QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#804593 | #9867. Flowers | Rubikun (Ibuki Mio)# | AC ✓ | 43ms | 9968kb | C++23 | 26.9kb | 2024-12-08 00:45:03 | 2024-12-08 00:45:03 |
Judging History
answer
// https://nyaannyaan.github.io/library/multiplicative-function/sum-of-multiplicative-function.hpp
#include <bits/stdc++.h>
using namespace std;
#define si(x) int(x.size())
//modint+畳み込み+逆元テーブル
// from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9
// (based on AtCoder STL)
#include <algorithm>
#include <array>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#include <utility>
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
for (long long a : {2, 7, 61}) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <type_traits>
#include <vector>
namespace atcoder {
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) {
if (n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
long long diff =
c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5] = {
0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
} // namespace atcoder
using mint=atcoder::modint;
const int mod=998244353,MAX=300005;
#define ll long long
mint inv[MAX],fac[MAX],finv[MAX];
void make(){
fac[0]=fac[1]=1;
finv[0]=finv[1]=1;
inv[1]=1;
for(int i=2;i<MAX;i++){
inv[i]=-inv[mod%i]*(mod/i);
fac[i]=fac[i-1]*i;
finv[i]=finv[i-1]*inv[i];
}
}
mint comb(ll a,ll b){
if(a<b) return 0;
return fac[a]*finv[b]*finv[a-b];
}
mint perm(ll a,ll b){
if(a<b) return 0;
return fac[a]*finv[a-b];
}
#pragma once
// Prime Sieve {2, 3, 5, 7, 11, 13, 17, ...}
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;
}
#pragma once
// f(p, c) : f(p^c) の値を返す
// black algorithmでp^cまとめて飛ぶ時に使う
// runでは累積和的なのを渡す
ll CN[44];
template <typename T, T (*f)(long long, long long)>
struct mf_prefix_sum {
using i64 = long long;
i64 M, sq, s;
vector<int> p;
int ps;
vector<T> buf;
T ans;
mf_prefix_sum(i64 m) : M(m) {
assert(m <= 1e15);
sq = sqrt(M);
while (sq * sq > M) sq--;
while ((sq + 1) * (sq + 1) <= M) sq++;
if (M != 0) {
i64 hls = quo(M, sq);
while (hls != 1 && quo(M, hls - 1) == sq) hls--;
s = hls + sq;
p = prime_enumerate(sq);
ps = p.size();
ans = T{};
}
}
// 素数の個数関数に関するテーブル
vector<T> pi_table() {
if (M == 0) return {};
i64 hls = s - sq;
vector<i64> hl(hls);
for (int i = 1; i < hls; i++) hl[i] = quo(M, i) - 1;
// M/hls = sq なので big はそれ未満を見ればいい (hl[0]はダミー)
vector<int> hs(sq + 1);
iota(begin(hs), end(hs), -1);
// small (hs[0]はダミー)
int pi = 0;
for (auto& x : p) {
i64 x2 = i64(x) * x;
i64 imax = min<i64>(hls, quo(M, x2) + 1);
for (i64 i = 1, ix = x; i < imax; ++i, ix += x) {
hl[i] -= (ix < hls ? hl[ix] : hs[quo(M, ix)]) - pi;
}
for (int n = sq; n >= x2; n--) hs[n] -= hs[quo(n, x)] - pi;
pi++;
}
// 漸化式に従う pはsq以下の素数が入っている
vector<T> res;
res.reserve(2 * sq + 10);
for (auto& x : hl) res.push_back(x);
for (int i = hs.size(); --i;) res.push_back(hs[i]);
assert((int)res.size() == s);
return res;
// [ダミー(0)] + [M/1,M/2,...,M/(hls-1)] + [sq,sq-1,...,2,1] の順
}
// 素数の prefix sum に関するテーブル
vector<T> prime_sum_table() {
if (M == 0) return {};
i64 hls = s - sq;
vector<T> h(s);
T inv2 = T{2}.inverse();
for (int i = 1; i < hls; i++) {
T x = quo(M, i);
h[i] = x * (x + 1) * inv2 - 1;
}
for (int i = 1; i <= sq; i++) {
T x = i;
h[s - i] = x * (x + 1) * inv2 - 1;
}
for (auto& x : p) {
T xt = x;
T pi = h[s - x + 1];
