#include <iostream>
#include <cassert>
#include <iomanip>
#include <algorithm>
#include <string>
#include <bitset>
#include <vector>
#include <cmath>
#include <deque>
#include <queue>
#include <stack>
#include <map>
#include <set>
#ifndef LOCAL
#include <bits/stdc++.h>
#define cerr if(false)cerr
#endif
using namespace std;
using ll = long long;
const int N = 1e6 + 66;
int cycle;
vector<int>g[N];
int n;
int used[N];
void dfsdfs(int v, int p = -1) {
used[v] = 1;
for (int to : g[v]) if (to != p) {
if (used[to] == 1) cycle = 1;
if (used[to] == 0) dfsdfs(to, v);
}
used[v] = 2;
}
int d[N];
queue<int>q;
int p[N];
int bfs(int v) {
for (int i = 1 ; i <= n ; ++ i) d[i] = ((int)g[i].size() == 1 ? -2 : -1);
d[v] = 0;
p[v] = 0;
q.push(v);
while (q.size()) {
v = q.front(); q.pop();
for (int to : g[v]) if (d[to] == -1) {
d[to] = d[v] + 1;
p[to] = v;
q.push(to);
}
}
for (int i = 1 ; i <= n ; ++ i) if (d[i] > d[v]) v = i;
return v;
}
vector<int>temp;
void go(int v) {
used[v] = 1;
if ((int)g[v].size() == 1) return;
temp.emplace_back(v);
for (int to : g[v]) if (!used[to] && (int)g[to].size() > 1) {
go(to);
temp.emplace_back(v);
}
}
int go(int v, int p1, int d = 1) {
if (d == 3) return 1;
for (int to : g[v]) if (to != p1 && go(to, v, d+1)) return 1;
return 0;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int m;
cin >> n >> m;
if (n == 1) {
cout << "YES\n1\n1";
return 0;
}
if (n == 2) {
cout << "YES\n2\n1 1";
return 0;
}
while (m--) {
int a, b;
cin >> a >> b;
g[a].emplace_back(b);
g[b].emplace_back(a);
}
for (int i = 1 ; i <= n ; ++ i) {
int cnt = 0;
for (int j : g[i]) cnt += go(j, i, 1);
if (cnt >= 3) {
cout << "NO";
return 0;
}
}
for (int i = 1 ; i <= n ; ++ i) if (!used[i]) {
dfsdfs(i);
}
if (cycle) {
cout << "NO";
return 0;
}
for (int i = 1 ; i <= n ; ++ i) used[i] = 0;
vector<int>ans;
int v = -1;
for (int u = 1 ; u <= n ; ++ u) if ((int)g[u].size() >= 2) v = u;
assert(v != -1);
temp.clear();
int x = bfs(v);
int y = bfs(x);
int z = y;
for (int i = 1 ; i <= n ; ++ i) used[i] = 0;
while (z > 0) {
used[z] = 1;
z = p[z];
}
z = y;
while (z > 0) {
go(z);
z = p[z];
}
for (int i : temp) ans.emplace_back(i);
if ((int)temp.size() % 2 == 0) reverse(temp.begin(), temp.end());
for (int i : temp) ans.emplace_back(i);
cout << "YES\n";
cout << ans.size() << "\n";
for (int i : ans) cout << i << " ";
}
