結果
| 問題 | No.3687 Coprime Count |
| コンテスト | |
| ユーザー |
 miscalc
|
| 提出日時 | 2026-09-11 05:16:21 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 8 ms / 2,000 ms |
| + 15µs | |
| コード長 | 58,174 bytes |
| 記録 | |
| コンパイル時間 | 4,607 ms |
| コンパイル使用メモリ | 387,244 KB |
| 実行使用メモリ | 6,400 KB |
| 最終ジャッジ日時 | 2026-09-11 05:16:30 |
| 合計ジャッジ時間 | 5,924 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge3_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 10 |
ソースコード
#define SINGLE_TESTCASE
#define FAST_IO
#define INF 4'000'000'000'000'000'037LL
#define EPS 1e-11
// https://github.com/miscalculation53/library/tree/wip/template/template_all.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_all_but_modint.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_types.hpp
#include <bits/stdc++.h>
using namespace std;
using ld = decltype(EPS);
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
using tllll = tuple<ll, ll, ll, ll>;
#define vc vector
template <class T>
using vvc = vc<vc<T>>;
template <class T>
using vvvc = vc<vc<vc<T>>>;
using vb = vc<bool>;
using vl = vc<ll>;
using vpll = vc<pll>;
using vtlll = vc<tlll>;
using vtllll = vc<tllll>;
using vstr = vc<string>;
using vvb = vvc<bool>;
using vvl = vvc<ll>;
template <class T>
using pql = priority_queue<T, vc<T>, greater<T>>;
template <class T>
using pqg = priority_queue<T>;
using i128 = __int128_t;
using u128 = __uint128_t;
i128 stoi128(const string &s)
{
const bool neg = s.front() == '-';
u128 res = 0;
for (int i = neg; i < (int)s.size(); i++)
res = 10 * res + s[i] - '0';
if (neg)
return -i128(res - 1) - 1;
return i128(res);
}
string i128tos(i128 x)
{
if (x == 0) return "0";
string sign = "", res = "";
u128 ux;
if (x < 0)
ux = u128(-(x + 1)) + 1, sign = "-";
else
ux = x;
while (ux > 0)
{
res += '0' + ux % 10;
ux /= 10;
}
reverse(res.begin(), res.end());
return sign + res;
}
istream &operator>>(istream &is, i128 &a)
{
string s;
is >> s;
a = stoi128(s);
return is;
}
ostream &operator<<(ostream &os, const i128 &a)
{
os << i128tos(a);
return os;
}
#define cauto const auto
// https://github.com/miscalculation53/library/tree/wip/template/template_rep.hpp
#define overload4(_1,_2,_3,_4,name,...) name
#define rep1(i,n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++)
#define rep2(i,l,r) for (ll i = ll(l), rrrrr = ll(r); i < rrrrr; i++)
#define rep3(i,l,r,d) for (ll i = ll(l), rrrrr = ll(r), ddddd = ll(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repi1(i,n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi2(i,l,r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)
#define repi3(i,l,r,d) for (int i = int(l), rrrrr = int(r), ddddd = int(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)
#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
#define fem(...) for (auto &__VA_ARGS__)
// https://github.com/miscalculation53/library/tree/wip/template/template_math.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/is_integral_ext.hpp
template <class T>
constexpr bool is_integral_ext = is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>;
template <class T>
constexpr bool is_signed_ext = is_signed_v<T> || is_same_v<T, i128>;
template <class T>
constexpr bool is_unsigned_ext = is_unsigned_v<T> || is_same_v<T, u128>;
// https://github.com/miscalculation53/library/tree/wip/utils/default_infty.hpp
namespace default_infty_detail
{
template <class T, class = void>
struct has_infty : false_type {};
template <class T>
struct has_infty<T, void_t<decltype(T::infty())>> : true_type {};
template <class T>
inline constexpr bool unsupported = false;
}
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divceil(U a, V b) { return T(a) / T(b) + (T(a) % T(b) && (T(a) ^ T(b)) >= 0); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T safemod(U a, V b) { return T(a) - T(b) * divfloor<T>(a, b); }
template <class T = ll, class U, class V>
constexpr T ipow(U a, V b)
{
assert(b >= 0);
if (b == 0)
return 1;
if (a == 0 || a == 1)
return a;
if (a < 0 && a == -1)
return b & 1 ? -1 : 1;
T res = 1, tmp = a;
while (true)
{
if (b & 1)
res *= tmp;
b >>= 1;
if (b == 0)
break;
tmp *= tmp;
}
return res;
}
template <class T = ll, class A, class K>
constexpr T iroot(A a, K k)
{
assert(a >= 0 && k >= 1);
if (a <= 1 || k == 1)
return a;
if (k == 2)
{
const T aa = T(a);
T x = T(sqrtl((long double)a));
while (x > aa / x)
x--;
while (x < numeric_limits<T>::max())
{
const T y = x + 1;
if (y > aa / y)
break;
x = y;
}
return x;
}
auto isok = [&](T x) -> bool
{
if (x == 0)
return true;
T res = 1, k2 = k;
while (true)
{
if (k2 & 1)
{
if (res > T(a) / x)
return false;
res *= x;
}
k2 >>= 1;
if (k2 == 0)
break;
if (x > T(a) / x)
return false;
x *= x;
}
return res <= T(a);
};
T x = pow(a, 1.0 / k);
bool up = true;
while (!isok(x))
up = false, x--;
if (up)
{
while (x < numeric_limits<T>::max() && isok(x + 1))
x++;
}
return x;
}
template <class T = ll, class A, class K>
constexpr T iroot_ceil(A a, K k)
{
T x = iroot<T>(a, k);
return ipow<T>(x, k) == a ? x : x + 1;
}
// https://github.com/miscalculation53/library/tree/wip/template/template_vector.hpp
#define ALL(a) (a).begin(), (a).end()
template <class T = ll, class V>
inline T SZ(const V &x) { return x.size(); }
#define eb emplace_back
#define LMD(x,fx) ([&](const auto &x) { return fx; })
#define GEN_VEC(n,i,fi) (gen_vec(n, LMD(i, fi)))
// https://github.com/miscalculation53/library/tree/wip/template/template_algo.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/resolved_infty.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/resolved_value.hpp
template <class V, class Equal = equal_to<>>
void unique(V &v, Equal equal = {}) { v.erase(std::unique(ALL(v), equal), v.end()); }
template <class V, class Compare = less<>, class Equal = equal_to<>>
void sortunique(V &v, Compare comp = {}, Equal equal = {})
{
sort(ALL(v), comp);
unique(v, equal);
}
template <class T>
vvc<T> top(const vvc<T> &a)
{
if (a.empty())
return {};
const int n = a.size(), m = a[0].size();
vvc<T> b(m, vc<T>(n));
repi(i, n)
{
assert(SZ<int>(a[i]) == m);
repi(j, m) b[j][i] = a[i][j];
}
return b;
}
vstr top(const vstr &a)
{
vvc<char> a_(a.size());
repi(i, SZ<int>(a)) a_[i] = {ALL(a[i])};
vvc<char> b_ = top(a_);
vstr b(b_.size());
repi(i, SZ<int>(b)) b[i] = {ALL(b_[i])};
return b;
}
template <class T, class = void>
struct has_e0 : false_type {};
template <class T>
struct has_e0<T, void_t<decltype(T::e0())>> : true_type {};
template <class T>
inline constexpr bool has_e0_v = has_e0<T>::value;
template <class T>
struct MonoidAdd
{
using S = T;
};
template <class T, auto infty = nullptr>
struct MonoidMin
{
using S = T;
};
template <class T, auto infty = nullptr>
struct MonoidMax
{
using S = T;
};
namespace internal
{
template <class M, class I, class = void>
struct HasMonoidPow : false_type
{
};
template <class M, class I>
struct HasMonoidPow<M, I, void_t<decltype(M::pow(declval<const typename M::S &>(), declval<I>()))>> : true_type
{
};
}
constexpr array<pll, 4> DRULgrid = {{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}};
constexpr array<pll, 4> DRULplane = {{{0, -1}, {1, 0}, {0, 1}, {-1, 0}}};
// https://github.com/miscalculation53/library/tree/wip/template/template_binsearch.hpp
template <class T>
struct is_random_access_iterator
{
static constexpr bool value = is_same_v<
typename iterator_traits<T>::iterator_category,
random_access_iterator_tag
>;
};
template <class T>
constexpr bool is_random_access_iterator_v = is_random_access_iterator<T>::value;
#define DEFAULT_COMP ranges::less
namespace internal
{
};
// https://github.com/miscalculation53/library/tree/wip/template/template_bit.hpp
template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }
inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); }
inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); }
inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); }
inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); }
inline constexpr ll popcount(ll x) { return std::popcount((ull)x); }
inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); }
inline constexpr ull lsb_pos(ull x) { assert(x != 0); return countr_zero(x); }
inline constexpr ull msb_pos(ull x) { assert(x != 0); return bit_width(x) - 1; }
inline constexpr ull lsb_mask(ull x) { assert(x != 0); return x & -x; }
inline constexpr ull msb_mask(ull x) { assert(x != 0); return bit_floor(x); }
inline constexpr bool btest(ull x, uint k) { return (x >> k) & 1; }
inline constexpr bool bsubset(ull x, ull y) { return (x & y) == x; }
inline constexpr bool bsupset(ull x, ull y) { return (x & y) == y; }
inline constexpr ull bsetminus(ull x, ull y) { return x & ~y; }
// https://github.com/miscalculation53/library/tree/wip/template/template_inout.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_dump.hpp
#define CPP_DUMP_DEFINE_DATA(...)
