Spiral |
| Time limit: | 1.50 s |
| Memory limit: | 256 MB |
|
A grid of size $(2n+1)\times(2n+1)$ has been constructed as follows. Number $1$ has been placed in the center square, number $2$ has been placed to the right of it, and the following numbers have been placed along the spiral counterclockwise.
Your task is to calculate answers for $q$ queries where the sum of numbers in an rectangular region in the grid is requested (modulo $10^9+7$). For example, in the following grid $n=2$ and the sum of numbers in the gray region is $74$:
Input
The first input line contains two integers $n$ and $q$: the size of the grid and the number of queries.
After this, there are $q$ lines, each containing four integers $x_1$, $y_1$, $x_2$ and $y_2$ ($-n \le x_1\le x_2 \le n$, $-n \le y_1 \le y_2 \le n$). This means that you should calculate the sum of numbers in a rectangular region with corners $(x_1, y_1)$ and $(x_2, y_2)$.
Output
You should output the answer for each query (modulo $10^9+7$).
Example
Input:
2 3
0 -2 1 1
-1 0 1 0
1 2 1 2
Output:
74
9
14
Subtasks
In all subtasks $1 \le q \le 100$.
Subtask 1 (12 points)
Subtask 2 (15 points)
- $1 \le n \le 10^9$
- $x_1=x_2$ and $y_1=y_2$
Subtask 3 (17 points)
Subtask 4 (31 points)
- $1 \le n \le 10^9$
- $x_1=y_1=1$
Subtask 5 (25 points)
