#pragma GCC optimize ("O3") #include // clang-format off using namespace std; using ll = long long int; #define all(v) (v).begin(),(v).end() #define repeat(cnt,l) for(typename remove_const::type>::type cnt={};(cnt)<(l);++(cnt)) #define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt)) #define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt)) #define increase(cnt,b,e) for(auto cnt=(b);(cnt)<(e);++(cnt)) #define decrease(cnt,b,e) for(auto cnt=(b);(e)<=(cnt);--(cnt)) const long long MD = 1000000007; const long double PI = 3.1415926535897932384626433832795L; template inline ostream& operator <<(ostream &o, const pair p) { o << '(' << p.first << ':' << p.second << ')'; return o; } template inline T& chmax(T& to, const T& val) { return to = max(to, val); } template inline T& chmin(T& to, const T& val) { return to = min(to, val); } void bye(string s, int code = 0) { cout << s << endl; exit(code); } mt19937_64 randdev(8901016); template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution(l, h)(rand); } template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution(l, h)(rand); }template static ostream& operator<<(ostream& o, const std::vector& v) { o << "[ "; for(const auto& e : v) o< struct MyRangeFormat{ I b,e; MyRangeFormat(I _b, I _e):b(_b),e(_e){} }; template static ostream& operator<<(ostream& o, const MyRangeFormat& f) { o << "[ "; iterate(i,f.b,f.e) o<<*i<<' '; return o << ']'; } template struct MyMatrixFormat{ const I& p; long long n, m; MyMatrixFormat(const I& _p, long long _n, long long _m):p(_p),n(_n),m(_m){} }; template static ostream& operator<<(ostream& o, const MyMatrixFormat& f) { o<<'\n'; repeat(i,(f.n)) { repeat(j,f.m) o<(m,m+w)) #define FMTR(b,e) (MyRangeFormat(b,e)) #define FMTV(v) FMTR(v.begin(),v.end()) #define FMTM(m,h,w) (MyMatrixFormat(m,h,w)) #if defined(_WIN32) || defined(_WIN64) #define getc_x _getc_nolock #define putc_x _putc_nolock #elif defined(__GNUC__) #define getc_x getc_unlocked #define putc_x putc_unlocked #else #define getc_x getc #define putc_x putc #endif class MaiScanner { FILE* fp_; constexpr bool isvisiblechar(char c) noexcept { return (0x21<=(c)&&(c)<=0x7E); } public: inline MaiScanner(FILE* fp):fp_(fp){} template void input_integer(T& var) noexcept { var = 0; T sign = 1; int cc = getc_x(fp_); for (; cc < '0' || '9' < cc; cc = getc_x(fp_)) if (cc == '-') sign = -1; for (; '0' <= cc && cc <= '9'; cc = getc_x(fp_)) var = (var << 3) + (var << 1) + cc - '0'; var = var * sign; } inline int c() noexcept { return getc_x(fp_); } template::value, nullptr_t>::type = nullptr> inline MaiScanner& operator>>(T& var) noexcept { input_integer(var); return *this; } inline MaiScanner& operator>>(string& var) { int cc = getc_x(fp_); for (; !isvisiblechar(cc); cc = getc_x(fp_)); for (; isvisiblechar(cc); cc = getc_x(fp_)) var.push_back(cc); return *this; } template inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; class MaiPrinter { FILE* fp_; public: inline MaiPrinter(FILE* fp):fp_(fp){} template void output_integer(T var) noexcept { if (var == 0) { putc_x('0', fp_); return; } if (var < 0) putc_x('-', fp_), var = -var; char stack[32]; int stack_p = 0; while (var) stack[stack_p++] = '0' + (var % 10), var /= 10; while (stack_p) putc_x(stack[--stack_p], fp_); } inline MaiPrinter& operator<<(char