#include "bits/stdc++.h"
#define int long long
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
using namespace std;
const long long INF = 1ll << 60;
const int N = 1000 + 5;
vector<int> adj[N];
void dfs(int v) {
int ch = 0;
for (auto u: adj[v]) {
adj[u].erase(find(adj[u].begin(), adj[u].end(), v));
dfs(u);
if (adj[u].size()) ch++;
}
if (ch >= 2) {
cout << "NO\n";
exit(0);
}
}
signed main() {
ios::sync_with_stdio(0), cin.tie(0);
int n, m;
cin >> n >> m;
if (m >= n) {
cout << "NO\n";
return 0;
}
if (n <= 2) {
cout << "YES\n";
cout << n << '\n';
FOR(i, 0, n) cout << 1 << ' ';
return 0;
}
FOR(i, 1, n) {
int u, v; cin >> u >> v;
u--, v--;
adj[u].push_back(v);
adj[v].push_back(u);
}
int rt = 0;
FOR(i, 0, n) if (adj[i].size() == 1) rt = i;
dfs(rt);
cout << "YES\n";
cout << 2 * n - 4 << '\n';
FOR(i, 1, n - 1) cout << i + 1 << ' ';
FOR(i, 1, n - 1) cout << n - i << ' ';
cout << '\n';
return 0;
}
//Reading this fills you with DETERMINATION
//20:06:46
