#pragma once
#include "../../nt/residue/q/lib.hpp"
#include "../inv/lib.hpp"
#include "../shl/lib.hpp"
#include "../shr/lib.hpp"
namespace tifa_libs {
template <poly_c poly_t>
CEXP auto sqrt_fps(poly_t p, u32 n = 0) NE {
using mint = TPN poly_t::val_t;
std::optional<poly_t> ret;
if (!n) n = (u32)p.size();
cu32 cnt = u32(find_if(begin(p), begin(p) + n, [](cT_(mint) x) NE { return x.val() != 0; }) - begin(p));
if (cnt == n) [[unlikely]] {
ret.emplace(p.pre(n));
return ret;
}
if (cnt & 1) return ret;
poly_t ans{0};
p = shr_fps(p, cnt);
if (auto qres = qresidue(p[0].val(), mint::mod()); !qres) return ret;
else ans[0] = min(qres.value(), mint::mod() - qres.value());
auto i2 = mint(2).inv();
for (u32 i = 1; i < n; i *= 2) ans = (ans + p.pre(i * 2) * inv_fps(ans, i * 2)) * i2;
ret.emplace(shl_fps(ans.pre(n), cnt / 2));
return ret;
}
} // namespace tifa_libs
#line 2 "src/fps/sqrt/lib.hpp"
#line 2 "src/nt/residue/q/lib.hpp"
#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 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/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/inverse/lib.hpp"
#line 2 "src/nt/gl/inv_gcd/lib.hpp"
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#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/nt/gl/exgcd/lib.hpp"
#line 4 "src/nt/gl/exgcd/lib.hpp"
namespace tifa_libs {
// Binary exgcd
template <uint_c U, bool only_x = false>
CEXP auto exgcd_b(U a, U b) NE {
using T = to_sint_t<U>;
if CEXP (only_x) {
if (!a) return std::make_tuple(b, (T)0);
if (!b) return std::make_tuple(a, (T)1);
} else {
if (!a) return std::make_tuple(b, (T)0, (T) !!b);
if (!b) return std::make_tuple(a, (T)1, (T)0);
}
auto r = std::__countr_zero(a | b);
a >>= r, b >>= r;
T x = (T)a, y = (T)b, s = 1, t = 0, u = 0, v = 1;
while (x) {
while (!(x & 1))
if (x /= 2; !((s | t) & 1)) s /= 2, t /= 2;
else s = (s + (T)b) / 2, t = (t - (T)a) / 2;
while (!(y & 1))
if (y /= 2; !((u | v) & 1)) u /= 2, v /= 2;
else u = (u + (T)b) / 2, v = (v - (T)a) / 2;
if (x >= y) x -= y, s -= u, t -= v;
else y -= x, u -= s, v -= t;
}
if (y > 1) a /= (U)y, b /= (U)y;
if (a && (U)abs(v) >= a) {
const T _ = v / (T)a;
v -= _ * (T)a, u += _ * (T)b;
}
if (b && (U)abs(u) >= b) {
const T _ = u / (T)b;
u -= _ * (T)b, v += _ * (T)a;
}
if (const T u_ = u + (T)b, v_ = v - (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
if (const T u_ = u - (T)b, v_ = v + (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
if CEXP (only_x) return std::make_tuple(U(y << r), u);
else return std::make_tuple(U(y << r), u, v);
}
// @return then return tuple(g, x[, y]) s.t. g = gcd(a, b), xa + yb = g, |x| + |y| is the minimal (primary) and x <= y (secondarily)
template <sint_c T, bool only_x = false>
CEXP auto exgcd(T a, T b) NE {
using U = to_uint_t<T>;
if (auto [x, y] = minmax(a, b); x >= 0 && y <= T(U(-1) >> sizeof(U))) return exgcd_b<U, only_x>((U)a, (U)b);
if CEXP (only_x) {
T s = 1, u = 0;
while (b) {
T c = a / b;
std::tie(s, u, a, b) = std::make_tuple(u, s - u * c, b, a - b * c);
}
return std::make_tuple((U)a, s);
} else {
T s = 1, t = 0, u = 0, v = 1;
while (b) {
