Points Movement

题意翻译

一个数轴上有 $n$ 个点，$m$ 条线段。 第 $i$ 个点的初始位置为 $a_i$，第 $i$ 条线段的左右端点为 $l_i,r_i$。 定义一条线段 $i$ 被标记过仅当存在时刻存在一个点 $j$ 满足 $l_i\leq a_j\leq r_i$。 你可以进行下面的操作任意次： - 选择一个点 $i$，并使 $a_i$ 变为 $a_i+1,a_i-1$ 两数中的一个，代价为 $1$。 求使所有线段都被标记过的代价和最小值。$T$ 组数据。 保证： $1\leq T\leq 10^4;1\leq n,m,\sum n,\sum m\leq2\times10^5;$ $-10^9\leq a_i\leq10^9;-10^9\leq l_i\leq r_i\leq10^9;$

题目描述

There are $ n $ points and $ m $ segments on the coordinate line. The initial coordinate of the $ i $ -th point is $ a_i $ . The endpoints of the $ j $ -th segment are $ l_j $ and $ r_j $ — left and right endpoints, respectively. You can move the points. In one move you can move any point from its current coordinate $ x $ to the coordinate $ x - 1 $ or the coordinate $ x + 1 $ . The cost of this move is $ 1 $ . You should move the points in such a way that each segment is visited by at least one point. A point visits the segment $ [l, r] $ if there is a moment when its coordinate was on the segment $ [l, r] $ (including endpoints). You should find the minimal possible total cost of all moves such that all segments are visited.

输入输出格式

输入格式

The input consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Description of the test cases follows. The first line of each test case contains two integers $ n $ and $ m $ ( $ 1 \le n, m \le 2 \cdot 10^5 $ ) — the number of points and segments respectively. The next line contains $ n $ distinct integers $ a_1, a_2, \ldots, a_n $ ( $ -10^9 \le a_i \le 10^9 $ ) — the initial coordinates of the points. Each of the next $ m $ lines contains two integers $ l_j $ , $ r_j $ ( $ -10^9 \le l_j \le r_j \le 10^9 $ ) — the left and the right endpoints of the $ j $ -th segment. It's guaranteed that the sum of $ n $ and the sum of $ m $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

输出格式

For each test case print a single integer — the minimal total cost of all moves such that all segments are visited.

输入输出样例

输入样例 #1

2
4 11
2 6 14 18
0 3
4 5
11 15
3 5
10 13
16 16
1 4
8 12
17 19
7 13
14 19
4 12
-9 -16 12 3
-20 -18
-14 -13
-10 -7
-3 -1
0 4
6 11
7 9
8 10
13 15
14 18
16 17
18 19

输出样例 #1

5
22

说明

In the first test case the points can be moved as follows: - Move the second point from the coordinate $ 6 $ to the coordinate $ 5 $ . - Move the third point from the coordinate $ 14 $ to the coordinate $ 13 $ . - Move the fourth point from the coordinate $ 18 $ to the coordinate $ 17 $ . - Move the third point from the coordinate $ 13 $ to the coordinate $ 12 $ . - Move the fourth point from the coordinate $ 17 $ to the coordinate $ 16 $ . The total cost of moves is $ 5 $ . It is easy to see, that all segments are visited by these movements. For example, the tenth segment ( $ [7, 13] $ ) is visited after the second move by the third point. Here is the image that describes the first test case: