G. Observation Towers
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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

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).

Examples
Input
20 32 15 106 2 031 2010 113 4
Output
3 1 0

Input
10 22 91 234 55 61 10
Output
2 2 0