Pty loves graph

Given a undirected graph and a Hamiltonian cycle of it, output whether it is a planar graph.

For convenience, the indices of vertex are advancely relabeled so that the given Hamiltonian cycle is 1--2--3--4--...--(n-1)--n--1. The edges on this cycle are not given in the input.

Notice that there might be self loops and multiedges in the graph.

There are T test cases in total.

The first line contains one integer T – the number of test cases.

For each test case:

The first line, two positive integer N,M - the number of vertices and edge besides the Hamiltonian cycle. Following m lines, two positive integer x,y, representing an edge (x,y)

1 ≤ T ≤ 26
1 ≤ N,M ≤ 5×$10^5$ , $\sum N$,$ \sum M ≤ 3 \times 10^6$.
1 ≤ x,y ≤ N

For each test case, output ”Yes” or ”No” in one line.

2
5 5
1 3
1 4
2 4
2 5
3 5
4 4
1 3
2 4
2 2
1 2

No
Yes

2021“MINIEYE杯”中国大学生算法设计超级联赛（10）