#include<bits/stdc++.h>
#define fr first
#define sc second
using namespace std;
typedef long long ll;
typedef long double ld;
#define USING_ORDERED_SET 0
#if USING_ORDERED_SET
#include<bits/extc++.h>
using namespace __gnu_pbds;
template<class T>using ordered_set=tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
#endif
template<class T>void umax(T &a,T b){if(a<b)a=b;}
template<class T>void umin(T &a,T b){if(b<a)a=b;}
#ifdef juggernaut
#define printl(args...)printf(args)
#else
#define printl(args...)((void)0)
#endif
vector<int>g[1005];
bool vis[1005];
void dfs(int v,int p){
if(vis[v]){
puts("NO");
exit(0);
}
vis[v]=1;
for(int to:g[v])if(to!=p)dfs(to,v);
}
int main(){
int n;
ios_base::sync_with_stdio(0);
cin.tie(0);
int m;
cin>>n>>m;
while(m--){
int x,y;
cin>>x>>y;
g[x].push_back(y);
g[y].push_back(x);
}
dfs(1,0);
if(n==1){
puts("YES\n1\n1");
return 0;
}else if(n==2||n==3){
puts("YES\n2\n2 2");
return 0;
}
vector<int>vec;
if(n&1){
for(int i=2;i<n;i++)vec.push_back(i);
for(int i=2;i<n;i++)vec.push_back(i);
}else{
for(int i=2;i<n;i++)vec.push_back(i);
for(int i=n-1;i>1;i--)vec.push_back(i);
}
printf("YES\n%d\n",int(vec.size()));
for(int to:vec)printf("%d ",to);
}