#define dump(...)
#define local(...)
#define oj(...) __VA_ARGS__
#define local_oj(a,b) (b)
namespace fastio {
template <class T>
struct unsigned_integer
{
using type = make_unsigned_t<T>;
};
template <>
struct unsigned_integer<i128>
{
using type = u128;
};
template <>
struct unsigned_integer<u128>
{
using type = u128;
};
template <class T>
using unsigned_integer_t = typename unsigned_integer<T>::type;
static constexpr uint32_t SIZ = 1 << 17;
char ibuf[SIZ];
char obuf[SIZ];
char out[100];
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SIZ - pir + pil, stdin);
pil = 0;
if (pir < SIZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd1(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (c <= ' ');
}
void rd1(string &x) {
x.clear();
while (true) {
if (pil == pir) load();
while (pil < pir && ibuf[pil] <= ' ') ++pil;
if (pil < pir) break;
}
while (true) {
uint32_t p = pil;
while (pil < pir && ibuf[pil] > ' ') ++pil;
x.append(ibuf + p, pil - p);
if (pil < pir) {
++pil;
return;
}
load();
}
}
template <typename T>
void rd1_real(T &x) {
string s;
rd1(s);
if constexpr (!is_same_v<T, long double>)
{
auto [p, ec] = from_chars(s.data(), s.data() + s.size(), x);
if (ec == errc{} && p == s.data() + s.size()) return;
}
if constexpr (is_same_v<T, long double>)
x = stold(s);
else
x = stod(s);
}
template <bool check_buffer = true, typename T>
void rd1_integer(T &x) {
using U = unsigned_integer_t<T>;
bool minus = false;
U val = 0;
if constexpr (check_buffer)
if (pil + 100 > pir) load();
uint32_t p = pil;
while (ibuf[p] < '-') ++p;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (ibuf[p] == '-') minus = true, ++p;
}
while ('0' <= ibuf[p]) val = val * 10 + (ibuf[p++] & 15);
pil = p;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (minus)
{
const U min_abs = U(numeric_limits<T>::max()) + 1;
x = val == min_abs ? numeric_limits<T>::lowest() : -T(val);
}
else x = T(val);
}
else
x = T(val);
}
void rd1(int &x) { rd1_integer(x); }
void rd1(ll &x) { rd1_integer(x); }
void rd1(i128 &x) { rd1_integer(x); }
void rd1(uint &x) { rd1_integer(x); }
void rd1(ull &x) { rd1_integer(x); }
void rd1(u128 &x) { rd1_integer(x); }
void rd1(double &x) { rd1_real(x); }
void rd1(long double &x) { rd1_real(x); }
template <class... T>
void read(T &...x) {
if constexpr (sizeof...(T) <= SIZ / 100 &&
((!is_same_v<T, char> &&
(is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>)) && ...)) {
if (pil + 100 * sizeof...(T) > pir) load();
(rd1_integer<false>(x), ...);
}
else
(rd1(x), ...);
}
void wt1(const char c) {
if (por == SIZ) flush();
obuf[por++] = c;
}
void wt1(string_view s) {
while (!s.empty()) {
if (por == SIZ) flush();
size_t n = min<size_t>(s.size(), SIZ - por);
memcpy(obuf + por, s.data(), n);
por += n;
s.remove_prefix(n);
}
}
template <typename T>
void wt1_integer(T x) {
if (por > SIZ - 100) flush();
using U = unsigned_integer_t<T>;
U ux;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (x < 0)
obuf[por++] = '-', ux = U(0) - U(x);
else
ux = U(x);
}
else
ux = x;
int outi;
for (outi = 96; ux >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[ux % 10000], 4);
ux /= 10000;
}
if (ux >= 1000) {
memcpy(obuf + por, pre.num[ux], 4);
por += 4;
} else if (ux >= 100) {
memcpy(obuf + por, pre.num[ux] + 1, 3);
por += 3;
} else if (ux >= 10) {
int q = (ux * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (ux - q * 10) | '0';
por += 2;
} else
obuf[por++] = ux | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt1_real(T x) {
if constexpr (!is_same_v<T, long double>)
{
auto [p, ec] = to_chars(out, out + sizeof(out), x, chars_format::fixed, 15);
if (ec == errc{}) {
wt1(string_view(out, p));
return;
}
}
ostringstream oss;
oss << fixed << setprecision(15) << x;
wt1(oss.str());
}
void wt1(int x) { wt1_integer(x); }
template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void wt1(T x) { wt1_integer(x); }
void wt1(i128 x) { wt1_integer(x); }
void wt1(u128 x) { wt1_integer(x); }
void wt1(double x) { wt1_real(x); }
void wt1(long double x) { wt1_real(x); }
template <class T, class U>
void wt1(const pair<T, U> &val);
template <class... T>
void wt1(const tuple<T...> &tpl);
template <class T, size_t S>
void wt1(const array<T, S> &val);
template <class T>
void wt1(const vector<T> &val);
template <class... T>
void write(T &&...x) {
(wt1(std::forward<T>(x)), ...);
}
template <class... T>
void print(T &&...x) {
if constexpr (sizeof...(T))
{
int i = 0;
((i++ ? wt1(' ') : void(), wt1(std::forward<T>(x))), ...);
}
wt1('\n');
}
}
struct Dummy {
Dummy() { atexit(fastio::flush); }
} dummy;
namespace internal
{
template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }
};
#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define IN(T,...) T __VA_ARGS__; READ(__VA_ARGS__)
#define CHAR(...) IN(char, __VA_ARGS__)
#define INT(...) IN(int, __VA_ARGS__)
#define LL(...) IN(ll, __VA_ARGS__)
#define STR(...) IN(string, __VA_ARGS__)
#define ARR(T,n,...) array<T, n> __VA_ARGS__; READ(__VA_ARGS__)
#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define READVEC2(...) internal::READVEC2nodump(__VA_ARGS__); dump(__VA_ARGS__)
#define VEC(T,n,...) vc<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define VEC2(T,n,m,...) vvc<T> __VA_ARGS__; READVEC2(n, m, __VA_ARGS__)
#define READJAG(...) internal::READJAGnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define JAG(T,n,...) vvc<T> __VA_ARGS__; READJAG(n, __VA_ARGS__)
#define ENDL '\n'
#define WRITE fastio::write
#define PRINT fastio::print
#define PRINTEXIT(...) do { PRINT(__VA_ARGS__); exit(0); } while (false)
#define PRINTRETURN(...) do { PRINT(__VA_ARGS__); return; } while (false)
#define PRINTVEXIT(...) do { PRINTV(__VA_ARGS__); exit(0); } while (false)
#define PRINTVRETURN(...) do { PRINTV(__VA_ARGS__); return; } while (false)
namespace internal
{
};
namespace internal
{
};
#define UNZIP(vt,...) auto [__VA_ARGS__] = unzip(vt)
#define ZIP(vt,...) auto vt = zip(tuple{__VA_ARGS__})
// https://github.com/miscalculation53/library/tree/wip/template/template_random.hpp
mt19937_64 mt;
bool randbool(double p)
