#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/exp_of_formal_power_series"
#include "../../code/io/fastio.hpp"
#include "../../code/poly/exp_fps.hpp"
CEXP u32 MOD = 998244353;
#include "../../code/math/mint_s30.hpp"
#include "../../code/poly/polymtt.hpp"
using mint = tifa_libs::math::mint_s30<MOD>;
using poly = tifa_libs::math::polymtt<mint>;
int main() {
u32 n;
tifa_libs::fin >> n;
poly p(n);
tifa_libs::fin >> p.data();
tifa_libs::fout << tifa_libs::math::exp_fps(p).data();
return 0;
}
#line 1 "src/test_cpverifier/library-checker-math/exp_of_formal_power_series.pmtt-s30.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/exp_of_formal_power_series"
#line 1 "src/code/io/fastio.hpp"
#line 1 "src/code/fast/u32tostr.hpp"
#line 1 "src/code/util/util.hpp"
#include <bits/stdc++.h>
#define CEXP constexpr
#define TPN typename
#define CR const&
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t), __VA_ARGS__, __VA_ARGS__ CR>
#define fle_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i <= i##e; ++i)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;
using f32 = float;
using f64 = double;
using f128 = long double;
template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;
template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
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 T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;
template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;
using strn = std::string;
using strnv = std::string_view;
using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;
using namespace std::literals;
CEXP i8 operator""_i8(unsigned long long x) { return (i8)x; }
CEXP i16 operator""_i16(unsigned long long x) { return (i16)x; }
CEXP i32 operator""_i32(unsigned long long x) { return (i32)x; }
CEXP i64 operator""_i64(unsigned long long x) { return (i64)x; }
CEXP isz operator""_iz(unsigned long long x) { return (isz)x; }
CEXP u8 operator""_u8(unsigned long long x) { return (u8)x; }
CEXP u16 operator""_u16(unsigned long long x) { return (u16)x; }
CEXP u32 operator""_u32(unsigned long long x) { return (u32)x; }
CEXP u64 operator""_u64(unsigned long long x) { return (u64)x; }
CEXP usz operator""_uz(unsigned long long x) { return (usz)x; }
inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };
// std::sqrt(std::numeric_limits<FP>::epsilon())
template <std::floating_point FP>
CEXP inline FP eps_v = FP(1e-8L);
using std::numbers::pi_v;
namespace tifa_libs {
using std::min, std::max, std::swap;
template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }
} // namespace tifa_libs
#line 5 "src/code/fast/u32tostr.hpp"
namespace tifa_libs {
CEXP u32 u32tostr_si16(u64 x, char *s) {
if (x <= 9) {
*s = (char)(x | 0x30);
return 1;
} else if (x <= 99) {
u64 low = x;
u64 ll = ((low * 103) >> 9) & 0x1E;
low += ll * 3;
ll = ((low & 0xF0) >> 4) | ((low & 0x0F) << 8);
*(u16 *)s = (u16)(ll | 0x3030);
return 2;
}
return 0;
}
CEXP u32 u32tostr_si32(u64 x, char *s) {
u64 low = 0, ll = 0;
u32 digits = 0;
if (x <= 99) return u32tostr_si16(x, s);
low = x;
digits = (low > 999) ? 4 : 3;
ll = ((low * 5243) >> 19) & 0xFF;
low -= ll * 100;
low = (low << 16) | ll;
ll = ((low * 103) >> 9) & 0x1E001E;
low += ll * 3;
ll = ((low & 0x00F000F0) << 28) | (low & 0x000F000F) << 40;
ll |= 0x3030303000000000;
u8 *p = (u8 *)≪
if (digits == 4) *(u32 *)s = *(u32 *)(&p[4]);
else {
*(u16 *)s = *(u16 *)(&p[5]);
*(((u8 *)s) + 2) = p[7];
}
return digits;
}
CEXP u32 u32tostr(u64 x, char *s) {
u64 low = 0, ll = 0;
u32 digits = 0;
if (x <= 9999) return u32tostr_si32(x, s);
if (x < 100000000) {
if ((low = x) > 999999) digits = (low > 9999999) ? 8 : 7;
else digits = (low > 99999) ? 6 : 5;
} else {
u64 high = (x * 0x55E63B89) >> 57;
low = x - (high * 100000000);
digits = u32tostr_si16(high, s);
digits += 8;
}
ll = (low * 109951163) >> 40;
(low -= ll * 10000) |= ll << 32;
ll = ((low * 5243) >> 19) & 0x000000FF000000FF;
low -= ll * 100;
low = (low << 16) | ll;
ll = ((low * 103) >> 9) & 0x001E001E001E001E;
low += ll * 3;
ll = ((low & 0x00F000F000F000F0) >> 4) | (low & 0x000F000F000F000F) << 8;
ll = (ll >> 32) | (ll << 32) | 0x3030303030303030;
if (digits >= 8) memcpy(s + digits - 8, &ll, 8);
else {
u32 d = digits;
char *s1 = s, *pll = &(((char *)&ll)[8 - digits]);
if (d >= 4) {
memcpy(s1, pll, 4);
s1 += 4, pll += 4, d -= 4;
}
if (d >= 2) {
memcpy(s1, pll, 2);
s1 += 2, pll += 2, d -= 2;
}
if (d > 0) *(u8 *)s1 = *(u8 *)pll;
}
return digits;
}
} // namespace tifa_libs
#line 1 "src/code/util/traits.hpp"
#line 5 "src/code/util/traits.hpp"
namespace tifa_libs {
template <class T>
concept iterable_c = requires(T v) {
{ v.begin() } -> std::same_as<TPN T::iterator>;
