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test/1_mytest/primesum_mod6.test.cpp
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- Last update: 2026-09-28 10:13:21+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
my_template.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "nt/prime_sum_mod6.hpp"
void test_count() {
ll LIM = 10000;
vc<int> A1(LIM), A5(LIM);
for (auto&& p : prime_table(LIM))
if (p % 6 == 1) {
A1[p]++;
}
for (auto&& p : prime_table(LIM))
if (p % 6 == 5) {
A5[p]++;
}
A1 = cumsum<int>(A1, 0);
A5 = cumsum<int>(A5, 0);
FOR(N, LIM) {
Prime_Sum_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 : prime_table(LIM))
if (p % 6 == 1) {
A1[p] += p;
}
for (auto&& p : prime_table(LIM))
if (p % 6 == 5) {
A5[p] += p;
}
A1 = cumsum<int>(A1, 0);
A5 = cumsum<int>(A5, 0);
FOR(N, LIM) {
Prime_Sum_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(USE_PCH)
#include <my_template_compiled.hpp>
#else
#if defined(__GNUC__)
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
// 環境によってはコンパイル成功かつ実行時エラー
#pragma GCC target("avx2,popcnt")
#endif
#include <bits/stdc++.h>
#include <cassert>
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>
constexpr bool dependent_false = false;
template <class T>
constexpr T infty = [] {
static_assert(dependent_false<T>, "infty<T> is not defined");
return T{};
}();
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<i128>;
template <>
constexpr long double infty<long double> = infty<i128>;
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 pq_max = priority_queue<T>;
template <class T>
using pq_min = 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 FOR1_R(a) for (ll i = ll(a) - 1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = ll(a) - 1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload3(__VA_ARGS__, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#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
// require y > 0
template <typename T>
T floor(T x, T y) {
return x / y - (x % y < 0);
}
// require y > 0
template <typename T>
T ceil(T x, T y) {
return (x / y) + (x % y > 0);
}
// require y > 0
template <typename T>
T bmod(T x, T y) {
T r = x % y;
return (r < 0 ? r + y : r);
}
// require y > 0
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = x / y, r = x % y;
if (r < 0) --q, r += y;
return {q, r};
}
constexpr auto TEN = [] {
array<u64, 20> A{};
A[0] = 1;
for (int i = 1; i < 20; ++i) A[i] = 10 * A[i - 1];
return A;
}();
template <typename T, typename U>
T SUM(const U &A) {
return std::accumulate(A.begin(), A.end(), T{});
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
template <class C, class T>
inline long long LB(const C &c, const T &x) {
return lower_bound(c.begin(), c.end(), x) - c.begin();
}
template <class C, class T>
inline long long UB(const C &c, const T &x) {
return upper_bound(c.begin(), c.end(), x) - c.begin();
}
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <class T, class Container, class Compare>
T POP(priority_queue<T, Container, Compare> &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>
i128 binary_search(F check, i128 ok, i128 ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (1) {
i128 x = (ok + ng) / 2;
if (x == ok || x == ng) break;
(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) {
T c = max<T>(a, b);
bool changed = (c != a);
a = c;
return changed;
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
T c = min<T>(a, b);
bool changed = (c != a);
a = c;
return changed;
}
// bit operations
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_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (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 kth_bit(int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return x >> k & 1;
}
template <typename T>
struct all_bit {
static_assert(is_integral<T>::value);
T s;
all_bit(T s) : s(s) { assert(s >= 0); }
struct iter {
T s;
int operator*() const { return lowbit(s); }
void operator++() { s &= s - 1; }
bool operator!=(nullptr_t) const { return s; }
};
iter begin() const { return {s}; }
nullptr_t end() const { return nullptr; }
};
template <typename T>
struct all_subset {
static_assert(is_integral<T>::value);
T s;
all_subset(T s) : s(s) { assert(s >= 0); }
struct iter {
T s, t;
bool done = false;
T operator*() const { return t; }
void operator++() {
done = (t == 0);
t = (t - 1) & s;
}
bool operator!=(nullptr_t) const { return !done; }
};
iter begin() const { return {s, s}; }
nullptr_t end() const { return nullptr; }
};
constexpr u64 full_mask(int n) {
assert(0 <= n && n <= 64);
return n == 64 ? -1ULL : (1ULL << n) - 1;
}
u64 bit_reverse(u64 x) {
x = ((x & 0x5555555555555555ULL) << 1) | ((x >> 1) & 0x5555555555555555ULL);
x = ((x & 0x3333333333333333ULL) << 2) | ((x >> 2) & 0x3333333333333333ULL);
x = ((x & 0x0f0f0f0f0f0f0f0fULL) << 4) | ((x >> 4) & 0x0f0f0f0f0f0f0f0fULL);
x = ((x & 0x00ff00ff00ff00ffULL) << 8) | ((x >> 8) & 0x00ff00ff00ff00ffULL);
x = ((x & 0x0000ffff0000ffffULL) << 16) | ((x >> 16) & 0x0000ffff0000ffffULL);
x = (x << 32) | (x >> 32);
return x;
}
// ? 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>
vc<T> cumsum(const vc<U> &A, int off = 1) {
int N = A.size();
vc<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>
vc<int> argsort(const vc<T> &A) {
vc<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) {
first.reserve(first.size() + (others.size() + ... + 0));
(first.insert(first.end(), others.begin(), others.end()), ...);
}
// i128
template <class T, enable_if_t<is_same_v<T, i128>, int> = 0>
constexpr i128 abs(T x) {
return x < 0 ? -x : x;
}
constexpr i128 gcd(i128 a, i128 b) {
while (b != 0) {
i128 c = a % b;
a = b, b = c;
}
return abs(a);
}
#endif
#line 1 "nt/prime_table.hpp"
template <typename T = int>
vc<T> prime_table(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);
return {primes.begin(), primes.begin() + k};
}
#line 2 "nt/prime_sum.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 Prime_Sum {
ll N;
ll sqN;
vc<T> sum_lo, sum_hi;
bool calculated;
Prime_Sum(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 = prime_table<int>(sqN);
sum_lo.resize(sqN + 1);
sum_hi.resize(sqN + 1);
FOR(i, 1, sqN + 1) sum_lo[i] = f(i) - 1;
FOR(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 1 "nt/prime_table.hpp"
template <typename T = int>
vc<T> prime_table(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);
return {primes.begin(), primes.begin() + k};
}
#line 3 "nt/prime_sum_mod6.hpp"
template <typename T>
struct Prime_Sum_Mod_6 {
ll N;
ll sqN;
Prime_Sum<T> A, B;
Prime_Sum_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 : prime_table(LIM))
if (p % 6 == 1) {
A1[p]++;
}
for (auto&& p : prime_table(LIM))
if (p % 6 == 5) {
A5[p]++;
}
A1 = cumsum<int>(A1, 0);
A5 = cumsum<int>(A5, 0);
FOR(N, LIM) {
Prime_Sum_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 : prime_table(LIM))
if (p % 6 == 1) {
A1[p] += p;
}
for (auto&& p : prime_table(LIM))
if (p % 6 == 5) {
A5[p] += p;
}
A1 = cumsum<int>(A1, 0);
A5 = cumsum<int>(A5, 0);
FOR(N, LIM) {
Prime_Sum_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;
}