{
assert(0 <= p && p <= 1);
return bernoulli_distribution(p)(mt);
}
namespace internal
{
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/template_modint.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_static.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/larger_int.hpp
namespace larger_int_detail
{
}
template <class T>
struct larger_int
{
private:
static constexpr bool check();
static_assert(check());
public:
using type = T;
};
#define LARGER_INT(T,U) template <> struct larger_int<T> { using type = U; };
LARGER_INT(signed char, short)
LARGER_INT(short, int)
LARGER_INT(int, long long)
LARGER_INT(long, __int128_t)
LARGER_INT(long long, __int128_t)
LARGER_INT(unsigned char, unsigned short)
LARGER_INT(unsigned short, unsigned int)
LARGER_INT(unsigned int, unsigned long long)
LARGER_INT(unsigned long, __uint128_t)
LARGER_INT(unsigned long long, __uint128_t)
#undef LARGER_INT
template <class T>
struct Rational;
template <class T>
struct larger_int<Rational<T>>
{
using type = Rational<typename larger_int<T>::type>;
};
template <class T>
using larger_int_t = typename larger_int<T>::type;
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_isprime.hpp
namespace internal
{
template <class T>
constexpr ll powmod_constexpr(ll x, ll n, T m)
{
if (m == 1)
return 0;
using U = make_unsigned_t<T>;
using L = larger_int_t<U>;
U r = 1, y = safemod(x, m);
while (n)
{
if (n & 1)
r = L(r) * y % m;
y = L(y) * y % m;
n >>= 1;
}
return r;
}
template <auto n>
constexpr bool isprime = isprime_constexpr(n);
};
namespace internal
{
template <auto M>
struct policy_static
{
using mod_type = decltype(M);
using value_type = make_unsigned_t<mod_type>;
using calc_type = larger_int_t<value_type>;
static constexpr bool is_prime = isprime_constexpr(M);
static constexpr value_type init(value_type v) { return v; }
static constexpr mod_type val(value_type v);
};
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_barrett32.hpp
namespace internal
{
struct barrett32
{
uint m;
ull im;
explicit barrett32(uint m) : m(m), im((ull)(-1) / m + 1) {}
uint umod() const { return m; }
uint mul(uint a, uint b) const
{
ull z = a;
z *= b;
ull x = ull((u128(z) * im) >> 64);
ull y = x * m;
return uint(z - y + (z < y ? m : 0));
}
};
template <int id>
struct policy_barrett32
{
using value_type = uint;
using calc_type = ull;
using mod_type = int;
static constexpr bool is_prime = false;
static inline barrett32 reducer{998244353};
static value_type init(value_type v) { return v; }
static mod_type val(value_type v);
};
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_montgomery64.hpp
namespace internal
{
inline constexpr ull inv64(ull a)
{
ull x = a;
while (a * x != 1) x *= 2 - a * x;
return x;
}
struct montgomery64odd
{
ull m, im, sq;
explicit montgomery64odd(ull m) : m(m), im(inv64(m)), sq(-u128(m) % m) {}
ull umod() const { return m; }
ull reduce(u128 x) const
{
auto t = (x + u128(m) * (-im * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * sq); }
};
struct montgomery64
{
ull m, mx, imx, d, q;
uint b;
explicit montgomery64(ull m) : m(m)
{
b = countr_zero(m), mx = m >> b;
imx = inv64(mx);
d = powmod_constexpr((mx + 1) / 2, b, mx);
u128 sq = -u128(mx) % mx;
q = (1 + (((sq - 1) * d) << b)) % m;
}
ull umod() const { return m; }
ull reduce(u128 x) const
{
if (b == 0)
{
auto t = (x + u128(mx) * (-imx * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull p = x & MASK(b);
x = (x >> b) + p * d;
ull y = p << (64 - b);
auto t = (x + u128(mx) * (imx * (y - ull(x)))) >> (64 - b);
if (t >= m) { t -= m; if (t >= m) t -= m; }
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * q); }
};
template <int id>
struct policy_montgomery64_odd
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64odd reducer{(1LL << 61) - 1};
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v);
};
template <int id>
struct policy_montgomery64
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64 reducer{(1LL << 61) - 1};
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v);
};
};
// https://github.com/miscalculation53/library/tree/wip/math/extgcd.hpp
namespace internal
{
template <class Policy>
struct modint_impl
{
using V = typename Policy::value_type;
using M = typename Policy::mod_type;
using mint = modint_impl;
private:
V _v;
public:
modint_impl();
template <class T, typename = enable_if_t<is_integral_ext<T>>>
modint_impl(T v);
M val() const;
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; }
friend M safe_hash_key(const mint &x) { return x.val(); }
friend void rd1(mint &x)
{
long long a;
fastio::rd1(a);
x = a;
}
friend void wt1(const mint &x)
{
fastio::wt1(x.val());
}
};
};
template <int mod>
using static_modint32 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint32 = internal::modint_impl<internal::policy_barrett32<id>>;
template <ll mod>
using static_modint64 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint64_odd = internal::modint_impl<internal::policy_montgomery64_odd<id>>;
template <int id>
using dynamic_modint64 = internal::modint_impl<internal::policy_montgomery64<id>>;
using modint998244353 = static_modint32<998244353>;
using modint1000000007 = static_modint32<1000000007>;
using modint = dynamic_modint32<-1>;
using modint61 = static_modint64<(1LL << 61) - 1>;
using modint64 = dynamic_modint64<-1>;
template <class T>
struct is_modint : std::false_type
{
};
template <class Policy>
struct is_modint<internal::modint_impl<Policy>> : std::true_type
{
};
template <class T>
inline constexpr bool is_modint_v = is_modint<T>::value;
template <class T>
struct is_static_modint : false_type {};
template <int m>
struct is_static_modint<static_modint32<m>> : true_type {};
template <ll m>
struct is_static_modint<static_modint64<m>> : true_type {};
template <class T>
inline constexpr bool is_static_modint_v = is_static_modint<T>::value;
template <class T>
struct is_dynamic_modint : false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint32<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64_odd<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64<id>> : true_type {};
