#pragma once
#include "../binom/lib.hpp"
namespace tifa_libs {
template <class mint, class fact = fact_helper<mint>, bool with_sgn = true>
class stirling1 {
const binom<mint, fact> mCn;
vvec<mint> s;
public:
static CEXP u32 mod() NE { return mint::mod(); }
//! @param p MUST be prime
CEXPE stirling1() NE : mCn(mint::mod()), s(mint::mod()) {
u32 p = mint::mod();
assert(p < 32768), s[0] = {1};
flt_ (u32, i, 1, p) {
s[i].assign(i + 1, 0);
flt_ (u32, j, 0, i + 1) {
if (j) s[i][j] += s[i - 1][j - 1];
if (j < i) s[i][j] += s[i - 1][j] * (p - i + 1);
}
}
}
template <std::signed_integral T>
CEXP mint operator()(T m_, T n_) CNE {
retif_((n_ < 0 || n_ > m_) [[unlikely]], 0);
cu32 p = mod();
cu64 m = (u64)m_, n = (u64)n_, i = m / p;
if (i > n) return 0;
u64 a = (n - i) / (p - 1);
cu32 j = u32(m % p);
u32 b = u32((n - i) % (p - 1));
if (!b && j) {
if (b += p - 1; a) --a;
else return 0;
}
if (i < a || b > j) return 0;
mint res = mCn.lucas(i, a) * s[j][b];
if CEXP (with_sgn)
if ((i + a) & 1) res = -res;
return res;
}
template <std::unsigned_integral T>
CEXP mint operator()(T m_, T n_) CNE { return operator()(std::make_signed_t<T>(m_), std::make_signed_t<T>(n_)); }
};
} // namespace tifa_libs
#line 2 "src/comb/stirling1_smallp/lib.hpp"
#line 2 "src/comb/binom/lib.hpp"
#line 2 "src/math/fact/helper/lib.hpp"
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<T>;
template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>; template <class T, usz N> using carr = std::array<const T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>; template <class U, class T> using vvecp = vvec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, T)
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 2 "src/util/traits/math/lib.hpp"
// clang-format off
#line 4 "src/util/traits/math/lib.hpp"
namespace tifa_libs {
template <class T> concept char_c = std::same_as<T, char> || std::same_as<T, signed char> || std::same_as<T, unsigned char>;
#pragma GCC diagnostic ignored "-Wpedantic"
template <class T> concept s128_c = std::same_as<T, __int128_t> || std::same_as<T, __int128>;
template <class T> concept u128_c = std::same_as<T, __uint128_t> || std::same_as<T, unsigned __int128>;
template <class T> concept i128_c = s128_c<T> || u128_c<T>;
#pragma GCC diagnostic warning "-Wpedantic"
template <class T> concept imost64_c = std::integral<T> && sizeof(T) * __CHAR_BIT__ <= 64;
template <class T> concept smost64_c = imost64_c<T> && std::signed_integral<T>;
template <class T> concept umost64_c = imost64_c<T> && std::unsigned_integral<T>;
template <class T> concept int_c = i128_c<T> || imost64_c<T>;
template <class T> concept sint_c = s128_c<T> || smost64_c<T>;
template <class T> concept uint_c = u128_c<T> || umost64_c<T>;
template <class T> concept arithm_c = std::is_arithmetic_v<T> || int_c<T>;
template <class T> concept mint_c = requires(T x) { {x.mod()} -> uint_c; {x.val()} -> uint_c; };
template <class T> concept dft_c = requires(T x, std::vector<TPN T::data_t> v, u32 n) { {x.size()} -> std::same_as<u32>; x.bzr(n); x.dif(v, n); x.dit(v, n); };
template <class T> concept ntt_c = dft_c<T> && requires(T x) { T::max_size; T::G; };
template <class T> struct to_sint : std::make_signed<T> {};
template <> struct to_sint<u128> { using type = i128; };
template <> struct to_sint<i128> { using type = i128; };
template <class T> using to_sint_t = TPN to_sint<T>::type;
template <class T> struct to_uint : std::make_unsigned<T> {};
template <> struct to_uint<u128> { using type = u128; };
template <> struct to_uint<i128> { using type = u128; };
template <class T> using to_uint_t = TPN to_uint<T>::type;
template <arithm_c T> struct to_bigger : std::make_unsigned<T> {};
#define _(w,ww) template <> struct to_bigger<w> { using type = ww; }
#define _2(w,ww) _(i##w,i##ww); _(u##w,u##ww);
_2(8, 16); _2(16, 32); _2(32, 64); _2(64, 128); _(f32, f64); _(f64, f128);
#undef _2
#undef _
template <class T> using to_bigger_t = TPN to_bigger<T>::type;
template <arithm_c T> CEXP T inf_v = [] {
if CEXP(sint_c<T>) return T(to_uint_t<T>(-1) / 4 - 1);
