A16125 | 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 $4$

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 $2\cdot 10^5$ .

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.