template <class T>
inline constexpr bool is_dynamic_modint_v = is_dynamic_modint<T>::value;
template <typename, typename = void>
struct has_mod : std::false_type
{
};
template <typename T>
struct has_mod<T, std::void_t<decltype(T::mod())>> : std::true_type
{
};
template <class mint>
struct modint_less
{
bool operator()(const mint &a, const mint &b) const
{
if constexpr (is_modint_v<mint>)
return a.val() < b.val();
else
return a < b;
}
};
template <class mint>
struct modint_hash
{
auto operator()(const mint &x) const
{
if constexpr (is_modint_v<mint>)
return std::hash<decltype(x.val())>{}(x.val());
else
return std::hash<mint>{}(x);
}
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/power_table.hpp
template <class mint>
struct PowerTable
{
private:
decltype(mint::mod()) mod;
mint base;
vc<mint> pw;
public:
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/binomial.hpp
template <class T>
struct Binomial
{
private:
inline static decltype(T::mod()) mod;
public:
inline static vc<T> fac_, finv_, inv_;
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/stom.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/to_rational.hpp
// https://github.com/miscalculation53/library/tree/wip/math/svp2d.hpp
namespace cpp_dump
{
struct mint_to_rat_fn
{
template <class T>
constexpr auto operator()(const T &x) const -> decltype(mint_to_rat(x))
{
return mint_to_rat(x);
}
};
struct rat_closure : std::ranges::range_adaptor_closure<rat_closure>
{
template <typename T>
constexpr auto operator()(T &&t) const
{
if constexpr (!std::ranges::range<T> && std::invocable<mint_to_rat_fn, decltype(std::forward<T>(t))>)
{
return mint_to_rat_fn{}(std::forward<T>(t));
}
else if constexpr (std::ranges::range<T>)
{
using Ref = std::ranges::range_reference_t<T>;
if constexpr (std::invocable<mint_to_rat_fn, decltype(std::forward<Ref>(std::declval<Ref>()))>)
{
return std::forward<T>(t) | std::views::transform(mint_to_rat_fn{});
}
else if constexpr (std::ranges::range<Ref>)
{
return std::forward<T>(t) | std::views::transform([this](auto &&inner)
{ return (*this)(std::forward<decltype(inner)>(inner)); });
}
else
{
static_assert(false);
}
}
else
{
static_assert(false);
}
}
};
constexpr rat_closure rat()
{
return rat_closure{};
}
}
void init()
{
oj(mt.seed(random_device()()));
}
// https://github.com/miscalculation53/library/tree/wip/math/prime/sieve/multiplicative_prefix_sum.hpp
// https://github.com/miscalculation53/library/tree/wip/math/prime/sieve/dirichlet_prefix_sum.hpp
// https://github.com/miscalculation53/library/tree/wip/math/prime/sieve/dirichlet_convolution.hpp
// https://github.com/miscalculation53/library/tree/wip/math/prime/sieve/enumerate_multiplicative.hpp
// https://github.com/miscalculation53/library/tree/wip/algebra/algebra_basic_ops.hpp
// https://github.com/miscalculation53/library/tree/wip/algebra/algebra_base.hpp
template <class S_, auto op_, auto e_>
struct Monoid
{
using S = S_;
static constexpr auto op = op_;
static constexpr auto e = e_;
};
template <class S_, auto op_, auto e_, auto inv_>
struct Group
{
using S = S_;
static constexpr auto op = op_;
static constexpr auto e = e_;
static constexpr auto inv = inv_;
};
template <class S_, auto add_, auto e0_, auto mul_, auto e1_>
struct SemiRing
{
using S = S_;
static constexpr auto add = add_;
static constexpr auto e0 = e0_;
static constexpr auto mul = mul_;
static constexpr auto e1 = e1_;
};
template <class S_, auto add_, auto e0_, auto minus_, auto mul_, auto e1_>
struct Ring
{
using S = S_;
static constexpr auto add = add_;
static constexpr auto e0 = e0_;
static constexpr auto minus = minus_;
static constexpr auto mul = mul_;
static constexpr auto e1 = e1_;
};
template <class S_, auto add_, auto e0_, auto minus_, auto mul_, auto e1_, auto inv_>
struct Field
{
using S = S_;
static constexpr auto add = add_;
static constexpr auto e0 = e0_;
static constexpr auto minus = minus_;
static constexpr auto mul = mul_;
static constexpr auto e1 = e1_;
static constexpr auto inv = inv_;
};
template <class M>
struct OppositeMonoid
{
using S = typename M::S;
static constexpr auto e = M::e;
};
template <class G>
struct OppositeGroup
{
using S = typename G::S;
static constexpr auto e = G::e;
static constexpr auto inv = G::inv;
};
template <class M>
struct NormalAndOppositeMonoid
{
struct S
{
typename M::S normal;
typename M::S opposite;
S() {}
template <class... Args,
std::enable_if_t<std::is_constructible_v<typename M::S, Args...>, std::nullptr_t> = nullptr>
S(Args &&...args)
: normal(std::forward<Args>(args)...), opposite(normal) {}
S(const typename M::S &normal, const typename M::S &opposite) : normal(normal), opposite(opposite) {}
};
};
template <class G>
struct NormalAndOppositeGroup
{
struct S
{
typename G::S normal;
typename G::S opposite;
S() {}
template <class... Args,
std::enable_if_t<std::is_constructible_v<typename G::S, Args...>, std::nullptr_t> = nullptr>
S(Args &&...args)
: normal(std::forward<Args>(args)...), opposite(normal) {}
S(const typename G::S &normal, const typename G::S &opposite) : normal(normal), opposite(opposite) {}
};
};
template <class SR>
using MonoidOfSemiRingAdd = Monoid<typename SR::S, SR::add, SR::e0>;
template <class SR>
using MonoidOfSemiRingMul = Monoid<typename SR::S, SR::mul, SR::e1>;
template <class R>
using GroupOfRingAdd = Group<typename R::S, R::add, R::e0, R::minus>;
template <class K>
using GroupOfFieldMul = Group<typename K::S, K::mul, K::e1, K::inv>;
template <class Madd, class Mmul>
struct SemiRingFromMonoidMonoid
{
static_assert(is_same_v<typename Madd::S, typename Mmul::S>, "Madd::S and Mmul::S must be identical");
using S = typename Madd::S;
static constexpr auto add = Madd::op;
static constexpr auto e0 = Madd::e;
static constexpr auto mul = Mmul::op;
static constexpr auto e1 = Mmul::e;
};
template <class Gadd, class Mmul>
struct RingFromGroupMonoid
{
static_assert(is_same_v<typename Gadd::S, typename Mmul::S>, "Gadd::S and Mmul::S must be identical");
using S = typename Gadd::S;
static constexpr auto add = Gadd::op;
