#define PROBLEM "https://yukicoder.me/problems/no/408" #include #include #include #include #include #include #include #include #include using namespace std; // Nimber (64 bit) // Reference: // - https://en.wikipedia.org/wiki/Nimber // - https://kyopro-friends.hatenablog.com/entry/2020/04/07/195850 // - https://judge.yosupo.jp/submission/4542 (implementation idea) struct Nimber { using ull = unsigned long long; ull v; const static std::array, 256> small_table; const static std::array, 8>, 8> precalc; explicit operator bool() const { return v != 0; } Nimber(ull val = 0) : v(val) {} Nimber operator+(const Nimber &x) const { return Nimber(v ^ x.v); } Nimber operator-(const Nimber &x) const { return Nimber(v ^ x.v); } Nimber operator-() const { return *this; } Nimber &operator+=(const Nimber &x) { return *this = *this + x; } Nimber &operator-=(const Nimber &x) { return *this = *this + x; } template friend IStream &operator>>(IStream &is, Nimber &x) { ull v; return is >> v, x = Nimber(v), is; } template friend OStream &operator<<(OStream &os, const Nimber &x) { return os << x.v; } bool operator==(const Nimber &x) const { return v == x.v; } bool operator!=(const Nimber &x) const { return v != x.v; } bool operator<(const Nimber &x) const { return v < x.v; } static ull _rec(ull x, ull y) { if (x == 0 or y == 0) return 0; if (x < y) x ^= y, y ^= x, x ^= y; // Make x >= y if (y == 1) return x; for (int shift = 64 / 2;; shift >>= 1) { ull mask = (1ULL << shift) - 1; if (y >> shift) { ull v00 = _rec(x & mask, y & mask); ull v01 = _rec(x & mask, y >> shift); ull v10 = _rec(x >> shift, y & mask); ull v11 = _rec(x >> shift, y >> shift); return v00 ^ ((v01 ^ v10 ^ v11) << shift) ^ _rec(v11, 1ULL << (shift - 1)); } else if (x >> shift) { return (_rec(x >> shift, y) << shift) ^ _rec(x & mask, y); } } } Nimber operator*(const Nimber &x) const { ull ret = 0; for (int d = 0; d < 8; ++d) { for (int e = 0; e < 8; ++e) { ret ^= precalc[d][e][small_table[(v >> (d * 8)) & 255][(x.v >> (e * 8)) & 255]]; } } return Nimber(ret); } Nimber &operator*=(const Nimber &x) { return *this = *this * x; } }; const std::array, 256> Nimber::small_table = []() { std::array, 256> ret; for (int i = 0; i < 256; ++i) { for (int j = 0; j < 256; ++j) ret[i][j] = _rec(i, j); } return ret; }(); const std::array, 8>, 8> Nimber::precalc = []() { std::array, 8>, 8> ret; for (int d = 0; d < 8; ++d) { for (int e = 0; e < 8; ++e) { ull p = _rec(1ULL << (8 * d), 1ULL << (8 * e)); for (int i = 0; i < 256; ++i) ret[d][e][i] = _rec(p, i); } } return ret; }(); struct rand_int_ { using lint = long long; mt19937 mt; rand_int_() : mt(chrono::steady_clock::now().time_since_epoch().count()) {} lint operator()(lint x) { return this->operator()(0, x); } // [0, x) lint operator()(lint l, lint r) { uniform_int_distribution d(l, r - 1); return d(mt); } } rnd; int main() { cin.tie(nullptr), ios::sync_with_stdio(false); int N, M; cin >> N >> M; vector> edges; vector> eids(N + 1); while (M--) { int a, b; cin >> a >> b; --a, --b; Nimber w = rnd(1LL << 62); Nimber wn = rnd(1LL << 62); auto add_edge = [&](int s, int t, Nimber w) { int eid = edges.size(); eids[s].push_back(eid); edges.emplace_back(s, t, w); eids[t].push_back(eid + 1); edges.emplace_back(t, s, w); }; add_edge(a, b, w); if (a == 0) add_edge(b, N, wn); if (b == 0) add_edge(a, N, wn); } vector dp(edges.size()); for (int e = 0; e < int(edges.size()); ++e) { auto [s, t, w] = edges[e]; if (s == 0) dp[e] = w; } for (int t = 0; t < 4; ++t) { vector dpnxt(edges.size()); for (int now = 0; now < N; ++now) { Nimber sum = 0; for (auto e : eids[now]) { // e : now から出る // e ^ 1 : now に入る sum += dp[e ^ 1]; } for (auto e : eids[now]) { auto [s, t, w] = edges[e]; if (t != 0) dpnxt[e] += (sum - dp[e ^ 1]) * w; } } dp.swap(dpnxt); } for (auto e : eids[N]) { if (dp[e ^ 1]) { puts("YES"); return 0; } } puts("NO"); }