T c = a / b;
std::tie(s, t, u, v, a, b) = std::make_tuple(u, v, s - u * c, t - v * c, b, a - b * c);
}
return std::make_tuple((U)a, s, t);
}
}
} // namespace tifa_libs
#line 6 "src/nt/gl/inv_gcd/lib.hpp"
namespace tifa_libs {
template <uint_c T>
CEXP ptt<T> inv_gcd(T n, T mod) NE {
using U = to_sint_t<T>;
auto [g, x] = exgcd<U, true>(U(n % mod), (U)mod);
return {g, safe_mod(x, mod)};
}
} // namespace tifa_libs
#line 4 "src/nt/inverse/lib.hpp"
namespace tifa_libs {
// simple but slower: inv(n, mod) -> 1 < n ? mod - inv(mod % n, n) * mod / n : 1;
template <uint_c T, uint_c U>
CEXP U inverse(T n, U mod) NE {
auto [g, x] = inv_gcd(U(n % mod), mod);
assert(g == 1);
return x;
}
} // namespace tifa_libs
#line 5 "src/nt/residue/q/lib.hpp"
namespace tifa_libs {
CEXP auto qresidue(u64 a, u64 p) NE {
std::optional<u64> ret;
if (!(a %= p)) {
ret.emplace(0);
return ret;
}
auto f = [](u64 a, u64 p) NE { return qpow_mod(a, p / 2, p) == 1; };
if (!f(a, p)) return ret;
u64 r = 2;
while (f(r, p)) ++r;
csint n = std::countr_zero(p - 1);
cu64 m = (p - 1) >> n, g = qpow_mod(r, m, p), b = qpow_mod(a, m / 2, p), am = qpow_mod(a, m, p);
u64 e = 0;
flt_ (int, k, 1, n) e |= (u64)(qpow_mod(am * inverse(qpow_mod(g, e, p), p) % p, 1 << (n - 1 - k), p) == p - 1) << k;
ret.emplace(a * b % p * inverse(qpow_mod(g, e / 2, p), p) % p);
return ret;
}
} // namespace tifa_libs
#line 2 "src/fps/inv/lib.hpp"
#line 2 "src/fps/ds/poly_c/lib.hpp"
#line 2 "src/util/strip/lib.hpp"
#line 4 "src/util/strip/lib.hpp"
namespace tifa_libs {
// pred(x) == true ==> drop
template <common_range R, class F>
CEXP auto lstrip_view(R CR range, F&& pred) NE {
auto v = range | views::drop_while(std::forward<F>(pred));
return subrange{begin(v), end(v)};
}
// pred(x) == true ==> drop
template <common_range R, class F>
CEXP auto rstrip_view(R CR range, F&& pred) NE {
auto v = range | views::reverse | views::drop_while(std::forward<F>(pred));
return subrange{end(v).base(), begin(v).base()};
}
// pred(x) == true ==> drop
template <common_range R, class F>
CEXP auto strip_view(R CR range, F&& pred) NE {
auto v = range | views::drop_while(std::forward<F>(pred)) | views::reverse | views::drop_while(std::forward<F>(pred));
return subrange{end(v).base(), begin(v).base()};
}
} // namespace tifa_libs
#line 2 "src/util/traits/others/lib.hpp"
// clang-format off
#line 4 "src/util/traits/others/lib.hpp"
namespace tifa_libs {
//! only for template without non-type argument
template <class, template <class...> class> CEXP bool specialized_from_v = false;
template <template <class...> class T, class... Args> CEXP bool specialized_from_v<T<Args...>, T> = true;
static_assert(specialized_from_v<vecu, std::vector>);
template <class T> concept container_c = common_range<T> && !std::is_array_v<std::remove_cvref_t<T>> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;
template <class T> concept istream_c = std::derived_from<T, std::istream> || std::derived_from<T, std::wistream> || requires(T is) { is.peek(); };
template <class T> concept ostream_c = std::derived_from<T, std::ostream> || std::derived_from<T, std::wostream> || requires(T os) { os.flush(); };
