#pragma once
#include "../../../math/iroot/sqrt/lib.hpp"
#include "../../../math/qpow/mod/lib.hpp"
#include "../../../nt/lsieve/impl1/lib.hpp"
#include "../../../nt/mod/barrett/lib.hpp"
namespace tifa_libs {
namespace gen_ipowi_impl_ {
struct ls_ipowi {
static inline u64 mod;
vecuu ipowi;
protected:
cu32 B;
vvecuu fp, fpb;
u32 pre_j{0}, gap{0};
u64 now_r{1};
arr<u64, 355> p{1}; // maximal prime gaps: g_n=354 => p_n=4,302,407,359
CEXPE ls_ipowi(u32 n) NE : ipowi(n), B{isqrt(n)}, fp(B + 1, vecuu(B + 1)), fpb(B + 1, vecuu(B + 1)) {
if (n) ipowi[0] = 1;
if (n > 1) ipowi[1] = 1;
}
void prime(u32 p) NE {
if (ipowi[p] = qpow_mod(p, p, mod); p <= B) {
fp[p][0] = 1;
barrett<0> brt(mod, ipowi[p]);
flt_ (u32, j, 1, B + 1)
fp[p][j] = brt.reduce(fp[p][j - 1]);
fpb[p][0] = 1;
brt.reset(mod, fp[p].back());
flt_ (u32, j, 1, B + 1)
fpb[p][j] = brt.reduce(fpb[p][j - 1]);
}
}
void coprime(u32 i, u32 j) NE {
if (j <= pre_j) now_r = 1, pre_j = gap = 0;
const barrett<0> brt(mod, ipowi[i]);
if (cu32 new_gap = j - pre_j; new_gap > gap) {
flt_ (u32, x, gap + 1, new_gap + 1) p[x] = brt.reduce(p[x - 1]);
gap = new_gap;
}
now_r = mul_mod_u(now_r, p[j - pre_j], mod);
ipowi[i * j] = mul_mod_u(mul_mod_u(fp[j][i % B], fpb[j][i / B], mod), now_r, mod);
pre_j = j;
}
void not_coprime(u32 i, u32 j) NE { coprime(i, j); }
};
} // namespace gen_ipowi_impl_
// i^i from i=0..n-1
CEXP vecuu gen_ipowi(u32 n, u64 mod) NE {
retif_((n < 2) [[unlikely]], vecuu(n, 1));
gen_ipowi_impl_::ls_ipowi::mod = mod;
return lsieve<gen_ipowi_impl_::ls_ipowi>(n).ipowi;
}
// i^i from i=0..n-1
template <class mint>
CEXP vec<mint> gen_ipowi(u32 n) NE {
vec<mint> ans(n);
auto _ = gen_ipowi(n, mint::mod());
flt_ (u32, i, 0, n) ans[i] = _[i];
return ans;
}
} // namespace tifa_libs
#line 2 "src/comb/seq/ipowi/lib.hpp"
#line 2 "src/math/iroot/sqrt/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/math/iroot/sqrt/lib.hpp"
namespace tifa_libs {
CEXP u32 isqrt(u64 x) NE {
retif_((!x) [[unlikely]], 0);
#pragma GCC diagnostic ignored "-Wconversion"
csint sh = 31 - (std::bit_width(x) - 1) / 2;
#pragma GCC diagnostic warning "-Wconversion"
u32 u = [](u64 x) NE {
CEXP arr<u8, 192> TAB{128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 144, 145, 146, 147, 148, 149, 150, 151, 151, 152, 153, 154, 155, 156, 156, 157, 158, 159, 160, 160, 161, 162, 163, 164, 164, 165, 166, 167, 167, 168, 169, 170, 170, 171, 172, 173, 173, 174, 175, 176, 176, 177, 178, 179, 179, 180, 181, 181, 182, 183, 183, 184, 185, 186, 186, 187, 188, 188, 189, 190, 190, 191, 192, 192, 193, 194, 194, 195, 196, 196, 197, 198, 198, 199, 200, 200, 201, 201, 202, 203, 203, 204, 205, 205, 206, 206, 207, 208, 208, 209, 210, 210, 211, 211, 212, 213, 213, 214, 214, 215, 216, 216, 217, 217, 218, 219, 219, 220, 220, 221, 221, 222, 223, 223, 224, 224, 225, 225, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 232, 232, 233, 233, 234, 234, 235, 235, 236, 237, 237, 238, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253, 253, 254, 254, 255, 255, 255};
u32 u = TAB[(x >> 56) - 64];
u = (u << 7) + (u32)(x >> 41) / u;
return (u << 15) + (u32)((x >> 17) / u);
}(x << 2 * sh);
u >>= sh, u -= (u64)u * u > x;
return u;
}
} // namespace tifa_libs
#line 2 "src/math/qpow/mod/lib.hpp"
#line 2 "src/math/mul_mod/lib.hpp"
#line 2 "src/math/safe_mod/lib.hpp"
#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 4 "src/math/safe_mod/lib.hpp"
namespace tifa_libs {
template <int_c T>
CEXP T safe_mod(T x, to_uint_t<T> mod) NE {
if CEXP (sint_c<T>) {
if (x <= -(T)mod || x >= (T)mod) x %= (T)mod;
retif_((x < 0), x + (T)mod, x);
} else {
retif_((x >= mod), x % mod, x);
}
}
} // namespace tifa_libs
#line 4 "src/math/mul_mod/lib.hpp"
namespace tifa_libs {
