CF1832F Zombies

Polycarp plays a computer game in a post-apocalyptic setting. The zombies have taken over the world, and Polycarp with a small team of survivors is defending against hordes trying to invade their base. The zombies are invading for $ x $ minutes starting from minute $ 0 $ . There are $ n $ entrances to the base, and every minute one zombie attempts to enter through every entrance. The survivors can defend the entrances against the zombies. There are two options: - manually — shoot the zombies coming through a certain entrance; - automatically — set up an electric fence on a certain entrance to fry the zombies. If an entrance is defended either or both ways during some minute, no zombie goes through. Every entrance is defended by a single dedicated survivor. The $ i $ -th entrance is defended manually from minute $ l_i $ until minute $ r_i $ , non-inclusive — $ [l_i, r_i) $ . There are $ k $ generators that can be used to defend the entrances automatically. Every entrance should be connected to exactly one generator, but a generator can be connected to multiple entrances (or even none of them). Each generator will work for exactly $ m $ consecutive minutes. Polycarp can choose when to power on each generator independently of each other, the $ m $ minute long interval should be fully inside the $ [0, x) $ time interval. Polycarp is a weird gamer. He wants the game to be as difficult as possible for him. So he wants to connect each entrance to a generator and choose the time for each generator in such a way that as many zombies as possible enter the base. Please, help him to achieve that!

The first line contains four integers $ n, k, x $ and $ m $ ( $ 1 \le k \le n \le 2000 $ ; $ 1 \le m \le x \le 10^9 $ ) — the number of entrances, the number of generators, the duration of the zombie invasion and the duration of all generators. The $ i $ -th of the next $ n $ lines contains two integers $ l_i $ and $ r_i $ ( $ 0 \le l_i < r_i \le x $ ) — the time interval the $ i $ -th entrance is defended manually.

Print a single integer — the largest number of zombies that can enter the base after Polycarp connects each entrance to some generator and chooses the time for each generator.