Graph Game

Consider the following game on an undirected graph G. There are two players, a red color player R and a blue color player B. Initially all edges of G are uncolored. The two players alternately color an uncolored edge of G with their color until all edges are colored. The goal of B is that in the end, the blue-colored edges form a connected spanning subgraph of G. A connected spanning subgraph of G is a connected subgraph that contains all the vertexes of graph G. The goal of R is to prevent B from achieving his goal.

Assume that R starts the game. Suppose that both players play in the smartest way. Your task is to find out whether B will win the game.

The input contains several test cases, ended by a line of “-1 -1”.
Each test case begins with a line of two integers n ( 1 <= n <= 10) and m (0 <= m <= 30), indicating the number of vertexes and edges in the graph. All vertexes are numbered from 0 to n-1.
Then m lines follow. Each line contains two integers p and q ( 0 <= p, q < n) , indicating there is an edge between vertex p and vertex q.
It is possible that the graph contains more than one edge between two vertexes and self-loops.

For each test case print a line which is either "YES" or "NO" indicating B will win the game or not.

3 4
0 1
1 2
2 0
0 2
4 6
1 0
1 2
2 0
0 2
3 0
1 0
-1 -1

YES
NO

2009 Asia Ningbo Regional Contest Hosted by NIT