CEXP i64 mul_mod_s(i64 a, i64 b, u64 mod) NE {
if (std::bit_width((u64)abs(a)) + std::bit_width((u64)abs(b)) < 64) return safe_mod(a * b % (i64)mod, mod);
return safe_mod((i64)((i128)a * b % mod), mod);
}
CEXP u64 mul_mod_u(u64 a, u64 b, u64 mod) NE {
if (std::bit_width(a) + std::bit_width(b) <= 64) return a * b % mod;
return (u64)((u128)a * b % mod);
}
} // namespace tifa_libs
#line 4 "src/math/qpow/mod/lib.hpp"
namespace tifa_libs {
CEXP u64 qpow_mod(u64 a, u64 b, u64 mod) NE {
u64 res(1);
for (a %= mod; b; b >>= 1, a = mul_mod_u(a, a, mod)) {
while (!(b & 1)) b >>= 1, a = mul_mod_u(a, a, mod);
res = mul_mod_u(res, a, mod);
}
return res;
}
} // namespace tifa_libs
#line 2 "src/nt/lsieve/impl1/lib.hpp"
#line 4 "src/nt/lsieve/impl1/lib.hpp"
namespace tifa_libs {
template <class... Ts>
struct lsieve : Ts... {
vecb not_prime;
vecu primes;
CEXPE lsieve(u32 n) NE : Ts(n)..., not_prime(n) {
if (n < 2) return;
// clang-format off
primes.reserve((usz)max(127, int(n * (n >= 2e5 ? 1.6 : 1.7) / std::bit_width(n) + 1)));
// clang-format on
flt_ (u32, i, 2, n) {
if (!not_prime[i]) primes.push_back(i), (Ts::prime(i), ...);
for (auto j : primes) {
if (i * j >= n) break;
not_prime[i * j] = true;
if (i % j) (Ts::coprime(i, j), ...);
else {
(Ts::not_coprime(i, j), ...);
break;
}
}
}
primes.shrink_to_fit();
}
};
} // namespace tifa_libs
#line 2 "src/nt/mod/barrett/lib.hpp"
#line 4 "src/nt/mod/barrett/lib.hpp"
namespace tifa_libs {
template <u64 MOD, u64 B_ = 1>
struct barrett {
static CEXP u64 B = B_ % MOD, R = ((u128)B << 64) / MOD;
static CEXP u64 reduce(u64 a) NE {
if (u64 q = u64((u128)a * R >> 64); (a = a * B - q * MOD) >= MOD) a -= MOD;
return a;
}
};
template <> // dynamic
struct barrett<0> {
u64 mod, b, r;
CEXP barrett() NE = default;
CEXPE barrett(u64 mod, u64 b = 1) NE { reset(mod, b); }
CEXP void reset(u64 mod_, u64 b_ = 1) NE { assert(mod_), mod = mod_, b = b_ % mod, r = (u64(((u128)b << 64) / mod)); }
ND CEXP u64 reduce(u64 a) CNE {
if (cu64 q = u64((u128)a * r >> 64); (a = a * b - q * mod) >= mod) a -= mod;
return a;
}
};
} // namespace tifa_libs
#line 7 "src/comb/seq/ipowi/lib.hpp"
namespace tifa_libs {
namespace gen_ipowi_impl_ {
struct ls_ipowi {
static inline u64 mod;
vecuu ipowi;
protected:
cu32 B;
vvecuu fp, fpb;
u32 pre_j{0}, gap{0};
u64 now_r{1};
arr<u64, 355> p{1}; // maximal prime gaps: g_n=354 => p_n=4,302,407,359
CEXPE ls_ipowi(u32 n) NE : ipowi(n), B{isqrt(n)}, fp(B + 1, vecuu(B + 1)), fpb(B + 1, vecuu(B + 1)) {
if (n) ipowi[0] = 1;
if (n > 1) ipowi[1] = 1;
}
void prime(u32 p) NE {
if (ipowi[p] = qpow_mod(p, p, mod); p <= B) {
fp[p][0] = 1;
barrett<0> brt(mod, ipowi[p]);
flt_ (u32, j, 1, B + 1)
fp[p][j] = brt.reduce(fp[p][j - 1]);
fpb[p][0] = 1;
brt.reset(mod, fp[p].back());
flt_ (u32, j, 1, B + 1)
fpb[p][j] = brt.reduce(fpb[p][j - 1]);
}
}
void coprime(u32 i, u32 j) NE {
if (j <= pre_j) now_r = 1, pre_j = gap = 0;
const barrett<0> brt(mod, ipowi[i]);
if (cu32 new_gap = j - pre_j; new_gap > gap) {
flt_ (u32, x, gap + 1, new_gap + 1) p[x] = brt.reduce(p[x - 1]);
gap = new_gap;
}
now_r = mul_mod_u(now_r, p[j - pre_j], mod);
ipowi[i * j] = mul_mod_u(mul_mod_u(fp[j][i % B], fpb[j][i / B], mod), now_r, mod);
pre_j = j;
}
void not_coprime(u32 i, u32 j) NE { coprime(i, j); }
};
} // namespace gen_ipowi_impl_
// i^i from i=0..n-1
CEXP vecuu gen_ipowi(u32 n, u64 mod) NE {
retif_((n < 2) [[unlikely]], vecuu(n, 1));
gen_ipowi_impl_::ls_ipowi::mod = mod;
return lsieve<gen_ipowi_impl_::ls_ipowi>(n).ipowi;
}
// i^i from i=0..n-1
template <class mint>
CEXP vec<mint> gen_ipowi(u32 n) NE {
vec<mint> ans(n);
auto _ = gen_ipowi(n, mint::mod());
flt_ (u32, i, 0, n) ans[i] = _[i];
return ans;
}
} // namespace tifa_libs
src/comb/seq/ipowi/lib.hpp