#1185232 (C++23) No.3688 LCM Sum

• 問題: No.3688 LCM Sum
• ユーザー: ooaiu
• 提出日時: 2026-09-09 16:37:20
• 言語: C++23 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: TLE
• 実行時間: -
• コード長: 16,443 bytes
• コンパイル時間: 3,735 ms
• コンパイル使用メモリ: 452,272 KB
• 実行使用メモリ: 245,324 KB
• 最終ジャッジ日時: 2026-09-09 16:38:35
• 合計ジャッジ時間: 60,540 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge3_0

ファイルパターン	結果
sample	TLE * 3
other	TLE * 11

ソースコード

/*https://nyaannyaan.github.io/library/multiplicative-function/enamurate-multiplicative-function.hpp*/
#include <bits/stdc++.h>
using namespace std;
#line 2 "multiplicative-function/enamurate-multiplicative-function.hpp"

#line 2 "prime/prime-enumerate.hpp"

vector<int> prime_enumerate(int N) {
    vector<bool> sieve(N / 3 + 1, 1);
    for (int p = 5, d = 4, i = 1, sqn = sqrt(N); p <= sqn; p += d = 6 - d, i++) {
        if (!sieve[i]) continue;
        for (int q = p * p / 3, r = d * p / 3 + (d * p % 3 == 2), s = 2 * p,
                 qe = sieve.size();
             q < qe; q += r = s - r)
            sieve[q] = 0;
    }
    vector<int> ret{2, 3};
    for (int p = 5, d = 4, i = 1; p <= N; p += d = 6 - d, i++)
        if (sieve[i]) ret.push_back(p);
    while (!ret.empty() && ret.back() > N) ret.pop_back();
    return ret;
}
#line 2 "template/template.hpp"
using namespace std;

#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
    template <typename... Args>
    P(Args... args) : pair<T, U>(args...) {}

    using pair<T, U>::first;
    using pair<T, U>::second;

    P& operator+=(const P& r) {
        first += r.first;
        second += r.second;
        return *this;
    }
    P& operator-=(const P& r) {
        first -= r.first;
        second -= r.second;
        return *this;
    }
    P& operator*=(const P& r) {
        first *= r.first;
        second *= r.second;
        return *this;
    }
    template <typename S>
    P& operator*=(const S& r) {
        first *= r, second *= r;
        return *this;
    }
    P operator+(const P& r) const { return P(*this) += r; }
    P operator-(const P& r) const { return P(*this) -= r; }
    P operator*(const P& r) const { return P(*this) *= r; }
    template <typename S>
    P operator*(const S& r) const {
        return P(*this) *= r;
    }
    P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T& t) {
    return t.size();
}

template <typename T, typename U>
inline bool amin(T& x, U y) {
    return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T& x, U y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T>& v) {
    return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T>& v) {
    return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T>& v) {
    return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T>& v, const T& a) {
    return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T>& v, const T& a) {
    return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
    long long ret = 1, x = 10;
    for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
    return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T& t, const U& u) {
    return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T>& v, bool rev = false) {
    vector<T> ret(v.size() + 1);
    if (rev) {
        for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
    } else {
        for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
    }
    return ret;
};

template <typename T>
vector<T> mkuni(const vector<T>& v) {
    vector<T> ret(v);
    sort(ret.begin(), ret.end());
    ret.erase(unique(ret.begin(), ret.end()), ret.end());
    return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
    vector<int> ord(N);
    iota(begin(ord), end(ord), 0);
    sort(begin(ord), end(ord), f);
    return ord;
}

template <typename T>
vector<int> mkinv(vector<T>& v) {
    int max_val = *max_element(begin(v), end(v));
    vector<int> inv(max_val + 1, -1);
    for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
    return inv;
}

vector<int> mkiota(int n) {
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    return ret;
}

template <typename T>
T mkrev(const T& v) {
    T w{v};
    reverse(begin(w), end(w));
    return w;
}

template <typename T>
bool nxp(T& v) {
    return next_permutation(begin(v), end(v));
}

