CF1857D.Strong Vertices

Given two arrays $a$ and $b$, both of length $n$. Elements of both arrays indexed from $1$ to $n$. You are constructing a directed graph, where edge from $u$ to $v$ ($u\neq v$) exists if $a_u-a_v \ge b_u-b_v$.

A vertex $V$ is called strong if there exists a path from $V$ to all other vertices.

A path in a directed graph is a chain of several vertices, connected by edges, such that moving from the vertex $u$, along the directions of the edges, the vertex $v$ can be reached.

Your task is to find all strong vertices.

For example, if $a=[3,1,2,4]$ and $b=[4,3,2,1]$, the graph will look like this:

The graph has only one strong vertex with number $4$

给定两个长度均为 $n$ 的数组 $a$ 和 $b$，两个数组的元素下标均从 $1$ 到 $n$。你需要构造一个有向图，其中存在一条从顶点 $u$ 指向顶点 $v$（$u \neq v$）的有向边，当且仅当满足不等式 $a_u - a_v \ge b_u - b_v$。

若存在一条从顶点 $V$ 出发、可到达图中所有其他顶点的有向路径，则称顶点 $V$ 为强顶点。

有向图中的一条路径是指若干顶点构成的序列，相邻顶点之间由有向边连接，且沿边的方向可以从起始顶点 $u$ 到达终点顶点 $v$。

你的任务是找出所有的强顶点。

例如，当 $a = [3,1,2,4]$ 且 $b = [4,3,2,1]$ 时，所构造的图如下所示：

该图中唯一的强顶点编号为 $4$。

The first line contains an integer $t$ ($1\le t\le 10^4$) — the number of test cases.

The first line of each test case contains an integer $n$ ($2 \le n \le 2\cdot 10^5$) — the length of $a$ and $b$.

The second line of each test case contains $n$ integers $a_1,a_2 \dots a_n$ ($-10^9 \le a_i \le 10^9$) — the array $a$.

The third line of each test case contains $n$ integers $b_1,b_2 \dots b_n$ ($-10^9 \le b_i \le 10^9$) — the array $b$.

It is guaranteed that the sum of $n$ for all test cases does not exceed $2\cdot 10^5$.

第一行包含一个整数 $t$（$1\le t\le 10^4$）—— 测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$2 \le n \le 2\cdot 10^5$）—— 数组 $a$ 和 $b$ 的长度。

每个测试用例的第二行包含 $n$ 个整数 $a_1,a_2 \dots a_n$（$-10^9 \le a_i \le 10^9$）—— 数组 $a$。

每个测试用例的第三行包含 $n$ 个整数 $b_1,b_2 \dots b_n$（$-10^9 \le b_i \le 10^9$）—— 数组 $b$。

保证所有测试用例的 $n$ 之和不超过 $2\cdot 10^5$。

For each test case, output two lines: in the first line, output the number of strong vertices, and in the second line, output all strong vertices in ascending order.

对于每个测试用例，输出两行：第一行输出强顶点的数量，第二行按升序输出所有强顶点。

The first sample is covered in the problem statement.

For the second sample, the graph looks like this:

The graph has two strong vertices with numbers $3$ and $5$. Note that there is a bidirectional edge between vertices $3$ and $5$.

In the third sample, the vertices are connected by a single directed edge from vertex $2$ to vertex $1$, so the only strong vertex is $2$.

In the fourth sample, all vertices are connected to each other by bidirectional edges, so there is a path from every vertex to any other vertex.

第一个样例已在题目描述中给出。

对于第二个样例，图的结构如下：

该图有两个强顶点，编号分别为 $3$ 和 $5$。注意，顶点 $3$ 与顶点 $5$ 之间存在一条无向边。

在第三个样例中，顶点之间仅由一条从顶点 $2$ 指向顶点 $1$ 的有向边连接，因此唯一的强顶点是 $2$。

在第四个样例中，所有顶点两两之间均通过无向边相连，因此任意顶点到其余任一顶点均存在路径。