#include "bits/stdc++.h" using namespace std; #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; template static void amin(T &x, U y) { if (y < x) x = y; } template static void amax(T &x, U y) { if (x < y) x = y; } struct GFLookup { static const int Deg = 16; using Word = uint16_t; enum : uint32_t { Poly = 0x1002d, Mask = 0x10000, Order = 0xffff, }; array pow, log; GFLookup() { uint32_t a = 1; for (uint32_t i = 0; i < Order; ++ i) { pow[i] = (Word)a; log[a] = (Word)i; a <<= 1; if (a & Mask) a ^= Poly; } } Word mul(Word x, Word y) const { if (x == 0 || y == 0) return 0; uint32_t k = (uint32_t)log[x] + log[y]; if (k >= Order) k -= Order; return pow[k]; } }; int main() { random_device rd; using F = uint16_t; auto random = [&rd]() { return uint16_t(rd() & (GFLookup::Mask - 1)); }; struct Edge { int u, v; F value; }; GFLookup gf; const int K = 4; //See: "Parameterized Algorithms" Ch.10.4.1 auto solve = [&gf, K](int N, const vector &edges, const vector> &y) { F totalSum = 0; vector ySum(N); vector> dp; rep(X, 1 << K) { rep(i, N) { F sum = 0; rep(k, K) if (X >> k & 1) sum ^= y[i][k]; ySum[i] = sum; } dp.assign(K, vector(N)); for (const Edge &e : edges) if(e.u == 0 && e.v != 0) dp[0][e.v] ^= gf.mul(e.value, ySum[e.v]); rep(k, K - 1) { for (const Edge &e : edges) if (e.v != 0) { F x = dp[k][e.u]; if (x != 0) dp[k + 1][e.v] ^= gf.mul(gf.mul(x, e.value), ySum[e.v]); } } for (const Edge &e : edges) if (e.v == 0) totalSum ^= gf.mul(dp[K - 1][e.u], e.value); } return totalSum != 0; }; int N; int M; while (~scanf("%d%d", &N, &M)) { vector edges(M * 2); for (int i = 0; i < M; ++ i) { int u, v; scanf("%d%d", &u, &v), -- u, -- v; edges[i * 2 + 0] = { u, v, random() }; edges[i * 2 + 1] = { v, u, random() }; } vector> y(N, vector(K)); rep(i, N) rep(k, K) y[i][k] = random(); bool ans = solve(N, edges, y); if (!ans) { puts("NO"); continue; } puts("YES"); #if 0 //実際の解の構成 //"Fast Witness Extraction Using a Decision Oracle" vector U(edges.size()); vector tmpVis(edges.size()); vector tmpEdges; vector id(N, -1); auto checkAndCut = [random, solve, K, &id, &edges, &U, &tmpVis, &tmpEdges](const vector &A) { for (int i : A) tmpVis[i] = true; int N = 0; id[0] = N ++; for (int i : U) if (!tmpVis[i]) { const Edge &e = edges[i]; if (id[e.u] == -1) id[e.u] = N ++; if (id[e.v] == -1) id[e.v] = N ++; tmpEdges.push_back(Edge{ id[e.u], id[e.v], random() }); } vector> y(N, vector(K)); rep(i, N) rep(k, K) y[i][k] = random(); bool result = solve(N, tmpEdges, y); for (int i : U) if (!tmpVis[i]) { const Edge &e = edges[i]; id[e.u] = id[e.v] = -1; } id[0] = -1; if (result) U.erase(remove_if(U.begin(), U.end(), [&](int i) { return tmpVis[i]; }), U.end()); for (int i : A) tmpVis[i] = false; tmpEdges.clear(); return result; }; iota(U.begin(), U.end(), 0); vector W; queue> Q; Q.push(U); while (!Q.empty()) { vector A = Q.front(); Q.pop(); if (A.size() == 1) { W.push_back(A[0]); continue; } vector A1(A.begin(), A.begin() + A.size() / 2); vector A2(A.begin() + A.size() / 2, A.end()); if (checkAndCut(A1)) { Q.push(A2); } else if(checkAndCut(A2)) { Q.push(A1); } else { Q.push(A1); Q.push(A2); } } U = W; while ((int)W.size() > K + 1) { if (checkAndCut(vector{W.back()})) W.pop_back(); else rotate(W.begin(), W.begin() + 1, W.end()); } assert(W.size() == K + 1); vector next(N, -1); for (int i : W) { auto e = edges[i]; assert(next[e.u] == -1); next[e.u] = e.v; } vector cycle = { 0 }; { int u = 0; rep(k, K) { u = next[u]; cycle.push_back(u); assert(u != -1); } assert(next[u] == 0); } /* for (int u : cycle) cerr << u + 1 << ' '; cerr << endl; */ #endif } return 0; }