} // namespace tifa_libs
// clang-format on
#line 5 "src/fps/ds/poly_c/lib.hpp"
namespace tifa_libs {
// clang-format off
enum class CCORE : u8 { FFT_R2, NTT3, NTT };
// clang-format on
namespace poly_impl_ {
template <class ccore>
requires requires(ccore cc, vec<TPN ccore::val_t> l, vec<TPN ccore::val_t> r, u32 sz) {
{ ccore::ct_cat } -> std::same_as<CCORE CR>;
cc.conv(l, r), cc.conv(l, r, sz);
}
struct poly : vec<TPN ccore::val_t> {
using ccore_t = ccore;
using val_t = ccore_t::val_t;
using data_t = vec<val_t>;
static inline ccore_t conv_core;
CEXPE poly(u32 sz = 1, cT_(val_t) val = val_t{}) NE : data_t(sz, val) {}
CEXP poly(TPN data_t::const_iterator begin, TPN data_t::const_iterator end) NE : data_t(begin, end) {}
CEXP poly(data_t CR v) NE : data_t(v) {}
CEXP poly(data_t&& v) NE : data_t(std::move(v)) {}
CEXP poly(itl<val_t> v) NE : data_t(v) {}
CEXP poly(common_range auto CR v) NE : data_t(begin(v), end(v)) {}
friend CEXP auto& operator>>(istream_c auto& is, poly& poly) NE {
for (auto& val : poly) is >> val;
return is;
}
friend CEXP auto& operator<<(ostream_c auto& os, poly CR poly) NE {
retif_((!poly.size()) [[unlikely]], os);
flt_ (u32, i, 1, (u32)poly.size()) os << poly[i - 1] << ' ';
return os << poly.back();
}
ND CEXP bool is_zero() CNE {
for (auto&& i : *this)
if (i != 0) return false;
return true;
}
CEXP val_t operator()(val_t x) CNE {
val_t ans = 0;
for (u32 i = data_t::size() - 1; ~i; --i) ans = ans * x + data_t::data()[i];
return ans;
}
template <class F>
requires requires(F f, u32 idx, val_t& val) { f(idx, val); }
CEXP void apply_range(u32 l, u32 r, F&& f) NE {
assert(l < r && r <= data_t::size());
flt_ (u32, i, l, r) f(i, data_t::data()[i]);
}
template <class F>
CEXP void apply(F&& f) NE { apply_range(0, (u32)data_t::size(), std::forward<F>(f)); }
ND CEXP poly pre(u32 sz) CNE {
if (sz <= this->size()) return {this->begin(), this->begin() + sz};
poly _ = *this;
_.resize(sz);
return _;
}
CEXP void strip() NE {
auto [_, r] = rstrip_view(*this, [](cT_(val_t) x) NE { return x.val() == 0; });
if (data_t::erase(r, this->end()); data_t::empty()) data_t::push_back(val_t(0));
}
friend poly stripped(poly CR p) NE {
poly ret(rstrip_view(p, [](cT_(val_t) x) NE { return x.val() == 0; }));
if (ret.empty()) return {0};
return ret;
}
CEXP void reverse(u32 n = 0) NE { std::ranges::reverse(data_t::begin(), data_t::begin() + (n ? n : (u32)data_t::size())); }
CEXP void conv(poly CR r, u32 ans_size = 0) NE { conv_core.conv(*this, r, ans_size); }
CEXP poly operator-() CNE {
poly ret = *this;
ret.apply([](u32, auto& v) NE { v = -v; });
return ret;
}
friend CEXP poly operator+(poly p, val_t c) NE {
p[0] += c;
return p;
}
friend CEXP poly operator+(val_t c, poly CR p) NE { return p + c; }
friend CEXP poly operator-(poly p, val_t c) NE {
p[0] -= c;
return p;
}
friend CEXP poly operator-(val_t c, poly CR p) NE { return p - c; }
CEXP poly& operator*=(val_t c) NE {
apply([&c](u32, auto& v) NE { v *= c; });
return *this;
}
friend CEXP poly operator*(poly p, val_t c) NE { return p *= c; }
