger’s seat is in the ik-th seat row and it is the jk-th seat on that row. Here, rows and seats are counted from front to rear and left to right, both starting from one. They satisfy 1 ≤ ik ≤ r and 1 ≤ jk ≤ 2s. Passengers are on distinct seats, that is, ik ≠ il or jk ≠ jl holds if k ≠ l.
The output should be one line containing a single integer, the minimum number of steps required for all the passengers to get off the car.
5 2 7 1 1 1 2 1 3 2 3 2 4 4 4 5 2
500 500 16 1 1 1 2 1 999 1 1000 2 1 2 2 2 999 2 1000 3 1 3 2 3 999 3 1000 499 500 499 501 499 999 499 1000