#define _CRT_SECURE_NO_WARNINGS #define _USE_MATH_DEFINES #include "bits/stdc++.h" #define rep(i, n) for(int i=0; i<(n); ++i) #define FOR(i, m, n) for(int i=(m); i<(n); ++i) #define rrep(i, n) for(int i=(n)-1; i>=0; --i) #define rfor(i, m, n) for(int i=(m); i>=(n); --i) #define sz(x) ((int)(x).size()) #define all(x) (x).begin(),(x).end() #define rall(x) (x).rbegin(),(x).rend() #define range_it(a, l, r) (a).begin() + (l), (a).begin() + (r) using namespace std; using LL = long long; using ld = long double; using VB = vector; using VVB = vector; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using VS = vector; using VD = vector; using PII = pair; using VP = vector; using PLL = pair; using VPL = vector; templateusing Grid = vector>; templateusing PQ = priority_queue; templateusing PQS = priority_queue, greater>; constexpr int inf = (int)1e9; constexpr LL inf_ll = (LL)1e18, MOD = 1000000007; constexpr ld PI = M_PI, EPS = 1e-12; templateinline void Sort(T& a)noexcept { sort(all(a)); } templateinline void RSort(T& a)noexcept { sort(rall(a)); } templateinline void Reverse(T& a)noexcept { reverse(all(a)); } templateinline void Unique(T& a)noexcept { a.erase(unique(all(a)), a.end()); } templateinline T Sorted(T a)noexcept { Sort(a); return a; } templateinline T RSorted(T a)noexcept { RSort(a); return a; } templateinline T Reversed(T a)noexcept { Reverse(a); return a; } templateinline T Uniqued(T a)noexcept { Unique(a); return a; } templateinline auto Max(const T& a)noexcept { return *max_element(all(a)); } templateinline auto Min(const T& a)noexcept { return *min_element(all(a)); } templateinline int MaxPos(const T& a)noexcept { return max_element(all(a)) - a.begin(); } templateinline int MinPos(const T& a)noexcept { return min_element(all(a)) - a.begin(); } templateinline int Count(const T& a, const U& v)noexcept { return count(all(a), v); } templateinline int Find(const T& a, const U& v)noexcept { auto pos = find(all(a), v); return pos == a.end() ? -1 : pos - a.begin(); } templateinline U Sum(const T& a, const U& v)noexcept { return accumulate(all(a), v); } templateinline int Lower(const T& a, const U& v)noexcept { return lower_bound(all(a), v) - a.begin(); } templateinline int Upper(const T& a, const U& v)noexcept { return upper_bound(all(a), v) - a.begin(); } templateinline void RemoveIf(T& a, P f)noexcept { a.erase(remove_if(all(a), f), a.end()); } templateinline T Age(T n, T m)noexcept { return (n + m - 1) / m; } templateinline T Age2(T n, T m)noexcept { return Age(n, m) * m; } templateinline T Tri(T n)noexcept { return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1); } templateinline T BIT(int b)noexcept { return T{ 1 } << b; } templateinline T Gcd(T n, T m)noexcept { return m ? Gcd(m, n % m) : n; } templateinline T Lcm(T n, T m)noexcept { return n / Gcd(n, m) * m; } templateinline T Pow(T a, T n)noexcept { T r = 1; while (n > 0) { if (n & 1)r *= a; a *= a; n /= 2; }return r; } templateinline T Powmod(T a, T n, T m = MOD)noexcept { T r = 1; while (n > 0) { if (n & 1)r = r * a % m, n--; else a = a * a % m, n /= 2; }return r; } templateinline bool chmax(T& a, const T& b)noexcept { if (a < b) { a = b; return true; } return false; } templateinline bool chmin(T& a, const T& b)noexcept { if (a > b) { a = b; return true; } return false; } templateinline bool inRange(const T& v, const T& min, const T& max)noexcept { return min <= v && v <= max; } inline string operator*(string s, int n)noexcept { string ret; rep(i, n)ret += s; return ret; } // --- input --- // #if defined(_WIN32) || defined(ONLINE_JUDGE) #define getchar_unlocked _getchar_nolock #define putchar_unlocked _putchar_nolock #endif inline int gc()noexcept { return getchar_unlocked(); } templateinline void InputF(T& v)noexcept { cin >> v; } inline void InputF(char& v)noexcept { while (isspace(v = gc())); } inline void InputF(string& v)noexcept { char c; for (InputF(c); !isspace(c); c = gc())v += c; } inline void InputF(int& v)noexcept { bool neg = false; v = 0; char c; InputF(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c); c = gc())v = v * 10 + (c - '0'); if (neg)v = -v; } inline void InputF(long long& v)noexcept { bool neg = false; v = 0; char c; InputF(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c); c = gc())v = v * 10 + (LL)(c - '0'); if (neg)v = -v; } inline void InputF(double& v)noexcept { double dp = 1; bool neg = false, adp = false; v = 0; char