DMOPC '18 Contest 6 P3 - Wish Upon a Star

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Points: 10 (partial)
Time limit: 2.0s
Java 5.0s
Python 5.0s
Memory limit: 256M

Author:
Problem type

Ainz is a master player of the DMMORPG Yggdrasil. Currently, he is preparing to class up!

The classes in Yggdrasil form a forest: that is, there exists at most 1 path between each pair of nodes. However, Ainz finds that someone has used a world item to add some number of extra edges!

Ainz can use the skill <<Wish Upon a Star>> to remove at most a single edge. He then asks you: is it possible to restore the graph to a forest?

Constraints

Subtask 1 [20%]

1 \leq N, M \leq 5\,000

Subtask 2 [80%]

1 \leq N, M \leq 200\,000

Input Specification

The first line of input will contain two space separated integers, N and M, respectively.
The next M lines will each contain two space separated integers, a_i and b_i, indicating there exists a bidirectional edge from a_i to b_i.

Output Specification

Output YES if the graph can be restored to a forest by removing at most one edge, and NO otherwise.

Sample Input 1

5 4
1 2
1 3
4 5
2 3

Sample Output 2

YES

Explanation for Sample Output 1

Removing the edge 2\to 3 makes the graph a forest.

Sample Input 2

4 2
1 2
3 4

Sample Output 2

YES

Explanation for Sample Output 2

The graph is already a forest.


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