/** * date : 2021-03-31 21:54:46 */ #define NDEBUG /** * date : 2021-03-31 21:18:51 */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; T &x() { return first; } const T &x() const { return first; } U &y() { return second; } const U &y() const { return second; } P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template void mem(T (&a)[N], int c) { memset(a, c, sizeof(T) * N); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector reord(const vector &v, const vector &ord) { int N = v.size(); vector ret(N); for (int i = 0; i < N; i++) ret[i] = v[ord[i]]; return ret; }; template vector mkiota(int N) { vector ret(N); iota(begin(ret), end(ret), 0); return ret; } template vector mkinv(vector &v, int max_val = -1) { if (max_val < (int)v.size()) max_val = v.size() - 1; vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } __attribute__((target("bmi"))) inline int lsb(const u64 &a) { return _tzcnt_u64(a); } __attribute__((target("bmi"))) inline int ctz(const u64 &a) { return _tzcnt_u64(a); } __attribute__((target("lzcnt"))) inline int msb(const u64 &a) { return 63 - _lzcnt_u64(a); } __attribute__((target("lzcnt"))) inline int clz64(const u64 &a) { return _lzcnt_u64(a); } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { a ^= (gbit(a, i) == b ? 0 : (T(b) << i)); } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug namespace DebugImpl { template struct is_specialize : false_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize::value, void>> : true_type { }; void dump(const char &t) { cerr << t; } void dump(const string &t) { cerr << t; } template ::value, nullptr_t> = nullptr> void dump(const U &t) { cerr << t; } template void dump(const T &t, enable_if_t::value> * = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if (is_signed::value) if (t == -Nyaan::inf) res = "-inf"; if (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if (is_signed::value) if (t == -Nyaan::infLL) res = "-inf"; } if (res.empty()) res = to_string(t); cerr << res; } template void dump(const pair &); template void dump(const pair &); template void dump(const T &t, enable_if_t::value> * = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template void dump(const pair &t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template void dump(const pair &t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template void trace(Head &&head, Tail &&...tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) #endif // macro #define each(x, v) for (auto &&x : v) #define each2(x, y, v) for (auto &&[x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define repc(i, a, cond) for (long long i = (a); (cond); i++) #define enm(i, val, vec) \ for (long long i = 0; i < (long long)(vec).size(); i++) \ if (auto &val = vec[i]; false) \ ; \ else #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define inc(...) \ char __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // namespace HashMapImpl { using u32 = uint32_t; using u64 = uint64_t; template struct HashMapBase; template struct itrB : iterator { using base = iterator; using ptr = typename base::pointer; using ref = typename base::reference; u32 i; HashMapBase *p; explicit constexpr itrB() : i(0), p(nullptr) {} explicit constexpr itrB(u32 _i, HashMapBase *_p) : i(_i), p(_p) {} explicit constexpr itrB(u32 _i, const HashMapBase *_p) : i(_i), p(const_cast *>(_p)) {} friend void swap(itrB &l, itrB &r) { swap(l.i, r.i), swap(l.p, r.p); } friend bool operator==(const itrB &l, const itrB &r) { return l.i == r.i; } friend bool operator!