c; InputF(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c) || c == '.'; c = gc()) { if (c == '.')adp = true; else if (adp)v += (c - '0') * (dp *= 0.1); else v = v * 10 + (c - '0'); } if (neg)v = -v; } templateinline void InputF(pair& v)noexcept { InputF(v.first); InputF(v.second); } templateinline void InputF(vector& v)noexcept { for (auto& e : v)InputF(e); } templateinline T input() { T v; InputF(v); return v; } struct InputV { int n, m; InputV(int N) :n(N), m(0) {} InputV(pair N) :n(N.first), m(N.second) {} templateoperator vector()noexcept { vector v(n); InputF(v); return v; } templateoperator vector>()noexcept { vector> v(n, vector(m)); InputF(v); return v; } }; struct Input { templateoperator T()noexcept { return input(); } int operator--(int) { int v; InputF(v); v--; return v; } InputV operator[](int n)noexcept { return InputV(n); } InputV operator[](pair n)noexcept { return InputV(n); } void operator()() {} templatevoid operator()(H&& h, T&& ...t) { InputF(h); operator()(forward(t)...); } templatearray, W> get(int H) { array, W> ret; rep(i, H)rep(j, W) { T x = *this; ret[j].push_back(x); } return ret; } }in; // --- output --- // struct BoolStr { const char* t, * f; BoolStr(const char* _t, const char* _f) :t(_t), f(_f) {} }Yes("Yes", "No"), yes("yes", "no"), YES("YES", "NO"), Int("1", "0"); struct DivStr { const char* d, * l; DivStr(const char* _d, const char* _l) :d(_d), l(_l) {} }spc(" ", "\n"), no_spc("", "\n"), end_line("\n", "\n"), comma(",", "\n"), no_endl(" ", ""); class Output { BoolStr B{ Yes }; DivStr D{ spc }; bool isPrint = true; void p(double v) { printf("%.20f", v); } void p(long double v) { printf("%.20Lf", v); } void p(int v) { printf("%d", v); } void p(LL v) { printf("%lld", v); } void p(char v) { putchar(v); } void p(bool v) { printf("%s", v ? B.t : B.f); } templatevoid p(const T& v) { cout << v; } templatevoid p(const pair& v) { p(v.first); printf("%s", D.d); p(v.second); } templatevoid p(const vector& v) { rep(i, sz(v)) { if (i)printf("%s", D.d); p(v[i]); } } templatevoid p(const vector>& v) { rep(i, sz(v)) { if (i)printf("%s", D.l); p(v[i]); } } void p(const BoolStr& v) { B = v; isPrint = false; } void p(const DivStr& v) { D = v; isPrint = false; } public: void operator()() { printf("%s", D.l); } templatevoid operator()(H&& h) { p(h); if (isPrint)printf("%s", D.l); isPrint = true; } templatevoid operator()(H&& h, T&& ...t) { p(h); if (isPrint)printf("%s", D.d); isPrint = true; operator()(forward(t)...); } templatevoid exit(T&& ...t) { operator()(forward(t)...); std::exit(EXIT_SUCCESS); } }out; // --- dump --- // #if __has_include("dump.hpp") #include "dump.hpp" #else #define dump(...) (void(0)) #endif // ---------------------------------------------------------------- // using Weight = long long; constexpr Weight INF = numeric_limits::max(); struct Edge { int to; Weight cost; Edge() :to(-1), cost(-1) {} Edge(int _to, Weight _cost = 1) :to(_to), cost(_cost) {} }; bool operator>(const Edge& e1, const Edge& e2) { return e1.cost > e2.cost; } struct Edge2 { int u, v; Weight cost; Edge2() :u(-1), v(-1), cost(0) {} Edge2(int _u, int _v, Weight _cost) :u(_u), v(_v), cost(_cost) {} }; using Edges = vector; using Graph = vector; using Array = vector; using Matrix = vector; using UnWeightedGraph = vector>; pair> ConnectedComponet(const UnWeightedGraph& g) { int V = g.size(), N = 0; VI id(V, -1); function dfs = [&](int ID, int v) { id[v] = ID; for (auto e : g[v]) if (id[e] == -1)dfs(ID, e); }; for (int i = 0; i < V; ++i) if (id[i] == -1)dfs(N++, i); return make_pair(N, id); } class UnionFind { vector par, sz; public: UnionFind(int n = 1) { init(n); } void init(int n) { par.resize(n); sz.resize(n); for (int i = 0; i < n; i++)par[i] = i, sz[i] = 1; } int root(int x) { if (par[x] == x)return x; else return par[x] = root(par[x]); } bool same(int x, int y) { return root(x) == root(y); } int size(int x) { return sz[root(x)]; } void unite(int x, int y) { x = root(x); y = root(y); if (x == y)return; par[y] = x; sz[x] += sz[y]; } }; int main() { int n = in, m = in; UnWeightedGraph g(n); UnionFind uf(n); VB flag(n); int p = -1; rep(i, m) { int a = in, b = in; p = a; g[a].push_back(b); g[b].push_back(a); uf.unite(a, b); flag[a] = true; flag[b] = true; } out(YES); if (uf.size(p) == Count(flag, true)) { VI d(n); rep(i, n)d[i] = sz(g[i]) % 2; int odd = Count(d, 1), even = Count(d, 0); if (even == n || odd == 2) { out.exit(true); } } out(false); }