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#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "my_template.hpp" #include "nt/primesum_mod6.hpp" void test_count() { ll LIM = 10000; vc<int> A1(LIM), A5(LIM); for (auto&& p: primetable(LIM)) if (p % 6 == 1) { A1[p]++; } for (auto&& p: primetable(LIM)) if (p % 6 == 5) { A5[p]++; } A1 = cumsum<int>(A1, 0); A5 = cumsum<int>(A5, 0); FOR(N, LIM) { PrimeSum_Mod_6<int> X(N); X.calc_count(); FOR(K, 1, N + 10) { assert(X[N / K] == mp(A1[N / K], A5[N / K])); } } } void test_sum() { ll LIM = 10000; vc<int> A1(LIM), A5(LIM); for (auto&& p: primetable(LIM)) if (p % 6 == 1) { A1[p] += p; } for (auto&& p: primetable(LIM)) if (p % 6 == 5) { A5[p] += p; } A1 = cumsum<int>(A1, 0); A5 = cumsum<int>(A5, 0); FOR(N, LIM) { PrimeSum_Mod_6<int> X(N); X.calc_sum(); FOR(K, 1, N + 10) { assert(X[N / K] == mp(A1[N / K], A5[N / K])); } } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test_count(); test_sum(); solve(); return 0; }
#line 1 "test/1_mytest/primesum_mod6.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 2 "nt/primetable.hpp" template <typename T = int> vc<T> primetable(int LIM) { ++LIM; const int S = 32768; static int done = 2; static vc<T> primes = {2}, sieve(S + 1); if (done < LIM) { done = LIM; primes = {2}, sieve.assign(S + 1, 0); const int R = LIM / 2; primes.reserve(int(LIM / log(LIM) * 1.1)); vc<pair<int, int>> cp; for (int i = 3; i <= S; i += 2) { if (!sieve[i]) { cp.eb(i, i * i / 2); for (int j = i * i; j <= S; j += 2 * i) sieve[j] = 1; } } for (int L = 1; L <= R; L += S) { array<bool, S> block{}; for (auto& [p, idx]: cp) for (int i = idx; i < S + L; idx = (i += p)) block[i - L] = 1; FOR(i, min(S, R - L)) if (!block[i]) primes.eb((L + i) * 2 + 1); } } int k = LB(primes, LIM + 1); return {primes.begin(), primes.begin() + k}; } #line 3 "nt/primesum.hpp" /* N と完全乗法的関数 f の prefix sum 関数 F を与える。 n = floor(N/d) となる n に対する sum_{p <= n} f(p) を計算する。 特に、素数の k 乗和や、mod m ごとでの素数の k 乗和が計算できる。 Complexity: O(N^{3/4}/logN) time, O(N^{1/2}) space. */ template <typename T> struct PrimeSum { ll N; ll sqN; vc<T> sum_lo, sum_hi; bool calculated; PrimeSum(ll N) : N(N), sqN(sqrtl(N)), calculated(0) {} // [1, x] ただし、x = floor(N, i) の形 T operator[](ll x) { assert(calculated); return (x <= sqN ? sum_lo[x] : sum_hi[double(N) / x]); } template <typename F> void calc(const F f) { auto primes = primetable<int>(sqN); sum_lo.resize(sqN + 1); sum_hi.resize(sqN + 1); FOR3(i, 1, sqN + 1) sum_lo[i] = f(i) - 1; FOR3(i, 1, sqN + 1) sum_hi[i] = f(double(N) / i) - 1; for (int p: primes) { ll pp = ll(p) * p; if (pp > N) break; int R = min(sqN, N / pp); int M = sqN / p; T x = sum_lo[p - 1]; T fp = sum_lo[p] - sum_lo[p - 1]; for (int i = 1; i <= M; ++i) sum_hi[i] -= fp * (sum_hi[i * p] - x); for (int i = M + 1; i <= R; ++i) sum_hi[i] -= fp * (sum_lo[N / (double(i) * p)] - x); for (int n = sqN; n >= pp; --n) sum_lo[n] -= fp * (sum_lo[n / p] - x); } calculated = 1; } void calc_count() { calc([](ll x) -> T { return x; }); } void calc_sum() { calc([](ll x) -> T { ll a = x, b = x + 1; if (!(x & 1)) a /= 2; if (x & 1) b /= 2; return T(a) * T(b); }); } }; #line 3 "nt/primesum_mod6.hpp" template <typename T> struct PrimeSum_Mod_6 { ll N; ll sqN; PrimeSum<T> A, B; PrimeSum_Mod_6(ll N) : N(N), sqN(sqrtl(N)), A(N), B(N) {} pair<T, T> operator[](ll x) { T a = A[x], b = B[x]; return {(a + b) / T(2), (a - b) / T(2)}; } void calc_count() { A.calc([](ll x) -> T { return ((x + 2) / 3 - (x % 6 == 4)); }); B.calc([](ll x) -> T { return ((x + 5) % 6 <= 3 ? 1 : 0); }); } void calc_sum() { A.calc([](ll x) -> T { ll n = (x + 2) / 3 - (x % 6 == 4); ll k = n / 2; if (n % 2 == 0) { return T(6 * k) * T(k); } return T(6 * k) * T(k) + T(6 * k + 1); }); B.calc([](ll x) -> T { ll n = (x + 2) / 3 - (x % 6 == 4); ll k = n / 2; if (n % 2 == 0) { return T(-4 * k); } return T(-4 * k + 6 * k + 1); }); } }; #line 4 "test/1_mytest/primesum_mod6.test.cpp" void test_count() { ll LIM = 10000; vc<int> A1(LIM), A5(LIM); for (auto&& p: primetable(LIM)) if (p % 6 == 1) { A1[p]++; } for (auto&& p: primetable(LIM)) if (p % 6 == 5) { A5[p]++; } A1 = cumsum<int>(A1, 0); A5 = cumsum<int>(A5, 0); FOR(N, LIM) { PrimeSum_Mod_6<int> X(N); X.calc_count(); FOR(K, 1, N + 10) { assert(X[N / K] == mp(A1[N / K], A5[N / K])); } } } void test_sum() { ll LIM = 10000; vc<int> A1(LIM), A5(LIM); for (auto&& p: primetable(LIM)) if (p % 6 == 1) { A1[p] += p; } for (auto&& p: primetable(LIM)) if (p % 6 == 5) { A5[p] += p; } A1 = cumsum<int>(A1, 0); A5 = cumsum<int>(A5, 0); FOR(N, LIM) { PrimeSum_Mod_6<int> X(N); X.calc_sum(); FOR(K, 1, N + 10) { assert(X[N / K] == mp(A1[N / K], A5[N / K])); } } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test_count(); test_sum(); solve(); return 0; }