template <typename T>
vector<vector<T>> product(const vector<T>& a) {
    vector<vector<T>> ret;
    vector<T> v;
    auto dfs = [&](auto rc, int i) -> void {
        if (i == (int)a.size()) {
            ret.push_back(v);
            return;
        }
        for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
    };
    dfs(dfs, 0);
    return ret;
}

template <typename T>
T Power(T a, long long n, const T& I, const function<void(T&)>& f) {
    T res = I;
    for (; n; f(a = a * a), n >>= 1) {
        if (n & 1) f(res = res * a);
    }
    return res;
}
template <typename T>
T Power(T a, long long n, const T& I = T{1}) {
    return Power(a, n, I, function<void(T&)>{[](T&) -> void {}});
}

template <typename T>
T Rev(const T& v) {
    T res = v;
    reverse(begin(res), end(res));
    return res;
}

template <typename T>
vector<T> Transpose(const vector<T>& v) {
    using U = typename T::value_type;
    if (v.empty()) return {};
    int H = v.size(), W = v[0].size();
    vector res(W, T(H, U{}));
    for (int i = 0; i < H; i++) {
        for (int j = 0; j < W; j++) {
            res[j][i] = v[i][j];
        }
    }
    return res;
}

template <typename T>
vector<T> Rotate(const vector<T>& v, int clockwise = true) {
    using U = typename T::value_type;
    int H = v.size(), W = v[0].size();
    vector res(W, T(H, U{}));
    for (int i = 0; i < H; i++) {
        for (int j = 0; j < W; j++) {
            if (clockwise) {
                res[W - 1 - j][i] = v[i][j];
            } else {
                res[j][H - 1 - i] = v[i][j];
            }
        }
    }
    return res;
}

}  // namespace Nyaan
#line 58 "template/template.hpp"

#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64& a) {
    return __builtin_popcountll(a);
}
inline int lsb(const u64& a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64& a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64& a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T& a, int i) {
    return (a >> i) & 1;
}
template <typename T>
inline void sbit(T& a, int i, bool b) {
    if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan
#line 61 "template/template.hpp"

#line 1 "template/inout.hpp"
namespace Nyaan {

template <typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream& operator>>(istream& is, pair<T, U>& p) {
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
    for (auto& x : v) is >> x;
    return is;
}

istream& operator>>(istream& is, __int128_t& x) {
    string S;
    is >> S;
    x = 0;
    int flag = 0;
    for (auto& c : S) {
        if (c == '-') {
            flag = true;
            continue;
        }
        x *= 10;
        x += c - '0';
    }
    if (flag) x = -x;
    return is;
}

istream& operator>>(istream& is, __uint128_t& x) {
    string S;
    is >> S;
    x = 0;
    for (auto& c : S) {
        x *= 10;
        x += c - '0';
    }
    return is;
}

ostream& operator<<(ostream& os, __int128_t x) {
    if (x == 0) return os << 0;
    if (x < 0) os << '-', x = -x;
    string S;
    while (x) S.push_back('0' + x % 10), x /= 10;
    reverse(begin(S), end(S));
    return os << S;
}
ostream& operator<<(ostream& os, __uint128_t x) {
    if (x == 0) return os << 0;
    string S;
    while (x) S.push_back('0' + x % 10), x /= 10;
    reverse(begin(S), end(S));
    return os << S;
}

void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

struct IoSetupNya {
    IoSetupNya() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetupnya;

}  // namespace Nyaan
#line 64 "template/template.hpp"

#line 1 "template/debug.hpp"
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U,
    typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U,
    typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

void dump(__int128_t t) {
    if (t == 0) cerr << 0;
    if (t < 0) cerr << '-', t = -t;
    string S;
    while (t) S.push_back('0' + t % 10), t /= 10;
    reverse(begin(S), end(S));
    cerr << S;
}

void dump(__uint128_t t) {
    if (t == 0) cerr << 0;
    string S;
    while (t) S.push_back('0' + t % 10), t /= 10;
    reverse(begin(S), end(S));
    cerr << S;
}

