#1160355 (C++23) No.3505 Sum of Prod of Root

• 問題: No.3505 Sum of Prod of Root
• ユーザー: porkleoi
• 提出日時: 2026-04-19 07:29:27
• 言語: C++23 (gcc 15.2.0 + boost 1.89.0)
• 結果: TLE
• 実行時間: -
• コード長: 6,763 bytes
• コンパイル時間: 2,140 ms
• コンパイル使用メモリ: 343,280 KB
• 実行使用メモリ: 30,572 KB
• 最終ジャッジ日時: 2026-04-19 07:29:58
• 合計ジャッジ時間: 7,004 ms
• ジャッジサーバーID （参考情報）: judge1_1 / judge1_1

ファイルパターン	結果
sample	-- * 1
other	AC * 3 TLE * 1 -- * 9

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = a; i < b; i++)
#define rrep(i, a, b) for (int i = a-1; i >= b; i--)
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vvvi> vvvvi;
typedef vector<string> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<vvc> vvvc;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<vvll> vvvll;
typedef vector<vvvll> vvvvll;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<vvd> vvvd;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<bool> vb;
typedef vector<vd> vvb;
typedef vector<vvd> vvvb;
typedef vector<pair<int, int>> vpi;
typedef vector<pair<ll, ll>> vpll;
typedef pair<int, int> pi;
typedef vector<pi> vpi;
typedef vector<vpi> vvpi;
typedef pair<ll, ll> pll;
typedef vector<pll> vpll;
typedef vector<vpll> vvpll;
typedef tuple<int, int, int> tui3;
typedef tuple<ll, ll, ll> tull3;
typedef priority_queue<int, vector<int>, greater<int>> pqi;
typedef priority_queue<vi, vector<vi>, greater<vi>> pqvi;
typedef priority_queue<pi, vector<pi>, greater<pi>> pqpi;
typedef priority_queue<ll, vector<ll>, greater<ll>> pqll;
typedef priority_queue<vll, vector<vll>, greater<vll>> pqvll;
typedef priority_queue<pll, vector<pll>, greater<pll>> pqpll;
typedef priority_queue<pll, vector<pll>, less<pll>> rpqpll;
typedef priority_queue<int, vector<int>, less<int>> rpqi;
typedef priority_queue<vi, vector<vi>, less<vi>> rpqvi;
typedef priority_queue<tui3, vector<tui3>, greater<tui3>> pqtui3;
typedef priority_queue<tui3, vector<tui3>, less<tui3>> rpqtui3;
typedef priority_queue<tull3, vector<tull3>, greater<tull3>> pqtull3;
typedef priority_queue<tull3, vector<tull3>, less<tull3>> rpqtull3;
#define yes(ans) if(ans)cout << "yes"<< endl; else cout << "no" << endl
#define Yes(ans) if(ans)cout << "Yes"<< endl; else cout << "No" << endl
#define YES(ans) if(ans)cout << "YES"<< endl ;else cout << "NO" << endl
#define pos(ans) if(ans)cout << "Possible"<< endl ;else cout << "Impossible" << endl
#define printv(vec) {rep(i, 0, vec.size()) cout << vec[i] << ' '; cout << endl;}
#define printvv(vec) rep(i, 0, vec.size()) {rep(j, 0, vec[i].size()) cout << vec[i][j] << ' '; cout << endl;};
#define printvvv(vec) rep(i, 0, vec.size()) { rep(j, 0, vec[i].size()) { rep(k, 0, vec[i][j].size()) cout << vec[i][j][k] << ' '; cout << "	"; }cout << endl; };
#define all(x) x.begin(), x.end()
#define so(x) sort(all(x))
#define re(x) reverse(all(x))
#define rso(x) sort(x.rbegin(), x.rend())
#define vco(x, a) count(all(x), a)
#define per(x) next_permutation(all(x))
#define out(x) cout << x << endl
#define iINF 2147483647
#define llINF 9223372036854775807
#define INF 4000000000000000000
#define mod 998244353
#define mod2 1000000007
template<typename T> bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;}
template<typename T> bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;}

template<int MOD> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr int getmod() { return MOD; }
    constexpr Fp operator - () const noexcept {
        return val ? MOD - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD>& x) noexcept {
        return os << x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};
using mint = Fp<mod>;
typedef vector<mint> vm;
typedef vector<vm> vvm;
typedef vector<vvm> vvvm;
typedef vector<vvvm> vvvvm;

ll sqrt(ll x){
    ll l = 0, r = 3037000500;
    while(r-l>1){
        ll m = l+(r-l)/2;
        if(m*m>x) r = m;
        else l = m;
    }
    return l;
}

ll ksqrt(ll n, ll k){
    ll l = 0, r = 3037000500;
    while(r-l>1){
        ll m = l+(r-l)/2;
        ll x = 1;
        bool p = true;
        rep(i, 0, k){
            if((ld)x-(ld)n/(ld)m>0){
                p = false;
                break;
            }
            x *= m;
        }
        if(x>n || !p) r = m;
        else l = m;
    }
    return l;
}

int main() {
    ll n; cin >> n;
    set<ll> st;
    rep(i, 1, 1e6){
        ll x = 1;
        rep(j, 1, 65){
            if((ld)x-ld(n)/ld(i)>0) break;
            x *= i;
            if(j>=3) st.insert(x);
        }
    }
    st.insert(n+1);
    vll a;
    for(auto c:st) a.push_back(c);
    mint ans = 0;
    rep(i, 0, a.size()-1){
        ll p = a[i], q = a[i+1]-1;
        ll s1 = sqrt(p-1)+1, t1 = sqrt(q+1)-1;
        // cout << p << ' ' << q << ' ' << s1 << ' ' << t1 << endl;
        mint x = 1;
        rep(j, 3, 65) x *= ksqrt(p, j);
        mint s = s1, t = t1;
        if(s1<=t1){
            ans += (t*(t+1)*(t+2)*(t*(t*8+11)+1)-(s-1)*s*(s+1)*(s*(s*8-5)-2))/20*x;
            ans += (s*s-p)*(s*s+p-1)/2*(s-1)*x;
            ans += ((t+1)*(t+1)*(-1)+q+1)*((t+1)*(t+1)+q)/2*(t+1)*x;
        }
        else if(s1-t1==1){
            ans += (s*s-p)*(s*s-1+p)/2*(s-1)*x;
            ans += ((t+1)*(t+1)*(-1)+q+1)*((t+1)*(t+1)+q)/2*(t+1)*x;
        }
        else{
            ans += ((mint)p+q)*(mint(q-p+1))/2*(s+t)/2*x;
        }
        // cout << ans << endl;
    }
    cout << ans << endl;
}