friend CEXP poly operator*(val_t c, poly p) NE { return p *= c; }
CEXP poly& operator+=(poly CR r) NE {
retif_((r.empty()) [[unlikely]], *this);
data_t::resize(max(data_t::size(), r.size())), apply_range(0, (u32)r.size(), [&r](u32 i, auto& v) NE { v += r[i]; });
return *this;
}
friend CEXP poly operator+(poly l, poly CR r) NE { return l += r; }
CEXP poly& operator-=(poly CR r) NE {
retif_((r.empty()) [[unlikely]], *this);
data_t::resize(max(data_t::size(), r.size()));
apply_range(0, (u32)r.size(), [&r](u32 i, auto& v) NE { v -= r[i]; });
return *this;
}
friend CEXP poly operator-(poly l, poly CR r) NE { return l -= r; }
CEXP poly& operator*=(poly CR r) NE {
if (r.empty()) {
data_t::resize(1), *data_t::data() = 0;
return *this;
}
conv(r);
return *this;
}
friend CEXP poly operator*(poly l, poly CR r) NE { return l *= r; }
CEXP auto operator<=>(poly CR r) CNE {
auto l_ = stripped(*this), r_ = stripped(r);
if (l_.size() != r_.size()) return l_.size() <=> r_.size();
return std::lexicographical_compare_three_way(l_.rbegin(), l_.rend(), r_.rbegin(), r_.rend());
}
CEXP bool operator==(poly CR r) CNE { return std::is_eq(*this <=> r); }
};
} // namespace poly_impl_
template <class T>
concept poly_c = std::same_as<T, poly_impl_::poly<TPN T::ccore_t>>;
} // namespace tifa_libs
#line 4 "src/fps/inv/lib.hpp"
namespace tifa_libs {
template <poly_c poly_t>
CEXP auto inv_fps(poly_t CR p, u32 n = 0) NE {
if (assert(p[0] != 0); !n) n = (u32)p.size();
poly_t a{p[0].inv()};
for (u32 i = 1; i < n; i *= 2) a = (a * 2 - (a * a * p).pre(i * 2)).pre(i * 2);
return a.pre(n);
}
} // namespace tifa_libs
#line 2 "src/fps/shl/lib.hpp"
#line 4 "src/fps/shl/lib.hpp"
namespace tifa_libs {
CEXP auto shl_fps(poly_c auto CR p, usz x) NE {
retif_((!x) [[unlikely]], p);
auto _ = p;
fill(begin(_), std::shift_right(begin(_), end(_), (isz)x), 0);
return _;
}
} // namespace tifa_libs
#line 2 "src/fps/shr/lib.hpp"
#line 4 "src/fps/shr/lib.hpp"
namespace tifa_libs {
CEXP auto shr_fps(poly_c auto CR p, usz x) NE {
retif_((!x) [[unlikely]], p);
auto _ = p;
fill(std::shift_left(begin(_), end(_), (isz)x), end(_), 0);
return _;
}
CEXP auto shr_strip_fps(poly_c auto CR p, usz x) NE {
auto _ = p;
_.erase(std::shift_left(begin(_), end(_), (isz)x), end(_));
return _;
}
} // namespace tifa_libs
#line 7 "src/fps/sqrt/lib.hpp"
namespace tifa_libs {
template <poly_c poly_t>
CEXP auto sqrt_fps(poly_t p, u32 n = 0) NE {
using mint = TPN poly_t::val_t;
std::optional<poly_t> ret;
if (!n) n = (u32)p.size();
cu32 cnt = u32(find_if(begin(p), begin(p) + n, [](cT_(mint) x) NE { return x.val() != 0; }) - begin(p));
if (cnt == n) [[unlikely]] {
ret.emplace(p.pre(n));
return ret;
}
if (cnt & 1) return ret;
poly_t ans{0};
p = shr_fps(p, cnt);
if (auto qres = qresidue(p[0].val(), mint::mod()); !qres) return ret;
else ans[0] = min(qres.value(), mint::mod() - qres.value());
auto i2 = mint(2).inv();
for (u32 i = 1; i < n; i *= 2) ans = (ans + p.pre(i * 2) * inv_fps(ans, i * 2)) * i2;
ret.emplace(shl_fps(ans.pre(n), cnt / 2));
return ret;
}
} // namespace tifa_libs
src/fps/sqrt/lib.hpp