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
    cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
    string res;
    if (t == Nyaan::inf) res = "inf";
    if constexpr (is_signed<T>::value) {
        if (t == -Nyaan::inf) res = "-inf";
    }
    if constexpr (sizeof(T) == 8) {
        if (t == Nyaan::infLL) res = "inf";
        if constexpr (is_signed<T>::value) {
            if (t == -Nyaan::infLL) res = "-inf";
        }
    }
    if (res.empty()) res = to_string(t);
    cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
    cerr << "[ ";
    for (auto it = t.begin(); it != t.end();) {
        dump(*it);
        cerr << (++it == t.end() ? "" : ", ");
    }
    cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
    cerr << "( ";
    dump(t.first);
    cerr << ", ";
    dump(t.second);
    cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
    cerr << "[ ";
    for (int i = 0; i < t.second; i++) {
        dump(t.first[i]);
        cerr << (i == t.second - 1 ? "" : ", ");
    }
    cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
    cerr << " ";
    dump(head);
    if (sizeof...(tail) != 0) cerr << ",";
    trace(std::forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                                \
    do {                                        \
        cerr << "## " << #__VA_ARGS__ << " = "; \
        DebugImpl::trace(__VA_ARGS__);          \
    } while (0)
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...)                               \
    do {                                        \
        cerr << "## " << #__VA_ARGS__ << " = "; \
        DebugImpl::trace(__VA_ARGS__);          \
    } while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"

#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)     \
    int __VA_ARGS__; \
    in(__VA_ARGS__)
#define inl(...)           \
    long long __VA_ARGS__; \
    in(__VA_ARGS__)
#define ins(...)        \
    string __VA_ARGS__; \
    in(__VA_ARGS__)
#define in2(s, t)                             \
    for (int i = 0; i < (int)s.size(); i++) { \
        in(s[i], t[i]);                       \
    }
#define in3(s, t, u)                          \
    for (int i = 0; i < (int)s.size(); i++) { \
        in(s[i], t[i], u[i]);                 \
    }
#define in4(s, t, u, v)                       \
    for (int i = 0; i < (int)s.size(); i++) { \
        in(s[i], t[i], u[i], v[i]);           \
    }
#define die(...)                 \
    do {                         \
        Nyaan::out(__VA_ARGS__); \
        return;                  \
    } while (0)
#line 70 "template/template.hpp"

#line 5 "multiplicative-function/enamurate-multiplicative-function.hpp"


template <typename T, T (*f)(int, int, int)>
struct enamurate_multiplicative_function {
    enamurate_multiplicative_function(int _n)
        : ps(prime_enumerate(_n)), a(_n + 1, T()), n(_n), p(ps.size()) {}

    vector<T> run() {
        a[1] = 1;
        dfs(-1, 1, 1);
        return a;
    }

   private:
    vector<int> ps;
    vector<T> a;
    int n, p;
    void dfs(int i, long long x, T y) {
        a[x] = y;
        if (y == T()) return;
        for (int j = i + 1; j < p; j++) {
            long long nx = x * ps[j];
            long long dx = ps[j];
            if (nx > n) break;
            for (int c = 1; nx <= n; nx *= ps[j], dx *= ps[j], ++c) {
                dfs(j, nx, y * f(dx, ps[j], c));
            }
        }
    }
};

/**
 * @brief 乗法的関数の列挙
 */
#include <atcoder/modint>
using mint = atcoder::modint998244353;
int N, M;
const int maxn = 30'000'001;
mint f(int n, int p, int e) {
    return mint(1 - p) / n;
}
mint s(int n) { return mint(long(n) * (n + 1)); }
int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cin >> N >> M;
    if (N > M) swap(N, M);
    enamurate_multiplicative_function<mint, f> A(maxn);
    auto mu = A.run();
    mint ans;
    for (int g = 1; g <= N; g++) {
        ans += mu[g] * g * g * s(N / g) * s(M / g);
    }
    ans *= mint::raw(2).inv().pow(2);
    cout << ans.val() << "\n";
}