static constexpr auto e0 = Gadd::e;
static constexpr auto minus = Gadd::inv;
static constexpr auto mul = Mmul::op;
static constexpr auto e1 = Mmul::e;
};
template <class Gadd, class Gmul>
struct FieldFromGroupGroup
{
static_assert(is_same_v<typename Gadd::S, typename Gmul::S>, "Gadd::S and Gmul::S must be identical");
using S = typename Gadd::S;
static constexpr auto add = Gadd::op;
static constexpr auto e0 = Gadd::e;
static constexpr auto minus = Gadd::inv;
static constexpr auto mul = Gmul::op;
static constexpr auto e1 = Gmul::e;
static constexpr auto inv = Gmul::inv;
};
template <class T, class = void>
struct has_e1 : false_type {};
template <class T>
struct has_e1<T, void_t<decltype(T::e1())>> : true_type {};
template <class T>
inline constexpr bool has_e1_v = has_e1<T>::value;
template <class T>
struct MonoidMul
{
using S = T;
static constexpr S op(S a, S b) { return a * b; }
static constexpr S e()
{
if constexpr (has_e1_v<S>)
return S::e1();
else
return 1;
}
};
template <class T>
struct GroupAddSub
{
using S = T;
static constexpr S op(S a, S b) { return a + b; }
static constexpr S e()
{
if constexpr (has_e0_v<S>)
return S::e0();
else
return S{};
}
static constexpr S inv(S a) { return -a; }
template <class I, class = decltype(declval<S>() * declval<I>())>
static constexpr S pow(const S &a, I k) { return a * k; }
};
template <class T>
struct GroupMulDiv
{
using S = T;
};
template <class T, auto infty = nullptr>
using SemiRingMinPlus = SemiRingFromMonoidMonoid<MonoidMin<T, infty>, MonoidAdd<T>>;
template <class T, auto infty = nullptr>
using SemiRingMaxPlus = SemiRingFromMonoidMonoid<MonoidMax<T, infty>, MonoidAdd<T>>;
template <class T>
using RingAddSubMul = RingFromGroupMonoid<GroupAddSub<T>, MonoidMul<T>>;
template <class T>
using FieldAddSubMulDiv = FieldFromGroupGroup<GroupAddSub<T>, GroupMulDiv<T>>;
// https://github.com/miscalculation53/library/tree/wip/math/prime/sieve/linear_sieve.hpp
// https://github.com/miscalculation53/library/tree/wip/math/prime/prime_power.hpp
template <class P>
struct PrimePower
{
P p;
int e;
P pe;
PrimePower() : p(-1), e(-1), pe(-1) {}
PrimePower(P p, int e, P pe) : p(p), e(e), pe(pe) {}
};
tuple<int, ll, ll> ord_pow_div(ll n, ll m)
{
assert(m >= 2);
if (m == 2)
{
int e = countr_zero(n);
return {e, 1LL << e, n >> e};
}
if (n % m != 0)
return {0, 1, n};
n /= m;
if (n % m != 0)
return {1, m, n};
n /= m;
ll m2 = m * m;
auto [f, m2f, nn] = ord_pow_div(n, m2);
int e = 2 + 2 * f;
ll me = m2f * m2;
if (nn % m == 0)
e++, me *= m, nn /= m;
return {e, me, nn};
}
template <class P>
vc<PrimePower<P>> factorized_mul
(const vc<PrimePower<P>> &fac1, const vc<PrimePower<P>> &fac2)
{
const int n = fac1.size(), m = fac2.size();
vc<PrimePower<P>> fac;
fac.reserve(n + m);
int i = 0, j = 0;
while (i < n && j < m)
{
if (fac1[i].p < fac2[j].p)
fac.emplace_back(fac1[i++]);
else if (fac1[i].p > fac2[j].p)
fac.emplace_back(fac2[j++]);
else
{
using U = larger_int_t<P>;
fac.emplace_back(fac1[i].p, fac1[i].e + fac2[j].e,
U(fac1[i].pe) * U(fac2[j].pe));
i++, j++;
}
}
fac.insert(fac.end(), fac1.begin() + i, fac1.end());
fac.insert(fac.end(), fac2.begin() + j, fac2.end());
return fac;
}
struct LinearSieve
{
public:
static int n;
static vc<PrimePower<int>> lpf_;
static vc<int> primes;
static void reserve(int n_)
{
if (n_ <= n)
return;
n = max(n_, 2 * n);
lpf_.resize(n + 1);
for (int d = 2; d <= n; d++)
{
if (lpf_[d].p == -1)
{
lpf_[d] = PrimePower<int>(d, 1, d);
primes.eb(d);
}
fec(p : primes)
{
if (p > n / d || p > lpf_[d].p)
break;
if (lpf_[d].p == p)
lpf_[p * d] = PrimePower<int>(p, lpf_[d].e + 1, lpf_[d].pe * p);
else
lpf_[p * d] = PrimePower<int>(p, 1, p);
}
}
}
template <class P = int>
static PrimePower<P> lpf(int n)
{
assert(n >= 1);
reserve(n);
return lpf_[n];
}
static bool is_prime(int n)
{
if (n <= 1)
return false;
return lpf(n).p == n;
}
static int Omega(int n)
{
assert(1 <= n);
static vc<unsigned char> table{0, 0};
if (n >= int(table.size()))
{
reserve(n);
const int first = int(table.size());
table.resize(n + 1);
for (int i = first; i <= n; i++)
table[i] = table[i / lpf_[i].p] + 1;
}
return table[n];
}
};
vc<PrimePower<int>> LinearSieve::lpf_{};
int LinearSieve::n{};
vc<int> LinearSieve::primes{};
namespace internal
{
template <class M>
typename M::S multiplicative_monoid_power(typename M::S a, ll k)
{
assert(k >= 0);
if constexpr (HasMonoidPow<M, ll>::value)
return M::pow(a, k);
else
{
auto res = M::e();
while (k > 0)
{
if (k & 1)
res = M::op(res, a);
k >>= 1;
if (k > 0)
a = M::op(a, a);
}
return res;
}
}
template <class G>
typename G::S multiplicative_integer_multiple(typename G::S a, ll n)
{
if (n < 0)
{
a = G::inv(a);
return G::op(multiplicative_monoid_power<G>(a, -(n + 1)), a);
}
return multiplicative_monoid_power<G>(a, n);
}
template <class R>
struct multiplicative_integer_embedding
{
};
template <class G, class M>
struct multiplicative_integer_embedding<RingFromGroupMonoid<G, M>>
{
static typename G::S get(ll n)
{ return multiplicative_integer_multiple<G>(M::e(), n); }
};
template <class G, class H>
struct multiplicative_integer_embedding<FieldFromGroupGroup<G, H>>
{
};
template <class R>
typename R::S multiplicative_from_integer(ll n)
{ return multiplicative_integer_embedding<R>::get(n); }
template <class R, class F, class Q>
decltype(auto) eval_primepower(const F &f, const Q &q)
{
if constexpr (is_invocable_v<const F &, const Q &>)
return f(q);
else
return f(q, R{});
}
}
inline constexpr auto e_primepower = [](const auto &q, auto ring)
{ return q.e == 0 ? decltype(ring)::e1() : decltype(ring)::e0(); };
inline constexpr auto zeta_primepower = [](const auto &, auto ring)
{ return decltype(ring)::e1(); };
inline constexpr auto id_primepower = [](const auto &q, auto ring)
{ return internal::multiplicative_from_integer<decltype(ring)>(q.pe); };
inline constexpr auto pow_primepower = [](ll k)
{
assert(k >= 0);
return [k](const auto &q, auto ring)
{
using R = decltype(ring);
return internal::multiplicative_monoid_power<MonoidOfSemiRingMul<R>>(
internal::multiplicative_from_integer<R>(q.pe), k);
