Velociraptors 301 P88665

When you go out from the toilet to go back to class you discover that a group of velociraptors has entered to the classroms and has devoured your classmates. The corridor where you are is closed: running away is impossible. Velociraptors, inside the classroms digesting, will go out at any moment to finish with you. Oh, well! It is known that this kind of things happen sometimes.

The corridor of your high school is represented by a segment of the real line from 0 to 2n−2, with n doors of n classroms, placed over the points 0, 2, 4, …, 2n−2 of the line. The toilet where you are going out from is placed at the point k with 0≤ k ≤ 2n−2 and even k. You as well as the velociraptors take 1 second to cover a distance unit over the line (velociraptors are already satisfied and they are not going to run for a miserable desert).

You are asked to, assuming that you know which velociraptors will go out from the classroms to devour you and the moments of time t_i that they will do it, and also assuming that these ones will head for you (wherever you are) as soon as they go out, say how many seconds you can extend your (brief but intense) life time making the right movements.

[r]

We consider that will be very useful to think in space-time diagrams as the one on the right, where it is illustrated a possible situaton for k=6 and n=11, where 3 velociraptors go out from the classroms placed in the points 2, 4 and 14 at the moments 6, 10 and 8 respectively. The correct answer to this case is 13.

Input

A test data contains various cases. Each case starts with three naturals n, m and k, with 0≤ k≤ 2n−2, 1≤ n≤ 10⁸ and 1≤ m ≤ 10000, where n and k are as it is describe in the wording and m is the number of velociraptors. The next m lines of the input contain a pair of numbers c_i, t_i, where c_i is the classroom that has devoured the i-th velociraptor and t_i is the moment of time that it will go out for its desert. It is fulfilled that 0≤ a_i≤ 2n−2 and 0≤ t_i≤ 10⁹ for any i, that c_i and t_i are even, and that all the c_i are different.

Output

For each case, your program must print in a line the time that you can extend your life. As times t_i and classrooms are even numbers it is fulfilled that the answer will always be an integer.

Scoring

• Test1:  45 Points 

  Test data with no more than 20 cases with n=m ≤ 100 and where the c_i appear sorted (as in the instance 1).

• Test2:  30 Points 

  Test data with no more than 20 cases with n≤ 1000 and m≤ 100 (as in the instances 2 and 3).

• Test3:  25 Points 

  Test data with no more than 20 cases of n≤ 10⁸ and m≤ 10⁴ (as in the instance 4).