c) noexcept { putc_x(c, fp_); return *this; } template::value, nullptr_t>::type = nullptr> inline MaiPrinter& operator<<(T var) noexcept { output_integer(var); return *this; } inline MaiPrinter& operator<<(const char* str_p) noexcept { while (*str_p) putc_x(*(str_p++), fp_); return *this; } inline MaiPrinter& operator<<(const string& str) { const char* p = str.c_str(); const char* l = p + str.size(); while (p < l) putc_x(*p++, fp_); return *this; } template void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; } }; MaiScanner scanner(stdin); MaiPrinter printer(stdout); // clang-format on // template template class Prime { int d_[Max + 1]; int n_; int li_[std::max(10000, Max / 10)]; public: constexpr Prime() : d_(), n_(), li_() { d_[0] = d_[1] = 0; for (int i = 2; i <= Max; i += 2) { d_[i] = 2; } n_ = 1; li_[0] = 2; int p = 3; for (p = 3; p * p <= Max; p += 2) { if (d_[p] != 0) continue; d_[p] = p; li_[n_++] = p; for (int j = p * p; j <= Max; j += p) { // i*i d_[j] = p; } } for (; p <= Max; p += 2) { if (d_[p] != 0) continue; d_[p] = p; li_[n_++] = p; } } constexpr inline bool isPrime(int x) const { return (x >= 2) && (x == 2 || d_[x] == x); } constexpr inline int size() const { return n_; } constexpr inline int operator[](int i) const { return li_[i]; } class iterator { const Prime& pl; int ptr = 0; public: constexpr iterator(const decltype(pl)& _pl, int _ptr = 0) : pl(_pl), ptr(_ptr) {} constexpr int operator*() const { return pl[ptr]; } constexpr iterator& operator++() { ptr++; return *this; } // prefix constexpr inline bool operator!=(const iterator& it) const { return ptr != it.ptr ? !(pl.n_ <= ptr && pl.n_ <= it.ptr) : false; } constexpr inline bool operator==(const iterator& it) const { return ptr != it.ptr ? (pl.n_ <= ptr && pl.n_ <= it.ptr) : true; } }; constexpr Prime::iterator begin() const { return Prime::iterator(*this, 0); } constexpr Prime::iterator end() const { return Prime::iterator(*this, n_); } std::map division(long long number) const { std::map div; // for large number for (int i = 0; (long long)Max <= number && i < n_; ++i) { long long p = li_[i]; int c = 0; while (number / p * p == number) ++c, number /= p; if (c > 0) div[(int)p] = c; } if ((long long)Max <= number) { // guess it's prime number. div[number] += 1; return div; } while (number >= 2) { long long p = d_[number]; int c = 0; while (number / p * p == number) ++c, number /= p; if (c > 0) div[(int)p] = c; } return div; } }; // // sqrt(10**10) = 10**5 より大きな素数を見る必要は無い。 // 調べたいのは合成数。 // H 以下の合成数に sqrt(H) を超える素数を素因数に持つ可能性はあるが、 // その場合は、常に sqrt(H) 未満の素数を必ず素因数に持つ。 // よって、高々 sqrt(H) までの素数を予め列挙しておけば十分である。 constexpr int kMaxPrime = 101010; Prime prime; ll L, H; // int main() { cin >> L >> H; pair best(0, 0); // < 素因数, 値> rrepeat(pi, prime.size()) { ll p = prime[pi]; // H 以下の値だけを見たいので、H < p な素数は興味がない。 // H == p ならば、H は素数なので、H は解から除外出来る if (H <= p) continue; // H 以下かつ、p の倍数を満たす最大値を求める。最大以外の値は興味が無い。 ll h = H/p*p; // L 未満なら制約違反の値なので除く。 if (h < L) continue; // 素数は対象外 if (h == p) continue; // p は h の最小の素因数とは限らないので、最小の素因数を求めよう // TODO: この部分のならし計算量が不明。2や3等の小さな素数のヒット率が高いので、 // O(n/logn)より確実に小さくなる。 ll minp = p; for (ll p2 : prime) { if (h/p2*p2 == h) { chmin(minp, p2); break; } } chmax(best, pair(minp, h)); } cout << best.second << endl; return 0; }