};
};
inline constexpr auto pow_inv_primepower = [](ll k)
{
assert(k >= 0);
return [k](const auto &q, auto ring)
{
using R = decltype(ring);
using S = typename R::S;
if (k == 0 || q.e == 0)
return R::e1();
if (S::mod() % q.p == 0)
return R::e0();
return internal::multiplicative_monoid_power<MonoidOfSemiRingMul<R>>(
R::inv(internal::multiplicative_from_integer<R>(q.pe)), k);
};
};
inline constexpr auto mobius_primepower = [](const auto &q, auto ring)
{
using R = decltype(ring);
return q.e == 0 ? R::e1() : q.e == 1 ? R::minus(R::e1()) : R::e0();
};
inline constexpr auto divisor_count_primepower = [](const auto &q, auto ring)
{ return internal::multiplicative_from_integer<decltype(ring)>(ll(q.e) + 1); };
inline constexpr auto divisor_sum_primepower = [](const auto &q, auto ring)
{
using R = decltype(ring);
return R::add(internal::multiplicative_from_integer<R>(q.pe),
internal::multiplicative_from_integer<R>((q.pe - 1) / (q.p - 1)));
};
inline constexpr auto divisor_k_primepower = [](ll k)
{
assert(k >= 0);
return [k](const auto &q, auto ring)
{
using R = decltype(ring);
const auto pk = internal::multiplicative_monoid_power<MonoidOfSemiRingMul<R>>(
internal::multiplicative_from_integer<R>(q.p), k);
auto res = R::e1();
for (int i = 0; i < q.e; i++)
res = R::add(R::mul(res, pk), R::e1());
return res;
};
};
inline constexpr auto totient_primepower = [](const auto &q, auto ring)
{ return internal::multiplicative_from_integer<decltype(ring)>(q.pe - q.pe / q.p); };
// https://github.com/miscalculation53/library/tree/wip/math/modint/inv_many.hpp
namespace internal
{
template <class R, class = void>
struct dirichlet_has_inv : false_type {};
template <class R>
struct dirichlet_has_inv<R, void_t<decltype(R::inv(declval<const typename R::S &>()))>> : true_type {};
template <class R>
struct dirichlet_modint_field : false_type {};
template <class S>
struct dirichlet_modint_field<FieldAddSubMulDiv<S>> : is_modint<S> {};
template <class R>
struct dirichlet_divisor
{
using S = typename R::S;
static constexpr bool exact_integer = is_integral_ext<S> && is_same_v<R, RingAddSubMul<S>>;
S value;
bool identity;
S operator()(const S &a) const
{
if (identity)
return a;
if constexpr (dirichlet_has_inv<R>::value)
return R::mul(a, value);
else if constexpr (exact_integer)
return a / value;
else
return R::minus(a);
}
};
}
template <class R>
struct DirichletSeries
{
using S = typename R::S;
private:
int n_;
vc<S> f_;
bool multiplicative_;
public:
friend DirichletSeries operator*(const S &a, const DirichletSeries &f) { return f * a; }
private:
public:
};
inline constexpr auto e_prefix_sum = [](ll n, auto ring)
{ return n == 0 ? decltype(ring)::e0() : decltype(ring)::e1(); };
inline constexpr auto zeta_prefix_sum = [](ll n, auto ring)
{ return internal::multiplicative_from_integer<decltype(ring)>(n); };
inline constexpr auto id_prefix_sum = [](ll n, auto ring)
{
using R = decltype(ring);
const auto a = internal::multiplicative_from_integer<R>(n % 2 == 0 ? n / 2 : n);
const auto b = n % 2 == 0
? R::add(internal::multiplicative_from_integer<R>(n), R::e1())
: internal::multiplicative_from_integer<R>(n / 2 + 1);
return R::mul(a, b);
};
namespace internal
{
template <int D>
struct dirichlet_root_prefix_sum_index
{
static_assert(D >= 1);
ll n, maximum;
int k, large;
vc<ll> large_value;
vc<int> raw_index;
};
template <>
struct dirichlet_root_prefix_sum_index<1>
{
ll n;
int k, large;
explicit dirichlet_root_prefix_sum_index(ll n) : n(n)
{
assert(n >= 0);
const ll root = iroot(n, 2), l = n / (root + 1);
k = int(root), large = int(l);
}
int size() const { return k + large; }
int index(ll v) const { return v <= k ? int(v) - 1 : size() - int(n / v); }
ll value(int i) const { return i < k ? ll(i) + 1 : n / (size() - i); }
};
using dirichlet_prefix_sum_index = dirichlet_root_prefix_sum_index<1>;
template <class R, class GetF>
typename R::S eval_dirichlet_prefix(const GetF &getF, ll n)
{
if constexpr (is_invocable_v<const GetF &, ll>)
return getF(n);
else
return getF(n, R{});
}
}
template <class R, int D = 1>
struct DirichletPrefixSum
{
using S = typename R::S;
private:
ll n_;
int k_, l_;
vc<S> small_, large_;
bool multiplicative_;
internal::dirichlet_root_prefix_sum_index<D> coordinates_;
struct same_shape {};
DirichletPrefixSum(const DirichletPrefixSum &a, same_shape)
: n_(a.n_), k_(a.k_), l_(a.l_), small_(k_ + 1, R::e0()),
large_(l_ + 1, R::e0()), multiplicative_(false), coordinates_(a.coordinates_) {}
int large_index(ll x) const
{
if constexpr (D == 1) return int(n_ / x);
else return coordinates_.raw_index[size_t(n_ / ipow<ll>(x, D))];
}
public:
DirichletPrefixSum() : DirichletPrefixSum(0) {}
explicit DirichletPrefixSum(ll n)
: n_(n), multiplicative_(false), coordinates_(n)
{
k_ = coordinates_.k, l_ = coordinates_.large;
small_.assign(k_ + 1, R::e0());
large_.assign(l_ + 1, R::e0());
}
template <class GetF, enable_if_t<is_invocable_v<const GetF &, ll>
|| is_invocable_v<const GetF &, ll, R>, int> = 0>
DirichletPrefixSum(ll n, const GetF &getF, bool multiplicative = false)
: DirichletPrefixSum(n)
{
for (int x = 1; x <= k_; x++)
small_[x] = internal::eval_dirichlet_prefix<R>(getF, x);
for (int i = 1; i <= l_; i++)
large_[i] = internal::eval_dirichlet_prefix<R>(getF, value(size() - i));
multiplicative_ = multiplicative;
assert(!multiplicative || n == 0 || small_[1] == R::e1());
}
static DirichletPrefixSum unit(ll n)
{ return DirichletPrefixSum(n, e_prefix_sum, true); }
ll n() const { return n_; }
int size() const { return k_ + l_; }
ll value(int i) const
{
assert(0 <= i && i < size());
if constexpr (D == 1) return i < k_ ? ll(i) + 1 : n_ / (size() - i);
else return i < k_ ? ll(i) + 1 : coordinates_.large_value[size() - i];
}
bool contains(ll x) const
{
if constexpr (D == 1)
return 0 <= x && x <= n_ && (x <= k_ || n_ / (n_ / x) == x);
else
return 0 <= x && x <= coordinates_.maximum
&& (x <= k_ || coordinates_.large_value[large_index(x)] == x);
}
const S &F(ll x) const
{
assert(contains(x));
return x <= k_ ? small_[size_t(x)] : large_[large_index(x)];