i64 x2 = i64(x) * x;
i64 imax = min<i64>(hls, quo(M, x2) + 1);
i64 ix = x;
for (i64 i = 1; i < imax; ++i, ix += x) {
h[i] -= ((ix < hls ? h[ix] : h[s - quo(M, ix)]) - pi) * xt;
}
for (int n = sq; n >= x2; n--) {
h[s - n] -= (h[s - quo(n, x)] - pi) * xt;
}
}
assert((int)h.size() == s);
return h;
}
void dfs(int i, int c, i64 prod, T cur, ll syu) {
CN[syu]++;
i64 lim = quo(M, prod);
if (lim >= 1LL * p[i] * p[i]) dfs(i, c + 1, p[i] * prod, cur, syu);
cur *= f(p[i], c);
CN[syu+1] += (buf[idx(lim)] - buf[idx(p[i])]);
//ans += cur * (buf[idx(lim)] - buf[idx(p[i])]);
int j = i + 1;
// p_j < 2**21 -> (p_j)^3 < 2**63
for (; j < ps && p[j] < (1 << 21) && 1LL * p[j] * p[j] * p[j] <= lim; j++) {
dfs(j, 1, prod * p[j], cur, syu+1);
}
for (; j < ps && 1LL * p[j] * p[j] <= lim; j++) {
CN[syu+1] ++;
T sm = f(p[j], 2);
int id1 = idx(quo(lim, p[j])), id2 = idx(p[j]);
CN[syu+2] += (buf[id1] - buf[id2]);
sm += f(p[j], 1) * (buf[id1] - buf[id2]);
ans += cur * sm;
}
}
// black algorithm
T run(const vector<T>& Fprime) {
if (M == 0) return {};
assert((int)Fprime.size() == s);
buf = Fprime;
//CN[1] = buf[idx(M)] + 1;
for (int i = 0; i < ps; i++) dfs(i, 1, p[i], 1, 1);
return ans;
}
vector<T> min_25_sieve(const vector<T>& Fprime) {
if(M == 0) return {};
assert((int)Fprime.size() == s);
vector<i64> ns{0};
for (int i = 1; i < s - sq; i++) ns.push_back(quo(M, i));
for (int i = sq; i > 0; i--) ns.push_back(i);
vector<T> F = Fprime, G = Fprime;
for (int j = p.size() - 1; j >= 0; j--) {
i64 P = p[j], pc = P, c = 1;
while (quo(M, P) >= pc) {
T f_p_c = f(P, c), f_p_cp1 = f(P, c + 1);
T Fprime_p = Fprime[idx(P)];
for (int i = 1; i < s; i++) {
i64 n = ns[i];
if (P * pc > n) break;
G[i] += f_p_c * (F[idx(quo(n, pc))] - Fprime_p) + f_p_cp1;
}
c++, pc *= P;
}
copy(begin(G), begin(G) + min<int>(s, idx(P * P) + 1), begin(F));
}
for (int i = 1; i < (int)ns.size(); i++) F[i] += 1;
return F;
}
i64 quo(i64 n, i64 d) { return double(n) / d; }
i64 idx(i64 n) { return n <= sq ? s - n : quo(M, n); }
};
/**
* @brief 乗法的関数のprefix sum
* @docs docs/multiplicative-function/sum-of-multiplicative-function.md
*/
ll N,M;
ll f(ll p,ll k){
return 1;
}
int main()
{
std::ifstream in("text.txt");
std::cin.rdbuf(in.rdbuf());
cin.tie(0);
ios::sync_with_stdio(false);
ll N,P;cin>>N>>P;
mint::set_mod(P);
mf_prefix_sum<ll,f>mf1(N);
auto h0=mf1.pi_table();
mf1.run(h0);
mint ans=1;
ll sum=0;
for(int j=1;j<=12;j++){
ans*=mint(j).pow(CN[j]);
sum+=CN[j];
}
cout<<ans.val()<<"\n";
}
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Test #1:
score: 100
Accepted
time: 1ms
memory: 7024kb
input:
5 998244353
output:
1
result:
ok 1 number(s): "1"
Test #2:
score: 0
Accepted
time: 1ms
memory: 7244kb
input:
10 998244353
output:
4
result:
ok 1 number(s): "4"
Test #3:
score: 0
Accepted
time: 40ms
memory: 9768kb
input:
10000000000 998244353
output:
889033323
result:
ok 1 number(s): "889033323"
Test #4:
score: 0
Accepted
time: 1ms
memory: 7096kb
input:
114514 690913931
output:
324700175
result:
ok 1 number(s): "324700175"
Test #5:
score: 0
Accepted
time: 1ms
memory: 7204kb
input:
1919180 834093847
output:
646537851
result:
ok 1 number(s): "646537851"
Test #6:
score: 0
Accepted
time: 0ms
memory: 7316kb
input:
906389 647338613
output:
169737221
result:
ok 1 number(s): "169737221"
Test #7:
score: 0
Accepted
time: 0ms
