Eulerian Circuit Checker

You are given an undirected graph defined by vertices and edges. Your task is to determine whether the graph contains an Eulerian Circuit. A graph has an Eulerian circuit if and only if every vertex with a nonzero degree is connected and each of these vertices has an even degree. In mathematical terms, for every vertex \( v \) with degree \( d(v) \), an Eulerian circuit exists if \( d(v) \equiv 0 \pmod{2} \) for all \( v \) and the subgraph consisting of vertices with nonzero degree is connected.

The input consists of one or more datasets. Each dataset starts with a line containing two integers \( n \) and \( m \), where \( n \) is the number of vertices (labeled from 1 to \( n \)) and \( m \) is the number of edges in the graph. The next \( m \) lines each contain two integers \( u \) and \( v \), representing an undirected edge between vertices \( u \) and \( v \). The input terminates with a line containing a single 0, which should not be processed.

inputFormat

The input is read from stdin and consists of multiple datasets. Each dataset is formatted as follows:

n m
u1 v1
u2 v2
... 
um vm

The end of input is indicated by a single line containing the number 0.

outputFormat

For each dataset, print a single line to stdout containing either "YES" if the graph contains an Eulerian circuit, or "NO" otherwise.

## sample

3 3
1 2
2 3
3 1
0

YES

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