=(const itrB &l, const itrB &r) { return l.i != r.i; } const ref operator*() const { return const_cast *>(p)->data[i]; } ref operator*() { return p->data[i]; } ptr operator->() const { return &(p->data[i]); } itrB &operator++() { assert(i != p->cap && "itr::operator++()"); do { i++; if (i == p->cap) break; if (p->flag[i] == true && p->dflag[i] == false) break; } while (true); return (*this); } itrB operator++(int) { itrB it(*this); ++(*this); return it; } itrB &operator--() { do { i--; if (p->flag[i] == true && p->dflag[i] == false) break; assert(i != 0 && "itr::operator--()"); } while (true); return (*this); } itrB operator--(int) { itrB it(*this); --(*this); return it; } }; template struct HashMapBase { using u32 = uint32_t; using u64 = uint64_t; using iterator = itrB; using itr = iterator; protected: template ::value, nullptr_t> = nullptr, enable_if_t::value, nullptr_t> = nullptr> inline u32 inner_hash(const K &key) const { return u32((u64(key ^ r) * 11995408973635179863ULL) >> shift); } template < typename K, enable_if_t::value, nullptr_t> = nullptr, enable_if_t::value, nullptr_t> = nullptr, enable_if_t::value, nullptr_t> = nullptr> inline u32 inner_hash(const K &key) const { u64 a = key.first ^ r; u64 b = key.second ^ r; a *= 11995408973635179863ULL; b *= 10150724397891781847ULL; return u32((a + b) >> shift); } template ::value, nullptr_t> = nullptr> inline u32 hash(const D &dat) const { return inner_hash(dat); } template < typename D = Data, enable_if_t::value, nullptr_t> = nullptr> inline u32 hash(const D &dat) const { return inner_hash(dat.first); } template ::value, nullptr_t> = nullptr> inline Key dtok(const D &dat) const { return dat; } template < typename D = Data, enable_if_t::value, nullptr_t> = nullptr> inline Key dtok(const D &dat) const { return dat.first; } void reallocate(u32 ncap) { vector ndata(ncap); vector nf(ncap); shift = 64 - __lg(ncap); for (u32 i = 0; i < cap; i++) { if (flag[i] == true && dflag[i] == false) { u32 h = hash(data[i]); while (nf[h]) h = (h + 1) & (ncap - 1); ndata[h] = data[i]; nf[h] = true; } } data.swap(ndata); flag.swap(nf); cap = ncap; dflag.resize(cap); fill(std::begin(dflag), std::end(dflag), false); } inline bool extend_rate(u32 x) const { return x * 2 >= cap; } inline bool shrink_rate(u32 x) const { return HASHMAP_DEFAULT_SIZE < cap && x * 10 <= cap; } inline void extend() { reallocate(cap << 1); } inline void shrink() { reallocate(cap >> 1); } public: u32 cap, s; vector data; vector flag, dflag; u32 shift; static u64 r; static constexpr uint32_t HASHMAP_DEFAULT_SIZE = 4; explicit HashMapBase() : cap(HASHMAP_DEFAULT_SIZE), s(0), data(cap), flag(cap), dflag(cap), shift(64 - __lg(cap)) {} itr begin() const { u32 h = 0; while (h != cap) { if (flag[h] == true && dflag[h] == false) break; h++; } return itr(h, this); } itr end() const { return itr(this->cap, this); } friend itr begin(const HashMapBase &h) { return h.begin(); } friend itr end(const HashMapBase &h) { return h.end(); } itr find(const Key &key) const { u32 h = inner_hash(key); while (true) { if (flag[h] == false) return this->end(); if (dtok(data[h]) == key) { if (dflag[h] == true) return this->end(); return itr(h, this); } h = (h + 1) & (cap - 1); } } bool contain(const Key &key) const { return find(key) != this->end(); } itr insert(const Data &d) { u32 h = hash(d); while (true) { if (flag[h] == false) { if (extend_rate(s + 1)) { extend(); h = hash(d); continue; } data[h] = d; flag[h] = true; ++s; return itr(h, this); } if (dtok(data[h]) == dtok(d)) { if (dflag[h] == true) { data[h] = d; dflag[h] = false; ++s; } return