D. Strong Verticestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputGiven 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 InputThe 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.OutputFor 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.ExampleInput
543 1 2 44 3 2 151 2 4 1 25 2 3 3 121 22 130 2 11 3 235 7 4-2 -3 -6Output
1
4 
2
3 5 
1
2 
3
1 2 3 
2
2 3 
NoteThe 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.
543 1 2 44 3 2 151 2 4 1 25 2 3 3 121 22 130 2 11 3 235 7 4-2 -3 -6
1 4  2 3 5  1 2  3 1 2 3  2 2 3  
['math', 'sortings', 'trees', '*1300']