Pudding Monsters

题意翻译

一个一维数轴上有n个布丁。 相邻的布丁会黏在一起，一段连续的布丁会黏成一个布丁块。 每次操作你可以选择一个布丁（块），并且指定一个方向，那么这个布丁（块）会沿着这个方向滑动直到撞上某个布丁。 数轴上有m个特殊的格子。 问你最多能让多少个特殊的格子上有布丁。 感谢@平凡的人 提供的翻译

题目描述

Have you ever played Pudding Monsters? In this task, a simplified one-dimensional model of this game is used. Imagine an infinite checkered stripe, the cells of which are numbered sequentially with integers. Some cells of the strip have monsters, other cells of the strip are empty. All monsters are made of pudding, so if there are two monsters in the neighboring cells, they stick to each other (literally). Similarly, if several monsters are on consecutive cells, they all stick together in one block of monsters. We will call the stuck together monsters a block of monsters. A detached monster, not stuck to anyone else, is also considered a block. In one move, the player can take any block of monsters and with a movement of his hand throw it to the left or to the right. The selected monsters will slide on until they hit some other monster (or a block of monsters). For example, if a strip has three monsters in cells $ 1 $ , $ 4 $ and $ 5 $ , then there are only four possible moves: to send a monster in cell $ 1 $ to minus infinity, send the block of monsters in cells $ 4 $ and $ 5 $ to plus infinity, throw monster $ 1 $ to the right (it will stop in cell $ 3 $ ), throw a block of monsters in cells $ 4 $ and $ 5 $ to the left (they will stop in cells $ 2 $ and $ 3 $ ). Some cells on the strip are marked with stars. These are the special cells. The goal of the game is to make the largest possible number of special cells have monsters on them. You are given the numbers of the special cells on a strip as well as the initial position of all monsters. What is the maximum number of special cells that will contain monsters in the optimal game?

输入输出格式

输入格式

The first line contains two integers $ n $ and $ m $ $ (1<=n<=10^{5}; 1<=m<=2000) $ — the number of monsters on the strip and the number of special cells. The second line contains $ n $ distinct integers — the numbers of the cells with monsters, then the third line contains $ m $ distinct integers — the numbers of the special cells. It is guaranteed that all the numbers of the cells are positive integers not exceeding $ 2·10^{5} $ .

输出格式

Print a single integer — the maximum number of special cells that will contain monsters in the optimal game.

输入输出样例

输入样例 #1

3 2
1 3 5
2 4

输出样例 #1

2

输入样例 #2

4 2
1 3 4 6
2 5

输出样例 #2

2

输入样例 #3

4 2
1 8 4 5
7 2

输出样例 #3

1

题意翻译

一个一维数轴上有n个布丁。 相邻的布丁会黏在一起，一段连续的布丁会黏成一个布丁块。 每次操作你可以选择一个布丁（块），并且指定一个方向，那么这个布丁（块）会沿着这个方向滑动直到撞上某个布丁。 数轴上有m个特殊的格子。 问你最多能让多少个特殊的格子上有布丁。 感谢@平凡的人 提供的翻译