結果
問題 | No.1781 LCM |
ユーザー |
|
提出日時 | 2024-11-10 06:48:22 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 3,558 ms / 5,000 ms |
コード長 | 3,876 bytes |
コンパイル時間 | 2,764 ms |
コンパイル使用メモリ | 230,464 KB |
実行使用メモリ | 56,652 KB |
最終ジャッジ日時 | 2024-11-10 06:48:53 |
合計ジャッジ時間 | 26,715 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 31 |
ソースコード
#include<bits/stdc++.h>using namespace std;#include<atcoder/modint>using namespace atcoder;using mint = modint998244353;using ll = long long;vector<bool> is_prime;vector<ll> Q_enum;vector<vector<int>> POW;unordered_map<ll, int> ID;vector<ll> DI;void enum_prime(ll N) {ll sq = sqrt(N);POW.resize(sq + 1);is_prime.assign(sq + 1, 1);is_prime[0] = is_prime[1] = 0;for (ll i = 0; i <= sq; i++) {if (is_prime[i]) {for (ll j = i * 2; j <= sq; j += i)is_prime[j] = 0;ll r = 1;int s = 0;while (r <= N) {s += (r % 3);POW[i].push_back(s % 3);r *= i;}}}return;}vector<int> sm, bg;void calc_Qenum(ll N) {ll sq = sqrt(N);sm.assign(sq + 100, -1);bg.assign(sq + 100, -1);for (int i = 1; i <= sq; i++) {Q_enum.emplace_back(N / i);ID[N / i] = ID.size();DI.push_back(N / i);}while (Q_enum.back() > 1) {ID[Q_enum.back() - 1] = ID.size();DI.push_back(Q_enum.back() - 1);Q_enum.emplace_back(Q_enum.back() - 1);}for (int i = 0; i < Q_enum.size(); i++) {ll n = Q_enum[i];if (n < sm.size())sm[n] = i;if (N / n < bg.size())bg[N / n] = i;}return;}ll A, B;mint sum_n(ll n, ll c) {if (c == 1) {return (n + 2) / 3 - 1;}if (c == 2)return (n + 1) / 3;else if (c == 0)return n / 3;return 1;}vector<mint> calc_Fprime(ll N) {ll sq = sqrt(N);int sz = Q_enum.size();vector<mint> F_pr(sz);for (int j = 0; j < sz; j++) {F_pr[j] = DI[j] - 1;}for (ll x = 2; x <= sq; x++) {if (is_prime[x]) {int y = (x - 1 < sm.size() ? sm[x - 1] : bg[N / (x - 1)]);for (int j = 0; j < sz; j++) {ll n = Q_enum[j];if (n < x * x)break;int u = (n / x < sm.size() ? sm[n / x] : bg[N / (n / x)]);if (Q_enum[u] != n / x) {cout << n << " " << x << " " << sq << " " << u<<" "<<Q_enum[u] << endl;}assert(Q_enum[u] == n / x);F_pr[j] -= mint(F_pr[u] - F_pr[y]);}}}return F_pr;}vector<mint> INV(100, 1);//f(p^e)auto g_calc = [](ll p, ll e) {return INV[e + 1];};vector<mint> Min_sieve(ll N, function<mint(ll, ll)> fn, vector<mint> F_pr) {int sz = Q_enum.size();vector<mint> L_DP(sz);for (int i = 0; i < sz; i++)L_DP[i] = F_pr[i];ll sq = sqrt(N);for (ll x = sq; x > 1; x--) {if (is_prime[x]) {int y = (x < sm.size() ? sm[x] : bg[N / (x)]);;for (int i = 0; i < sz; i++) {ll n = Q_enum[i];if (n < x * x)break;ll cnt = 1;for (ll c = x; c * x <= n; c *= x) {int id = (n / c < sm.size() ? sm[n / c] : bg[N / (n / c)]);L_DP[i] += fn(x, cnt) * (L_DP[id] - F_pr[y]) + fn(x, cnt + 1);cnt++;}}}}return L_DP;}void solve() {ll N, M;cin >> N >> M;swap(N, M);for (int i = 1; i < 100; i++) {INV[i] = mint(i).pow(M);}Q_enum.clear();ID.clear();DI.clear();calc_Qenum(N);ll sq = sqrt(N);// for(int i=0;i<Q_enum.size();i++){// ll n=Q_enum[i];// if(n<sq)cout<<bg[N/(N/n)]<<endl;// else cout<<sm[n]<<endl;// }vector<mint> FP = calc_Fprime(N);for (auto& p : FP)p *= INV[2];vector<mint> G_DP = Min_sieve(N, g_calc, FP);cout << (G_DP[ID[N]] + 1).val() << endl;}int main() {ios_base::sync_with_stdio(false);cin.tie(nullptr);enum_prime(1e11 + 1);solve();}