#pragma once
#include "../../conv/subset/lib.hpp"
namespace tifa_libs {
template <class T, u32 N = 21>
auto exp_fpssps(u32 n, vec<T> g) NE {
static conv_subset<T, N> ss;
assert(n <= N && g[0] == 0), g.resize(1 << n);
vec<T> h{1};
flt_ (u32, k, 1, n + 1) {
auto a = ss.conv(h, {begin(g) + (1 << (k - 1)), begin(g) + (1 << k)});
copy(a, std::back_inserter(h));
}
return h;
}
} // namespace tifa_libs
#line 2 "src/sps/exp/lib.hpp"
#line 2 "src/conv/subset/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 4 "src/conv/subset/lib.hpp"
namespace tifa_libs {
template <class T, u32 N>
struct conv_subset {
using arr_t = arr<T, N + 1>;
vecu pc;
CEXP void add(arr_t& l, cT_(arr_t) r, u32 d) CNE {
flt_ (u32, i, 0, d) l[i] += r[i];
}
CEXP void sub(arr_t& l, cT_(arr_t) r, u32 d) CNE {
flt_ (u32, i, d, N + 1) l[i] -= r[i];
}
public:
CEXP conv_subset() NE : pc(1u << N) {
flt_ (u32, i, 1, 1u << N) pc[i] = pc[i - (i & -i)] + 1;
}
CEXP void zeta(vec<arr_t>& a) CNE {
for (u32 w = 1; w < (u32)a.size(); w *= 2)
for (u32 k = 0; k < (u32)a.size(); k += w * 2)
flt_ (u32, i, 0, w) add(a[k + w + i], a[k + i], pc[k + w + i]);
}
CEXP void mobius(vec<arr_t>& a) CNE {
cu32 n = (u32)a.size();
for (u32 w = n >> 1; w; w /= 2)
for (u32 k = 0; k < n; k += w * 2)
flt_ (u32, i, 0, w) sub(a[k + w + i], a[k + i], pc[k + w + i]);
}
CEXP vec<arr_t> lift(spn<T> a) CNE {
vec<arr_t> A(a.size());
flt_ (u32, i, 0, (u32)a.size()) fill(A[i], T()), A[i][pc[i]] = a[i];
return A;
}
CEXP vec<T> unlift(spn<arr_t> A) CNE {
vec<T> a(A.size());
flt_ (u32, i, 0, (u32)A.size()) a[i] = A[i][pc[i]];
return a;
}
CEXP void prod(vec<arr_t>& A, spn<arr_t> B) CNE {
cu32 n = (u32)A.size(), d = (u32)std::countr_zero(n);
flt_ (u32, i, 0, n) {
arr_t c;
flt_ (u32, j, 0, d + 1)
for (u32 k = 0; k <= d - j; ++k) c[j + k] += A[i][j] * B[i][k];
A[i].swap(c);
}
}
CEXP vec<T> conv(spn<T> a, spn<T> b) CNE {
vec<arr_t> A = lift(a), B = lift(b);
zeta(A), zeta(B), prod(A, B), mobius(A);
return unlift(A);
}
};
} // namespace tifa_libs
#line 4 "src/sps/exp/lib.hpp"
namespace tifa_libs {
template <class T, u32 N = 21>
auto exp_fpssps(u32 n, vec<T> g) NE {
static conv_subset<T, N> ss;
assert(n <= N && g[0] == 0), g.resize(1 << n);
vec<T> h{1};
flt_ (u32, k, 1, n + 1) {
auto a = ss.conv(h, {begin(g) + (1 << (k - 1)), begin(g) + (1 << k)});
copy(a, std::back_inserter(h));
}
return h;
}
} // namespace tifa_libs
src/sps/exp/lib.hpp