結果

問題 No.2576 LCM Pattern
ユーザー miscalc
提出日時 2023-12-06 14:16:24
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 5 ms / 2,000 ms
コード長 7,308 bytes
コンパイル時間 4,983 ms
コンパイル使用メモリ 271,804 KB
最終ジャッジ日時 2025-02-18 08:29:13
ジャッジサーバーID
(参考情報)
judge2 / judge5
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ファイルパターン 結果
other AC * 23
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ソースコード

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プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
constexpr ll INF = 1LL << 60;
template<class T> bool chmin(T& a, T b) {if (a > b) {a = b; return true;} return false;}
template<class T> bool chmax(T& a, T b) {if (a < b) {a = b; return true;} return false;}
ll safemod(ll A, ll M) {ll res = A % M; if (res < 0) res += M; return res;}
ll divfloor(ll A, ll B) {if (B < 0) A = -A, B = -B; return (A - safemod(A, B)) / B;}
ll divceil(ll A, ll B) {if (B < 0) A = -A, B = -B; return divfloor(A + B - 1, B);}
ll pow_ll(ll A, ll B) {if (A == 0 || A == 1) {return A;} if (A == -1) {return B & 1 ? -1 : 1;} ll res = 1; for (int i = 0; i < B; i++) {res *= A;}
    return res;}
ll mul_limited(ll A, ll B, ll M = INF) { return B == 0 ? 0 : A > M / B ? M : A * B; }
ll pow_limited(ll A, ll B, ll M = INF) { if (A == 0 || A == 1) {return A;} ll res = 1; for (int i = 0; i < B; i++) {if (res > M / A) return M; res *=
    A;} return res;}
template<class T> void unique(vector<T> &V) {V.erase(unique(V.begin(), V.end()), V.end());}
template<class T> void sortunique(vector<T> &V) {sort(V.begin(), V.end()); V.erase(unique(V.begin(), V.end()), V.end());}
#define FINALANS(A) do {cout << (A) << '\n'; exit(0);} while (false)
template<class T> void printvec(const vector<T> &V) {int _n = V.size(); for (int i = 0; i < _n; i++) cout << V[i] << (i == _n - 1 ? "" : " ");cout <<
    '\n';}
template<class T> void printvect(const vector<T> &V) {for (auto v : V) cout << v << '\n';}
template<class T> void printvec2(const vector<vector<T>> &V) {for (auto &v : V) printvec(v);}
//*
#include <atcoder/all>
using namespace atcoder;
using mint = modint998244353;
//using mint = modint1000000007;
//using mint = modint;
//*/
bool isprime(ll n)
{
if (n == 1)
return false;
const vector<ll> as = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
const vector<ll> ps = {2, 3, 5, 13, 19, 73, 193, 407521, 299210837};
for (auto p : ps)
{
if (n == p)
return true;
if (n % p == 0)
return false;
}
ll d = n - 1;
int s = 0;
while (d % 2 == 0)
d /= 2, s++;
for (auto a : as)
{
ll a0 = 1;
for (ll d2 = d, tmp = a; d2 > 0; d2 /= 2, tmp = __int128_t(tmp) * tmp % n)
{
if (d2 % 2 == 1)
a0 = __int128_t(a0) * tmp % n;
}
if (a0 == 1 || a0 == n - 1)
continue;
for (int r = 1; r <= s; r++)
{
if (r == s)
return false;
a0 = __int128_t(a0) * a0 % n;
if (a0 == n - 1)
break;
}
}
return true;
}
ll getprimefactor(ll n)
{
if (isprime(n))
return n;
int m = pow(n, .125);
for (int c = 1; c < 100; c++)
{
auto f = [&](ll a) -> ll
{ return (__int128_t(a) * a + c) % n; };
ll x = 2, y = 2, prod = 1, g = 1;
while (g == 1)
{
for (int i = 0; i < m; i++)
{
x = f(x), y = f(f(y));
prod = __int128_t(prod) * (x - y) % n;
}
g = gcd(prod, n);
}
if (g == n)
continue;
return getprimefactor(g);