else if CEXP(uint_c<T>) return T(-1) / 2 - 1;
else return std::numeric_limits<T>::max() / 2 - 1;
}();
} // namespace tifa_libs
// clang-format on
#line 5 "src/math/fact/helper/lib.hpp"
namespace tifa_libs {
template <mint_c mint>
struct fact_helper {
using val_t = mint;
static CEXP u32 DEFAULT_MAX = 10'000'001;
static CEXP u64 mod() NE { return val_t::mod(); }
static inline vec<val_t> fact, ifact;
fact_helper() = delete;
// ensure fact.size() >= sz
static CEXP void ensure(u32 sz = DEFAULT_MAX) NE {
if (sz = max(2_u32, min((u32)mod(), sz)); sz <= fact.size()) return;
u32 pre = (u32)fact.size();
fact.resize(sz), ifact.resize(sz);
if (pre < 2) pre = 2, fact[0] = fact[1] = ifact[0] = ifact[1] = 1;
flt_ (u32, i, pre, sz) fact[i] = fact[i - 1] * i;
ifact.back() = fact.back().inv();
for (u32 i = sz - 1; i > pre; --i) ifact[i - 1] = ifact[i] * i;
}
static CEXP val_t get_fact(u64 n) NE {
if (n >= mod()) [[unlikely]]
return 0;
if (fact.empty()) [[unlikely]]
ensure();
if (n < fact.size()) [[likely]]
return fact[n];
val_t _ = fact.back() * n;
flt_ (u64, i, fact.size(), n) _ *= i;
return _;
}
static CEXP val_t get_ifact(u64 n) NE {
if (n >= mod()) [[unlikely]]
return 0;
if (fact.empty()) [[unlikely]]
ensure();
if (n < ifact.size()) [[likely]]
return ifact[n];
return get_fact(n).inv();
}
};
} // namespace tifa_libs
#line 4 "src/comb/binom/lib.hpp"
namespace tifa_libs {
template <class mint, class fact = fact_helper<mint>>
requires std::same_as<mint, TPN fact::val_t>
struct binom {
using fact_t = fact;
CEXPE binom(u32 max_m = fact::DEFAULT_MAX) NE { fact::ensure(max_m + 1); }
// $\binom{m}{n}$
CEXP mint mCn(uint_c auto m, uint_c auto n) CNE { retif_((m < n) [[unlikely]], 0, mPn(m, n) * fact::get_ifact(n)); }
// $\binom{m}{n}$
template <sint_c T>
CEXP mint mCn(T m, T n) CNE { retif_((m < n || n < 0) [[unlikely]], 0, mCn(to_uint_t<T>(m), to_uint_t<T>(n))); }
//! mint::mod() must be prime
template <int_c T>
CEXP mint lucas(T m, T n) CNE {
assert(mint::mod() > 1);
auto f = [this](auto&& f, auto m, auto n) NE -> mint { retif_((n == 0), 1, this->mCn(m % fact::mod(), n % fact::mod()) * f(f, m / fact::mod(), n / fact::mod())); };
retif_((m < n || n < 0) [[unlikely]], 0, f(f, to_uint_t<T>(m), to_uint_t<T>(n)));
}
// $\binom{m}{n} \cdot n!$
CEXP mint mPn(uint_c auto m, uint_c auto n) CNE { retif_((m < n) [[unlikely]], 0, fact::get_fact(m) * fact::get_ifact(m - n)); }
// $\binom{m}{n} \cdot n!$
template <sint_c T>
CEXP mint mPn(T m, T n) CNE { retif_((m < n || n < 0) [[unlikely]], 0, mPn(to_uint_t<T>(m), to_uint_t<T>(n))); }
// $[x^n] \frac{1}{(1-x)^m}$
CEXP mint mHn(uint_c auto m, uint_c auto n) CNE { retif_((n <= 0), n == 0, mCn(m + n - 1, n)); }
// $[x^n] \frac{1}{(1-x)^m}$
template <sint_c T>
CEXP mint mHn(T m, T n) CNE { retif_((m < 0 || n <= 0), n == 0, mHn(to_uint_t<T>(m), to_uint_t<T>(n))); }
};
} // namespace tifa_libs
#line 4 "src/comb/stirling1_smallp/lib.hpp"
namespace tifa_libs {
template <class mint, class fact = fact_helper<mint>, bool with_sgn = true>
class stirling1 {
const binom<mint, fact> mCn;
vvec<mint> s;
public:
static CEXP u32 mod() NE { return mint::mod(); }
//! @param p MUST be prime
CEXPE stirling1() NE : mCn(mint::mod()), s(mint::mod()) {
u32 p = mint::mod();
assert(p < 32768), s[0] = {1};
flt_ (u32, i, 1, p) {
s[i].assign(i + 1, 0);
flt_ (u32, j, 0, i + 1) {
if (j) s[i][j] += s[i - 1][j - 1];
if (j < i) s[i][j] += s[i - 1][j] * (p - i + 1);
}
}
}
template <std::signed_integral T>
CEXP mint operator()(T m_, T n_) CNE {
retif_((n_ < 0 || n_ > m_) [[unlikely]], 0);
cu32 p = mod();
cu64 m = (u64)m_, n = (u64)n_, i = m / p;
if (i > n) return 0;
u64 a = (n - i) / (p - 1);
cu32 j = u32(m % p);
u32 b = u32((n - i) % (p - 1));
if (!b && j) {
if (b += p - 1; a) --a;
else return 0;
}
if (i < a || b > j) return 0;
mint res = mCn.lucas(i, a) * s[j][b];
if CEXP (with_sgn)
if ((i + a) & 1) res = -res;
return res;
}
template <std::unsigned_integral T>
CEXP mint operator()(T m_, T n_) CNE { return operator()(std::make_signed_t<T>(m_), std::make_signed_t<T>(n_)); }
};
} // namespace tifa_libs
src/comb/stirling1_smallp/lib.hpp