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#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "my_template.hpp" #include "nt/sigma_0_sum.hpp" void test() { FOR(N, 1, 10000) { u64 ans = 0; FOR(x, 1, N + 1) ans += N / x; assert(ans == sigma_0_sum_small(N)); assert(ans == sigma_0_sum_large(N)); } u64 N = 1'000'000'000'000'000; u64 ANS = 34'693'207'724'724'246; // https://oeis.org/A057494 u64 a = sigma_0_sum_small(N); u64 b = sigma_0_sum_small(N); assert(a == ANS && b == ANS); } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } int main() { test(); solve(); }
#line 1 "test/1_mytest/sigma_0_sum.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #line 1 "my_template.hpp" #if defined(LOCAL) #include <my_template_compiled.hpp> #else // https://codeforces.com/blog/entry/96344 #pragma GCC optimize("Ofast,unroll-loops") // いまの CF だとこれ入れると動かない? // #pragma GCC target("avx2,popcnt") #include <bits/stdc++.h> using namespace std; using ll = long long; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template <class T> constexpr T infty = 0; template <> constexpr int infty<int> = 1'010'000'000; template <> constexpr ll infty<ll> = 2'020'000'000'000'000'000; template <> constexpr u32 infty<u32> = infty<int>; template <> constexpr u64 infty<u64> = infty<ll>; template <> constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000; template <> constexpr double infty<double> = infty<ll>; template <> constexpr long double infty<long double> = infty<ll>; using pi = pair<ll, ll>; using vi = vector<ll>; template <class T> using vc = vector<T>; template <class T> using vvc = vector<vc<T>>; template <class T> using vvvc = vector<vvc<T>>; template <class T> using vvvvc = vector<vvvc<T>>; template <class T> using vvvvvc = vector<vvvvc<T>>; template <class T> using pq = priority_queue<T>; template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; #define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__)) #define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template <typename T> T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template <typename T> T ceil(T x, T y) { return floor(x + y - 1, y); } template <typename T> T bmod(T x, T y) { return x - y * floor(x, y); } template <typename T> pair<T, T> divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template <typename T, typename U> T SUM(const vector<U> &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template <typename T> T POP(deque<T> &que) { T a = que.front(); que.pop_front(); return a; } template <typename T> T POP(pq<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(pqg<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(vc<T> &que) { T a = que.back(); que.pop_back(); return a; } template <typename F> ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template <typename F> double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc<int> s_to_vi(const string &S, char first_char) { vc<int> A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template <typename T, typename U> vector<T> cumsum(vector<U> &A, int off = 1) { int N = A.size(); vector<T> B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template <typename T> vector<int> argsort(const vector<T> &A) { vector<int> ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template <typename T> vc<T> rearrange(const vc<T> &A, const vc<int> &I) { vc<T> B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } template <typename T, typename... Vectors> void concat(vc<T> &first, const Vectors &... others) { vc<T> &res = first; (res.insert(res.end(), others.begin(), others.end()), ...); } #endif #line 3 "test/1_mytest/sigma_0_sum.test.cpp" #line 1 "nt/convex_floor_sum.hpp" // f: 凸, 非負, 単調増加を仮定 // above(x,y) : y > f(x) // slope(x,a,b) : f'(x) >= a/b // return : sum_[0,N) floor(f(x)) // https://qoj.ac/contest/1195/problem/6188 template <typename U, typename ANS_TYPE, typename F1, typename F2> ANS_TYPE convex_floor_sum(U N, F1 above, F2 slope) { if (N == 0) return 0; auto check = [&](U x, U y) -> bool { return x < N && above(x, y); }; using T = ANS_TYPE; auto max_add = [&](auto f, U& a, U& b, U c, U d) -> void { auto dfs = [&](auto& dfs, U c, U d) -> void { if (!f(a + c, b + d)) return; a += c, b += d, dfs(dfs, c + c, d + d); if (f(a + c, b + d)) a += c, b += d; }; dfs(dfs, c, d); }; assert(!above(0, 0)); U x = 0, y = 0; max_add([&](U x, U y) -> bool { return !above(x, y); }, x, y, 0, 1); ++y; T ANS = 2 * (y - 1); // [0,1) x [1,y) auto add_ANS = [&](U& x, U& y, U a, U b) -> void { U x0 = x, y0 = y; max_add(check, x, y, a, b); U n = (x - x0) / a; // (x0,y0) to (x,y) ANS += 2 * (y0 - 1) * (x - x0); ANS += (x - x0 + 1) * (y - y0 + 1) - (n + 1); }; add_ANS(x, y, 1, 0); vc<tuple<U, U, U, U>> SBT; SBT.eb(1, 0, 0, 1); while (x < N - 1) { U a, b, c, d; tie(a, b, c, d) = SBT.back(); if (!check(x + c, y + d)) { POP(SBT); continue; } auto f = [&](u64 a, u64 b) -> bool { if (x + a >= N) return 0; if (above(x + a, y + b)) return 0; if (slope(x + a, d, c)) return 0; return 1; }; max_add(f, a, b, c, d); if (check(x + a + c, y + b + d)) { max_add([&](U a, U b) -> bool { return check(x + a, y + b); }, c, d, a, b); SBT.eb(a, b, c, d); continue; } add_ANS(x, y, c, d); } ANS /= T(2); return ANS; } #line 2 "nt/sigma_0_sum.hpp" // sum_[1,N] sigma_0(n) template <typename T = u64> T sigma_0_sum_small(u64 N) { u32 sq = sqrtl(N); T ANS = 0; for (u32 d = 1; d <= sq; ++d) { ANS += N / d; } return 2 * ANS - u64(sq) * sq; } // https://oeis.org/A006218 // sigma0(1)+...+sigma0(N) = sum floor(N/i) template <typename T = u64> T sigma_0_sum_large(u64 N) { u32 sq = sqrtl(N); auto above = [&](u128 x, u128 y) -> bool { return y * (sq - x) > N; }; auto slope = [&](u128 x, u128 a, u128 b) -> bool { x = sq - x; return a * x * x <= N * b; }; T ANS = convex_floor_sum<u64, T>(sq, above, slope); return 2 * ANS - u64(sq) * sq; } template <typename T = u64> T sigma_0_sum(u64 N) { return (N < (1e14) ? sigma_0_sum_small<T>(N) : sigma_0_sum_large<T>(N)); } #line 5 "test/1_mytest/sigma_0_sum.test.cpp" void test() { FOR(N, 1, 10000) { u64 ans = 0; FOR(x, 1, N + 1) ans += N / x; assert(ans == sigma_0_sum_small(N)); assert(ans == sigma_0_sum_large(N)); } u64 N = 1'000'000'000'000'000; u64 ANS = 34'693'207'724'724'246; // https://oeis.org/A057494 u64 a = sigma_0_sum_small(N); u64 b = sigma_0_sum_small(N); assert(a == ANS && b == ANS); } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } int main() { test(); solve(); }