#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(abs(a), abs(b));}
ll lcm(ll a, ll b){return abs(a) / gcd(a, b) * abs(b);}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
double cur = rngesus(0, MASK(60) - 1);
cur /= MASK(60) - 1;
return l + cur * (r - l);
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
int n, m;
const int N = 1010;
vector<int> graph[N];
namespace Sub3{
int depth[N];
int color[N];
bool find_depth(int u, int p){
depth[u] = 1;
int cnt = 0;
bool ans = true;
for(int v: graph[u]) if (v != p){
color[v] = 1 - color[u];
ans = ans && find_depth(v, u);
maximize(depth[u], depth[v] + 1);
if (depth[v] > 2) cnt++;
}
if (cnt >= 2) return false;
return ans;
}
void dfs(int u, int p, vector<int> &nooky){
vector<int> child;
for(int v: graph[u])
if (v != p) child.push_back(v);
sort(ALL(child), [](int x, int y){return depth[x] > depth[y];});
if (depth[u] == 1) {
if (color[u] == 1) nooky.push_back(u);
return;
}
dfs(child[0], u, nooky);
nooky.push_back(u);
for(int i = 1; i < (int) child.size(); ++i){
if (depth[child[i]] >= 2){
nooky.push_back(child[i]);
nooky.push_back(u);
}
}
}
void solve(){
bool check = true;
int root = -1;
for(int i = 1; i <= n; ++i){
bool rootable = find_depth(i, 0);
if (rootable && graph[i].size() == 1) root = i;
int cnt = 0;
for(int j: graph[i]) if (depth[j] > 2) cnt++;
if (cnt > 2)
check = false;
}
if (!check){
cout << "NO\n";
exit(0);
}
if (root == -1) assert(false);
cout << "YES\n";
vector<int> nooky[2];
nooky[0] = nooky[1] = vector<int>(n * 5, 69);
for(int x = 0; x <= 1; ++x){
color[root] = x;
find_depth(root, 0);
for(int i = 1; i <= n; ++i) if (graph[i].size() == 1){
if (find_depth(i, 0)) {
vector<int> mongey;
dfs(i, 0, mongey);
if (nooky[x].size() > mongey.size()){
nooky[x] = mongey;
}
}
}
}
nooky[0].pop_back(); nooky[1].pop_back();
vector<int> ans(n * 5, 69);
for(int x = 0; x <= 1; ++x) for(int y = 0; y <= 1; ++y){
vector<int> cur = nooky[x];
if ((int)cur.size() % 2 == (x ^ y)) cur.push_back(1);
for(int j: nooky[y]) cur.push_back(j);
if (cur.size() < ans.size()) ans = cur;
}
cout << ans.size() << "\n";
printArr(ans);
exit(0);
}
}
void solve(){
cin >> n >> m;
if (m != n - 1) {
cout << "NO\n";
return;
}
if (n == 1){
cout << "YES\n1\n1\n";
return;
}
else if (n == 2){
cout << "YES\n2\n1 1\n";
return;
}
for(int i = 0; i < m; ++i){
int u, v; cin>> u >> v;
graph[u].push_back(v);
graph[v].push_back(u);
}
Sub3::solve();
}
int main(void){
ios::sync_with_stdio(0);cin.tie(0); cout.tie(0);
clock_t start = clock();
solve();
cerr << "Time elapsed: " << clock() - start << "ms!\n";
return 0;
}
