Description: Consider a segment of an OX axis from $$$1$$$ to $$$n$$$. There are $$$k$$$ observation towers on this segment. Each tower has two parameters — the coordinate $$$x_i$$$ and the height $$$h_i$$$. The coordinates of all towers are distinct. From tower $$$i$$$, you can see point $$$j$$$ if $$$|x_i - j| \le h_i$$$ (where $$$|a|$$$ is an absolute value of $$$a$$$). You can increase the height of any tower by $$$1$$$ for one coin. The height of each tower can be increased any number of times (including zero). You need to process $$$q$$$ independent queries. In the $$$i$$$-th query, two different points $$$l$$$ and $$$r$$$ are given. You need to calculate the minimum number of coins required to be able to see both of these points (from one tower or from different towers). Input Format: The first line contains two integers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 2 \cdot 10^5$$$; $$$1 \le k \le n$$$) — the length of the segment of an OX axis and the number of observation towers. The second line contains $$$k$$$ integers $$$x_1, x_2, \dots, x_k$$$ ($$$1 \le x_i \le n$$$) — the coordinates of the observation towers. The coordinates of all towers are distinct. The third line contains $$$k$$$ integers $$$h_1, h_2, \dots, h_k$$$ ($$$0 \le h_i \le n$$$) — the heights of the observation towers. The fourth line contains a single integer $$$q$$$ ($$$1 \le q \le 2 \cdot 10^5$$$) — the number of queries. Each of the next $$$q$$$ lines contains two integers $$$l$$$ and $$$r$$$ ($$$1 \le l < r \le n$$$) — the description of the next query. Output Format: For each query, output a single integer — the minimum number of coins required to be able to see both points (from one tower or from different towers). Note: None