}
void setF(ll x, const S &value)
{
assert(x >= 1 && contains(x));
(x <= k_ ? small_[size_t(x)] : large_[large_index(x)]) = value;
multiplicative_ = false;
}
private:
public:
DirichletPrefixSum operator-() const
{
DirichletPrefixSum res(*this);
for (int i = 1; i <= k_; i++)
res.small_[i] = R::minus(res.small_[i]);
for (int i = 1; i <= l_; i++)
res.large_[i] = R::minus(res.large_[i]);
res.multiplicative_ = false;
return res;
}
friend DirichletPrefixSum operator*(const S &a, const DirichletPrefixSum &f) { return f * a; }
private:
public:
};
// https://github.com/miscalculation53/library/tree/wip/ds/fenwick_tree/fenwick_tree.hpp
template <class G>
struct FenwickTree
{
using S = typename G::S;
private:
int n;
vc<S> dat;
public:
FenwickTree() {}
FenwickTree(int n) : n(n), dat(n + 1, G::e()) {}
S sum(int r) const
{
assert(0 <= r && r <= n);
S s = G::e();
while (r > 0)
{
s = G::op(s, dat[r]);
r -= r & -r;
}
return s;
}
void add(int i, S x)
{
assert(0 <= i && i < n);
i++;
while (i <= n)
{
dat[i] = G::op(dat[i], x);
i += i & -i;
}
}
};
namespace internal
{
template <class R>
DirichletPrefixSum<R> prime_prefix_sum_sieve(const DirichletPrefixSum<R> &a)
{
const ll n = a.n();
const int root = int(iroot(n, 2));
assert(n == 0 || a.F(1) == R::e1());
LinearSieve::reserve(root);
DirichletPrefixSum<R> dp(n, [&](ll x) { return R::add(a.F(x), R::minus(R::e1())); });
for (int p : LinearSieve::primes)
{
if (p > root) break;
const auto fp = R::add(a.F(p), R::minus(a.F(p - 1))), before = dp.F(p - 1);
auto update = [&](ll x)
{
dp.setF(x, R::add(dp.F(x), R::minus(R::mul(fp,
R::add(dp.F(x / p), R::minus(before))))));
};
for (ll j = 1; j <= n / (ll(root) + 1) && n / j >= ll(p) * p; j++) update(n / j);
for (ll x = root; x >= ll(p) * p; x--) update(x);
}
return dp;
}
template <class R, class GetPrimePower>
DirichletPrefixSum<R> multiplicative_prefix_sum_sieve(
const DirichletPrefixSum<R> &prime_sum, const GetPrimePower &f_primepower)
{
using S = typename R::S;
const ll n = prime_sum.n();
const int root = int(iroot(n, 2));
assert(n == 0 || prime_sum.F(1) == R::e0());
LinearSieve::reserve(root);
DirichletPrefixSum<R> res(n, [&](ll x) { return prime_sum.F(x); });
for (int pi = int(upper_bound(LinearSieve::primes.begin(), LinearSieve::primes.end(), root)
- LinearSieve::primes.begin()) - 1; pi >= 0; pi--)
{
const int p = LinearSieve::primes[pi];
vc<pair<ll, S>> powers;
for (ll q = p, e = 1;; q *= p, e++)
{
powers.emplace_back(q, internal::eval_primepower<R>(f_primepower, PrimePower<ll>(p, int(e), q)));
if (q > n / p) break;
}
const S before = prime_sum.F(p);
auto update = [&](ll x)
{
S value = res.F(x);
for (size_t e = 0; e + 1 < powers.size() && powers[e + 1].first <= x; e++)
{
value = R::add(value, R::mul(powers[e].second,
R::add(res.F(x / powers[e].first), R::minus(before))));
value = R::add(value, powers[e + 1].second);
}
res.setF(x, value);
};
for (ll j = 1; j <= n / (ll(root) + 1) && n / j >= ll(p) * p; j++) update(n / j);
for (ll x = root; x >= ll(p) * p; x--) update(x);
}
return DirichletPrefixSum<R>(n, [&](ll x) { return R::add(res.F(x), R::e1()); }, true);
}
template <class R>
struct multiplicative_sieve_updates
{
ll n, bound;
int root, large, top;
dirichlet_prefix_sum_index coordinates;
FenwickTree<GroupOfRingAdd<R>> bit;
explicit multiplicative_sieve_updates(ll n)
: n(n), root(int(iroot(n, 2))), large(int(n / (ll(root) + 1))),
top(min(large, int(iroot(n, 3)))), coordinates(n)
{
bound = n / (ll(top) + 1);
bit = FenwickTree<GroupOfRingAdd<R>>(root + large - top);
}
int index(ll x) const
{ return coordinates.index(x); }
void add(ll v, const typename R::S &value)
{
assert(1 <= v && v <= bound);
if (value != R::e0()) bit.add(index(v), value);
}
typename R::S operator[](ll x) const
{
assert(0 <= x && x <= bound);
return bit.sum(index(x) + 1);
}
template <class Apply>
void apply(DirichletPrefixSum<R> &dp, const Apply &op) const
{
for (int x = 1; x <= root; x++) dp.setF(x, op(dp.F(x), (*this)[x]));
for (int j = large; j > top; j--) dp.setF(n / j, op(dp.F(n / j), (*this)[n / j]));
}
};
template <class R>
DirichletPrefixSum<R> prime_prefix_sum_sieve_2_3(const DirichletPrefixSum<R> &a)
{
using S = typename R::S;
const ll n = a.n();
if (n == 0) return {};
assert(a.F(1) == R::e1());
const int root = int(iroot(n, 2)), cut = int(iroot(n, 6)), cube = int(iroot(n, 3));
LinearSieve::reserve(root);
vc<S> weight(root + 1, R::e0());
for (int p : LinearSieve::primes) { if (p > root) break; weight[p] = R::add(a.F(p), R::minus(a.F(p - 1))); }
DirichletPrefixSum<R> dp(n, [&](ll x) { return R::add(a.F(x), R::minus(R::e1())); });
internal::multiplicative_sieve_updates<R> delta(n);
const auto sub = [](const S &x, const S &y) { return R::add(x, R::minus(y)); };
auto lucy = [&](int p)
{
const S before = dp.F(p - 1);
auto update = [&](ll x) { dp.setF(x, sub(dp.F(x), R::mul(weight[p], sub(dp.F(x / p), before)))); };
for (int j = 1; j <= delta.large && n / j >= ll(p) * p; j++) update(n / j);
for (ll x = root; x >= ll(p) * p; x--) update(x);
};
size_t pi = 0;
while (pi < LinearSieve::primes.size() && LinearSieve::primes[pi] <= cut) lucy(LinearSieve::primes[pi++]);
for (; pi < LinearSieve::primes.size() && LinearSieve::primes[pi] <= cube; pi++)
{
const int p = LinearSieve::primes[pi];
const S before = dp.F(p - 1);
for (int j = 1; j <= delta.top && n / j >= ll(p) * p; j++)
{
const ll x = n / j, y = x / p;
S value = dp.F(y);
if (y <= delta.bound) value = sub(value, delta[y]);
dp.setF(x, sub(dp.F(x), R::mul(weight[p], sub(value, before))));
}
auto dfs = [&](auto &&self, ll v, size_t first, const S &f) -> void
{
if (v != p) delta.add(v, f);
for (size_t j = first; j < LinearSieve::primes.size(); j++)
{
const int q = LinearSieve::primes[j];
if (q > delta.bound / v) break;
self(self, v * q, j, R::mul(f, weight[q]));
}
};
dfs(dfs, p, pi, weight[p]);
}
delta.apply(dp, sub);
while (pi < LinearSieve::primes.size() && LinearSieve::primes[pi] <= root) lucy(LinearSieve::primes[pi++]);
return dp;
}
template <class R, class GetPrimePower>
DirichletPrefixSum<R> multiplicative_prefix_sum_sieve_2_3(
