#include using namespace std; using LL = long long int; #define incID(i, l, r) for(int i = (l) ; i < (r); ++i) #define decID(i, l, r) for(int i = (r) - 1; i >= (l); --i) #define incII(i, l, r) for(int i = (l) ; i <= (r); ++i) #define decII(i, l, r) for(int i = (r) ; i >= (l); --i) #define inc(i, n) incID(i, 0, n) #define dec(i, n) decID(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec1(i, n) decII(i, 1, n) #define inID(v, l, r) ((l) <= (v) && (v) < (r)) #define inII(v, l, r) ((l) <= (v) && (v) <= (r)) #define PB push_back #define EB emplace_back #define MP make_pair #define FI first #define SE second #define FR front() #define BA back() #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() auto setmin = [](auto & a, auto b) { return (b < a ? a = b, true : false); }; auto setmax = [](auto & a, auto b) { return (b > a ? a = b, true : false); }; auto setmineq = [](auto & a, auto b) { return (b <= a ? a = b, true : false); }; auto setmaxeq = [](auto & a, auto b) { return (b >= a ? a = b, true : false); }; #define SI(v) static_cast(v.size()) #define RF(e, v) for(auto & e: v) #define until(e) while(! (e)) #define if_not(e) if(! (e)) #define ef else if #define UR assert(false) #define IN(T, ...) T __VA_ARGS__; IN_(__VA_ARGS__); void IN_() { }; template void IN_(T & a, U & ... b) { cin >> a; IN_(b ...); }; template void OUT(T && a) { cout << a << endl; } template void OUT(T && a, U && ... b) { cout << a << " "; OUT(b ...); } // ---- ---- template class SegmentTree { private: int n, s; vector a; function f; T e; bool ok; public: SegmentTree() { n = 0; } SegmentTree(int nn, function ff, T ee) { init(nn, ff, ee); } void init(int nn, function ff, T ee) { n = nn; f = ff; e = ee; s = 1; while(s < n) { s *= 2; } a = vector(2 * s, e); ok = true; } void shift(int & p) { assert(inID(p, 0, n)); p += s; } void apply(int p, function g) { shift(p); g(a[p]); while(p > 1) { p /= 2; a[p] = f(a[2 * p], a[2 * p + 1]); } } T fold_ID(int l, int r) { assert(ok); assert(inII(l, 0, n)); l += s; assert(inII(r, 0, n)); r += s; r--; T x = e, y = e; while(l <= r) { if(l % 2 == 1) { x = f(x, a[l]); l++; } if(r % 2 == 0) { y = f(a[r], y); r--; } l /= 2; r /= 2; } return f(x, y); } T fold_II(int l, int r) { return fold_ID(l + 0, r + 1); } T fold_CI(int l, int r) { return fold_ID(l + 1, r + 1); } T fold_CD(int l, int r) { return fold_ID(l + 1, r + 0); } const T & operator[](int p) { shift(p); return a[p]; } T & ref(int p) { shift(p); ok = false; return a[p]; } void update() { dec(i, s) { a[i] = f(a[2 * i], a[2 * i + 1]); } ok = true; } }; #define OP(s) [&](auto & A, auto & B) { return s; } #define AP(s) [&](auto & A) { s; } // ---- auto fl = [](auto a, auto b) { assert(b != 0); return a / b - (a % b != 0 && ((a >= 0) != (b >= 0)) ? 1 : 0); }; auto ce = [](auto a, auto b) { assert(b != 0); return a / b + (a % b != 0 && ((a >= 0) == (b >= 0)) ? 1 : 0); }; auto mo = [](auto a, auto b) { assert(b != 0); a %= b; if(a < 0) { a += abs(b); } return a; }; int main() { const int M = 1'200'036, INF = M + 1; vector f(M + 1, INF); incII(i, 2, M) { if_not(f[i] == INF) { continue; } for(int j = i; j <= M; j += i) { setmin(f[j], i); } } IN(LL, l, h); LL n = h - l + 1; if(n < M) { vector s(n, INF); inc1(i, 100'000) { if_not(f[i] == i) { continue; } for(LL j = max(2LL, ce(l, i)) * i; j <= h; j += i) { setmin(s[j - l], i); } } pair ma = { -1, -1 }; dec(j, n) { if(s[j] == INF) { continue; } setmax(ma, make_pair(s[j], j + l)); } OUT(ma.SE); } else { SegmentTree> st(M + 1, OP(max(A, B)), { -1, -1 }); incII(i, 2, M) { st.ref(i) = { f[i], i }; } st.update(); LL r = 100'000; until(r * r <= h) { r--; } dec1(i, r) { if(i == 1) { UR; } if_not(f[i] == i) { continue; } assert(ce(h, i) <= M); auto ma = st.fold_II(ce(l, i), fl(h, i)); if(ma.FI >= i) { OUT(ma.SE * i); break; } } } /* pair ans = { -1, -1 }; incII(i_, l, h) { LL i = i_; incID(j_, 2, i) { LL j = j_; if(j * j > i) { break; } if(i % j == 0) { setmax(ans, make_pair(j, i)); break; } } } OUT(ans); */ }