}
assert(false);
}
vector<ll> factorize_fast(ll n)
{
vector<ll> res;
for (int p = 2; p < 100; p++)
{
while (n % p == 0)
{
n /= p;
res.emplace_back(p);
}
}
while (n > 1)
{
ll p = getprimefactor(n);
n /= p;
res.emplace_back(p);
}
sort(res.begin(), res.end());
return res;
}
vector<pll> to_vpll(const vector<ll> &ps)
{
vector<pll> pes;
for (auto p : ps)
{
if (pes.empty() || pes.back().first != p)
pes.emplace_back(make_pair(p, 1));
else
pes.back().second++;
}
return pes;
}
vector<ll> divisors(const vector<pll> &pes)
{
if (pes.empty())
return {1};
vector<ll> es(pes.size(), 0);
auto next_es = [&]() -> bool
{
es[0]++;
for (int i = 0; i < (int)es.size(); i++)
{
if (es[i] <= pes[i].second)
break;
if (i == (int)es.size() - 1)
return false;
es[i] = 0;
es[i + 1]++;
}
return true;
};
vector<ll> ds;
do
{
ll d = 1;
for (int i = 0; i < (int)es.size(); i++)
d *= pow_ll(pes[i].first, es[i]);
ds.emplace_back(d);
} while (next_es());
sort(ds.begin(), ds.end());
return ds;
}
// https://nyaannyaan.github.io/library/multiplicative-function/divisor-multiple-transform.hpp.html
struct ZetaMobiusDivisorMultiple
{
ll n;
vector<ll> ds, ps;
ZetaMobiusDivisorMultiple() {}
ZetaMobiusDivisorMultiple(ll n) : n(n)
{
/*
for (ll d = 1; d * d <= n; d++)
{
if (n % d == 0)
{
ds.emplace_back(d);
if (d * d != n)
ds.emplace_back(n / d);
}
}
sort(ds.begin(), ds.end());
for (ll p = 2; p * p <= n; p++)
{
if (n % p == 0)
{
ps.emplace_back(p);
while (n % p == 0)
n /= p;
}
}
if (n != 1)
ps.emplace_back(n);
//*/
//*
ps = factorize_fast(n);
ds = divisors(to_vpll(ps));
unique(ps);
//*/
}
// d f(d) d map
template<class T>
map<ll, T> func_to_map(const function<T(ll)> &f) const
{
map<ll, T> res;
for (auto d : ds)
res[d] = f(d);
return res;
}
// ζa(n) = Σ{d | n} a(d)
template<class T>
map<ll, T> zeta_divisor(const map<ll, T> &A) const
{
map<ll, T> B(A);
for (auto &p : ps)
{
for (auto &d : ds)
{
if (d > n / p)
break;
if (n % (d * p) == 0)
B[d * p] += B[d];
}
}
return B;
}
// μ ζ
// μa(n) = Σ{d | n} μ(n/d)a(d) cf.
template<class T>
map<ll, T> mobius_divisor(const map<ll, T> &A) const
{
map<ll, T> B(A);
for (auto &p : ps)
{
for (int i = (int)ds.size() - 1; i >= 0; i--)
{
ll d = ds[i];
if (d > n / p)
continue;
if (n % (d * p) == 0)
B[d * p] -= B[d];
}
}
return B;
}
// ζ'a(n) = Σ{n | m} a(m)
template<class T>
map<ll, T> zeta_multiple(const map<ll, T> &A) const
{
map<ll, T> B(A);
for (auto &p : ps)
{
for (int i = (int)ds.size() - 1; i >= 0; i--)
{
ll d = ds[i];
if (d > n / p)
continue;
if (n % (d * p) == 0)
B[d] += B[d * p];
}
}
return B;
}
// μ' ζ'
// μ'a(n) = Σ{n | m} μ(m/n)g(m)
template<class T>
map<ll, T> mobius_multiple(const map<ll, T> &A) const
{
map<ll, T> B(A);
for (auto &p : ps)
{
for (auto &d : ds)
{
if (d > n / p)
break;
if (n % (d * p) == 0)
B[d] -= B[d * p];
}
}
return B;
}
};
int main()
{
ll N, M;
cin >> N >> M;
ZetaMobiusDivisorMultiple zmdm(M);
map<ll, mint> sigma = zmdm.zeta_divisor(zmdm.func_to_map<mint>([&](ll) -> mint
{ return 1; }));
map<ll, mint> res = zmdm.mobius_divisor(zmdm.func_to_map<mint>([&](ll d) -> mint
{ return sigma[d].pow(N); }));
mint ans = res[M];
cout << ans.val() << endl;
}
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