itr(h, this); } h = (h + 1) & (cap - 1); } } // tips for speed up : // if return value is unnecessary, make argument_2 false. itr erase(itr it, bool get_next = true) { if (it == this->end()) return this->end(); s--; if (shrink_rate(s)) { Data d = data[it.i]; shrink(); it = find(dtok(d)); } int ni = (it.i + 1) & (cap - 1); if (this->flag[ni]) { this->dflag[it.i] = true; } else { this->flag[it.i] = false; } if (get_next) ++it; return it; } itr erase(const Key &key) { return erase(find(key)); } bool empty() const { return s == 0; } int size() const { return s; } void clear() { fill(std::begin(flag), std::end(flag), false); fill(std::begin(dflag), std::end(dflag), false); s = 0; } void reserve(int n) { if (n <= 0) return; n = 1 << min(23, __lg(n) + 2); if (cap < u32(n)) reallocate(n); } }; template uint64_t HashMapBase::r = chrono::duration_cast( chrono::high_resolution_clock::now().time_since_epoch()) .count(); } // namespace HashMapImpl /** * @brief Hash Map(base) (ハッシュマップ・基底クラス) */ template struct HashMap : HashMapImpl::HashMapBase> { using base = typename HashMapImpl::HashMapBase>; using HashMapImpl::HashMapBase>::HashMapBase; using Data = pair; Val &operator[](const Key &k) { typename base::u32 h = base::inner_hash(k); while (true) { if (base::flag[h] == false) { if (base::extend_rate(base::s + 1)) { base::extend(); h = base::hash(k); continue; } base::data[h].first = k; base::data[h].second = Val(); base::flag[h] = true; ++base::s; return base::data[h].second; } if (base::data[h].first == k) { if (base::dflag[h] == true) base::data[h].second = Val(); return base::data[h].second; } h = (h + 1) & (base::cap - 1); } } typename base::itr emplace(const Key &key, const Val &val) { return base::insert(Data(key, val)); } }; /* * @brief ハッシュマップ(連想配列) * @docs docs/hashmap/hashmap.md **/ namespace my_rand { // [0, 2^64 - 1) uint64_t rng() { static uint64_t x_ = uint64_t(chrono::duration_cast( chrono::high_resolution_clock::now().time_since_epoch()) .count()) * 10150724397891781847ULL; x_ ^= x_ << 7; return x_ ^= x_ >> 9; } // [l, r) int64_t randint(int64_t l, int64_t r) { assert(l < r); return l + rng() % (r - l); } // choose n numbers from [l, r) without overlapping vector randset(int64_t l, int64_t r, int64_t n) { assert(l <= r && n <= r - l); unordered_set s; for (int64_t i = n; i; --i) { int64_t m = randint(l, r + 1 - i); if (s.find(m) != s.end()) m = r - i; s.insert(m); } vector ret; for (auto &x : s) ret.push_back(x); return ret; } // [0.0, 1.0) double rnd() { union raw_cast { double t; uint64_t u; }; constexpr uint64_t p = uint64_t(1023 - 64) << 52; return rng() * ((raw_cast *)(&p))->t; } template void randshf(vector &v) { int n = v.size(); for (int loop = 0; loop < 2; loop++) for (int i = 0; i < n; i++) swap(v[i], v[randint(0, n)]); } } // namespace my_rand using my_rand::randint; using my_rand::randset; using my_rand::randshf; using my_rand::rnd; using my_rand::rng; using namespace Nyaan; void Nyaan::solve() { inl(K, N); vl a(K), b(K); in(a, b); vl aa = a; if (N < K) die(a[N]); V hash(K); rep(i, K) hash[i] = rng(); auto hs = [&](const vl &v) { u64 res = 0; rep(i, K) res += v[i] * hash[i]; return res; }; HashMap mp; mp[hs(a)] = K - 1; int shuki = -1; int hairu = -1; for (int i = K;; i++) { ll x = -infLL; rep(j, K) amax(x, min(a[i + j - K], b[j])); if(i == N) die(x); a.push_back(x); u64 h = 0; rep(j, K) h += hash[j] * a[i + j + 1 - K]; if (mp.find(h) != mp.end()) { hairu = mp[h]; shuki = mp[h] - i; break; } mp[h] = i; } for (int i = K;; i++) if (hairu <= i and i % shuki == N % shuki) die(a[i]); }