memory: 7292kb
input:
984569 661772093
output:
538193748
result:
ok 1 number(s): "538193748"
Test #8:
score: 0
Accepted
time: 2ms
memory: 7120kb
input:
929116 593924027
output:
205577710
result:
ok 1 number(s): "205577710"
Test #9:
score: 0
Accepted
time: 1ms
memory: 7188kb
input:
973649 756926927
output:
110478509
result:
ok 1 number(s): "110478509"
Test #10:
score: 0
Accepted
time: 1ms
memory: 7220kb
input:
952730 517371427
output:
369025161
result:
ok 1 number(s): "369025161"
Test #11:
score: 0
Accepted
time: 1ms
memory: 7284kb
input:
996362 731032373
output:
598082216
result:
ok 1 number(s): "598082216"
Test #12:
score: 0
Accepted
time: 1ms
memory: 7136kb
input:
994582 680360567
output:
196510965
result:
ok 1 number(s): "196510965"
Test #13:
score: 0
Accepted
time: 43ms
memory: 9844kb
input:
9807161842 610831159
output:
153249139
result:
ok 1 number(s): "153249139"
Test #14:
score: 0
Accepted
time: 41ms
memory: 9616kb
input:
9169908183 701443451
output:
324649616
result:
ok 1 number(s): "324649616"
Test #15:
score: 0
Accepted
time: 41ms
memory: 9832kb
input:
9201785456 640300459
output:
397372089
result:
ok 1 number(s): "397372089"
Test #16:
score: 0
Accepted
time: 39ms
memory: 9700kb
input:
9740261856 956479159
output:
176750230
result:
ok 1 number(s): "176750230"
Test #17:
score: 0
Accepted
time: 11ms
memory: 7936kb
input:
1359090224 992341157
output:
923341100
result:
ok 1 number(s): "923341100"
Test #18:
score: 0
Accepted
time: 11ms
memory: 8016kb
input:
2001052730 763501463
output:
562415935
result:
ok 1 number(s): "562415935"
Test #19:
score: 0
Accepted
time: 23ms
memory: 8736kb
input:
3905939101 828044311
output:
500302420
result:
ok 1 number(s): "500302420"
Test #20:
score: 0
Accepted
time: 26ms
memory: 9096kb
input:
4638306389 770966029
output:
436075816
result:
ok 1 number(s): "436075816"
Test #21:
score: 0
Accepted
time: 25ms
memory: 9088kb
input:
5420730405 818828191
output:
35679557
result:
ok 1 number(s): "35679557"
Test #22:
score: 0
Accepted
time: 34ms
memory: 9400kb
input:
6909084541 736712321
output:
307308305
result:
ok 1 number(s): "307308305"
Test #23:
score: 0
Accepted
time: 37ms
memory: 9608kb
input:
7857218570 793606399
output:
139036999
result:
ok 1 number(s): "139036999"
Test #24:
score: 0
Accepted
time: 31ms
memory: 9644kb
input:
8134885470 553667887
output:
209895871
result:
ok 1 number(s): "209895871"
Test #25:
score: 0
Accepted
time: 40ms
memory: 9880kb
input:
10000000000 966627661
output:
788042772
result:
ok 1 number(s): "788042772"
Test #26:
score: 0
Accepted
time: 0ms
memory: 7136kb
input:
1 998244853
output:
1
result:
ok 1 number(s): "1"
Test #27:
score: 0
Accepted
time: 2ms
memory: 7172kb
input:
2 998244853
output:
1
result:
ok 1 number(s): "1"
Test #28:
score: 0
Accepted
time: 1ms
memory: 7040kb
input:
3 998244853
output:
1
result:
ok 1 number(s): "1"
Test #29:
score: 0
Accepted
time: 2ms
memory: 7176kb
input:
4 998244853
output:
1
result:
ok 1 number(s): "1"
Test #30:
score: 0
Accepted
time: 40ms
memory: 9968kb
input:
10000000000 101453381
output:
91945195
result:
ok 1 number(s): "91945195"
Test #31:
score: 0
Accepted
time: 43ms
memory: 9696kb
input:
10000000000 101530493
output:
19287261
result:
ok 1 number(s): "19287261"
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score: 0
Extra Test Passed