const DirichletPrefixSum<R> &prime_sum, const GetPrimePower &f_primepower)
{
using S = typename R::S;
const ll n = prime_sum.n();
if (n == 0) return DirichletPrefixSum<R>::unit(0);
assert(prime_sum.F(1) == R::e0());
const int root = int(iroot(n, 2)), cut = int(iroot(n, 6)), cube = int(iroot(n, 3));
LinearSieve::reserve(root);
const auto &primes = LinearSieve::primes;
const size_t begin = upper_bound(primes.begin(), primes.end(), cube) - primes.begin();
vc<S> fp(root + 1, R::e0()), fp2(fp);
for (int p : primes)
{
if (p > root) break;
fp[p] = internal::eval_primepower<R>(f_primepower, PrimePower<ll>(p, 1, p));
fp2[p] = internal::eval_primepower<R>(f_primepower, PrimePower<ll>(p, 2, ll(p) * p));
}
const auto sub = [](const S &x, const S &y) { return R::add(x, R::minus(y)); };
DirichletPrefixSum<R> dp(n, [&](ll x)
{
S value = R::e1();
if (x <= cube) return value;
value = R::add(value, sub(prime_sum.F(x), prime_sum.F(cube)));
for (size_t j = begin; j < primes.size() && primes[j] <= x / primes[j]; j++)
{
const int p = primes[j];
value = R::add(value, R::add(fp2[p], R::mul(fp[p], sub(prime_sum.F(x / p), prime_sum.F(p)))));
}
return value;
});
internal::multiplicative_sieve_updates<R> delta(n);
for (size_t pi = begin; pi > 0;)
{
const int p = primes[--pi];
vc<pair<ll, S>> powers;
for (ll q = p, e = 1;; q *= p, e++)
{
powers.emplace_back(q, internal::eval_primepower<R>(f_primepower, PrimePower<ll>(p, int(e), q)));
if (q > n / p) break;
}
auto update = [&](ll x)
{
S value = dp.F(x);
for (const auto &[q, f] : powers)
{
if (q > x) break;
const ll y = x / q;
S previous = dp.F(y);
if (p > cut && y <= delta.bound) previous = R::add(previous, delta[y]);
value = R::add(value, R::mul(f, previous));
}
dp.setF(x, value);
};
if (p > cut)
{
for (int j = 1; j <= delta.top; j++) update(n / j);
auto dfs = [&](auto &&self, ll v, size_t i, int e, ll pe, const S &other) -> void
{
const int q = primes[i];
const S f = R::mul(other, e == 1 ? fp[q] :
internal::eval_primepower<R>(f_primepower, PrimePower<ll>(q, e, pe)));
delta.add(v, f);
if (q <= delta.bound / v) self(self, v * q, i, e + 1, pe * q, other);
for (size_t j = i + 1; j < primes.size() && primes[j] <= delta.bound / v; j++)
self(self, v * primes[j], j, 1, primes[j], f);
};
dfs(dfs, p, pi, 1, p, R::e1());
}
else
{
if (pi + 1 == begin || primes[pi + 1] > cut) delta.apply(dp, R::add);
for (int j = 1; j <= delta.large; j++) update(n / j);
for (int x = root; x >= p; x--) update(x);
}
}
if (cut < 2) delta.apply(dp, R::add);
return DirichletPrefixSum<R>(n, [&](ll x) { return dp.F(x); }, true);
}
inline constexpr ll multiplicative_prefix_sum_fenwick_threshold = 1'000'000;
}
template <class R>
DirichletPrefixSum<R> prime_prefix_sum(const DirichletPrefixSum<R> &g)
{
return g.n() < internal::multiplicative_prefix_sum_fenwick_threshold
? internal::prime_prefix_sum_sieve(g) : internal::prime_prefix_sum_sieve_2_3(g);
}
template <class R, class GetPrimePower>
DirichletPrefixSum<R> multiplicative_prefix_sum(const DirichletPrefixSum<R> &f_prime,
const GetPrimePower &f_primepower)
{
return f_prime.n() < internal::multiplicative_prefix_sum_fenwick_threshold
? internal::multiplicative_prefix_sum_sieve(f_prime, f_primepower)
: internal::multiplicative_prefix_sum_sieve_2_3(f_prime, f_primepower);
}
// https://github.com/miscalculation53/library/tree/wip/math/quotients.hpp
struct quotients
{
private:
ll n;
int d;
public:
quotients(ll n, int d = 1) : n(n), d(d)
{
assert(n >= 1 && d >= 1);
}
struct Iterator
{
private:
ll y, l, r;
const quotients &q;
public:
Iterator(ll y, ll l, ll r, const quotients &q) : y(y), l(l), r(r), q(q) {}
tuple<ll, ll, ll> operator*() const { return {y, l, r}; }
Iterator& operator++()
{
if (l == 0)
y = l = r = -1;
else
{
r = l;
y = q.n / ipow(r, q.d);
l = iroot(q.n / (y + 1), q.d);
}
return *this;
}
bool operator!=(const Iterator &other) const { return y != other.y; }
};
Iterator begin() const { return Iterator(1, iroot(n / 2, d), iroot(n, d), *this); }
Iterator end() const { return Iterator(-1, -1, -1, *this); }
};
struct quotients_ceil
{
private:
ll n;
int d;
public:
quotients_ceil(ll n, int d = 1) : n(n), d(d)
{
assert(n >= 1 && d >= 1);
}
struct Iterator
{
private:
ll y, l, r;
const quotients_ceil &q;
public:
Iterator(ll y, ll l, ll r, const quotients_ceil &q) : y(y), l(l), r(r), q(q) {}
tuple<ll, ll, ll> operator*() const { return {y, l, r}; }
Iterator& operator++()
{
if (l == 1)
y = l = r = -1;
else
{
r = l;
y = divceil(q.n, ipow(r - 1, q.d));
l = iroot(divceil(q.n, y), q.d);
}
return *this;
}
bool operator!=(const Iterator &other) const { return y != other.y; }
};
Iterator begin() const { return Iterator(2, iroot_ceil(divceil(n, 2), d), iroot_ceil(n, d), *this); }
Iterator end() const { return Iterator(-1, -1, -1, *this); }
};
void main2()
{
LL(N, M);
using mint = ull;
vl pts;
fec([ y, l, r ] : quotients(N)) pts.eb(l), pts.eb(r);
fec([ y, l, r ] : quotients(M)) pts.eb(l), pts.eb(r);
sortunique(pts);
dump(pts);
DirichletPrefixSum<RingAddSubMul<mint>> zetaN(N, zeta_prefix_sum);
DirichletPrefixSum<RingAddSubMul<mint>> zetaM(M, zeta_prefix_sum);
auto piN = prime_prefix_sum(zetaN);
auto piM = prime_prefix_sum(zetaM);
auto fN = multiplicative_prefix_sum(-piN, mobius_primepower);
auto fM = multiplicative_prefix_sum(-piM, mobius_primepower);
mint ans = 0;
rep(i, SZ(pts) - 1)
{
ll l = pts[i], r = pts[i + 1];
mint coefN = (N / r);
mint coefM = (M / r);
mint tmpr = fN.contains(r) ? fN.F(r) : fM.F(r);
mint tmpl = fN.contains(l) ? fN.F(l) : fM.F(l);
ans += coefN * coefM * (tmpr - tmpl);
dump(l, r, coefN, coefM, tmpr, tmpl);
}
PRINT(ans);
}
void test()
{
}
// https://github.com/miscalculation53/library/tree/wip/template/template_main.hpp
template <auto init, auto main2, auto test>
struct Main
{
Main()
{
cauto CERR = [](string val, string color)
{
string s = "\033[" + color + "m" + val + "\033[m";
};
CERR("\n[FAST_IO]\n\n", "32");
cout << fixed << setprecision(20);
init();
CERR("\n[SINGLE_TESTCASE]\n\n", "36");
main2();
}
};
Main<init, main2, test> main_dummy;
int main() {}