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title: "题解 - [BalticOI 2016 day1] [Luogu P4676] [LOJ 2782] Spiral" categories:
题目链接
<!-- more -->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 $74$ :
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 $y_2$ ($-n\leq x_1\leq x_2\leq n, -n\leq y_1\leq y_2\leq n$). This means that you should calculate the sum of numbers in a rectangular region with corners $(x_1,y_1)$ and $(x_2,y_2)$.
You should output the answer for each query (modulo $10^9+7$).
2 3
0 -2 1 1
-1 0 1 0
1 2 1 2
74
9
14
In all subtasks $1\leq q\leq100$.
$1\leq n\leq10^9$
$x_1=x_2$ and $y_1=y_2$
$1\leq n\leq10^9$
$x_1=y_1=1$
给一个螺旋矩阵, 每次询问给出一个子矩阵, 问子矩阵中的元素和
大力分讨
$O(q)$