{ v.end() } -> std::same_as<TPN T::iterator>;
};
template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<TPN T::value_type>> && !std::derived_from<T, std::basic_string_view<TPN T::value_type>>;
template <class T>
CEXP bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;
template <class T>
CEXP bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;
template <class T>
CEXP bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;
template <class T>
CEXP bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;
template <class T>
CEXP bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;
template <class T>
CEXP bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;
template <class T>
CEXP bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<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, vec<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>
CEXP bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;
template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
using type = u128;
};
template <>
struct to_sint<i128> {
using type = u128;
};
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;
} // namespace tifa_libs
#line 6 "src/code/io/fastio.hpp"
namespace tifa_libs {
namespace fastio_impl_ {
//! UB if EOF occured during reading
template <u32 BUF>
class fastin {
char bf_[BUF], *now_ = bf_, *end_ = bf_;
FILE *f_;
public:
explicit fastin(FILE *f = stdin) : f_(f) {}
char get() { return now_ == end_ && (end_ = (now_ = bf_) + fread(bf_, 1, BUF, f_), now_ == end_) ? EOF : *(now_)++; }
char peek() { return now_ == end_ && (end_ = (now_ = bf_) + fread(bf_, 1, BUF, f_), now_ == end_) ? EOF : *(now_); }
void rebind(FILE *f) {
f_ = f;
now_ = end_ = bf_;
}
bool iseof() { return peek() == EOF; }
template <class T>
requires(sint_c<T> && !char_c<T>)
fastin &read(T &n) {
bool is_neg = false;
char ch = get();
while (!isdigit(ch)) {
is_neg |= ch == '-';
ch = get();
}
n = 0;
while (isdigit(ch)) {
(n *= 10) += ch & 15;
ch = get();
}
if (is_neg) n = -n;
return *this;
}
template <class T>
requires(uint_c<T> && !char_c<T>)
fastin &read(T &n) {
char ch = get();
while (!isdigit(ch)) ch = get();
n = 0;
while (isdigit(ch)) {
(n *= 10) += ch & 15;
ch = get();
}
return *this;
}
template <mint_c T>
fastin &read(T &n) {
decltype(std::declval<T>().sval()) x;
read(x);
n = T(x);
return *this;
}
//! ignore cntrl and space
template <char_c T>
fastin &read(T &n) {
while (!isgraph(n = get()));
return *this;
}
fastin &read(char *n) {
char *n_ = n;
while (!isgraph(*n_ = get()));
while (isgraph(*(++n_) = get()));
*n_ = '\0';
return *this;
}
fastin &read(strn &n) {
n.clear();
char n_;
while (!isgraph(n_ = get()));
n.push_back(n_);
while (isgraph(n_ = get())) n.push_back(n_);
return *this;
}
template <class T, class U>
fastin &read(std::pair<T, U> &p) { return read(p.first).read(p.second); }
template <class... Ts>
fastin &read(std::tuple<Ts...> &p) {
std::apply([&](Ts &...targs) { ((read(targs)), ...); }, p);
return *this;
}
template <container_c T>
fastin &read(T &p) {
if (p.begin() == p.end()) return *this;
for (auto &i : p) read(i);
return *this;
}
fastin &getline(char *n) {
char *n_ = n;
while (!isprint(*n_ = get()));
while (isprint(*(++n_) = get()));
*n_ = '\0';
return *this;
}
fastin &getline(strn &n) {
char n_;
while (!isprint(n_ = get()));
n.push_back(n_);
while (isprint(n_ = get())) n.push_back(n_);
return *this;
}
//! NOT ignore cntrl and space
template <char_c T>
fastin &strict_read(T &n) {
n = get();
return *this;
}
template <class T>
fastin &operator>>(T &val) { return read(val); }
};
template <u32 BUF, u32 INTBUF>
class fastout {
char int_bf_[INTBUF], *now_ib_ = int_bf_;
FILE *f_;
char *now_, bf_[BUF];
const char *const end_ = bf_ + BUF;
public:
explicit fastout(FILE *file = stdout) : f_(file), now_(bf_) {}
fastout &operator=(fastout CR r) {
if (&r == this) return *this;
f_ = r.f_;
now_ = bf_ + (r.now_ - r.bf_);
memcpy(bf_, r.bf_, sizeof(*bf_) * (r.now_ - r.bf_));
return *this;
}
fastout(fastout CR r) { *this = r; }
~fastout() { flush(); }
void flush() {
fwrite(bf_, 1, usz(now_ - bf_), f_);
now_ = bf_;
}
void rebind(FILE *file) { f_ = file; }
template <char_c T>
fastout &write(T n) {
if (now_ == end_) flush();
*(now_++) = n;
return *this;
}
fastout &write(const char *n) {
usz len = strlen(n), l_;
const char *n_ = n;
while (now_ + len >= end_) {
memcpy(now_, n_, l_ = usz(end_ - now_));
now_ += l_;
n_ += l_;
len -= l_;
flush();
}
memcpy(now_, n_, len);
now_ += len;
return *this;
}
template <class T>
requires(sint_c<T> && !char_c<T>)
fastout &write(T n) {
if (n < 0) {
write('-');
n = -n;
}
return write(to_uint_t<T>(n));
}
template <class T>
requires(uint_c<T> && !char_c<T>)
fastout &write(T n) {
if CEXP (sizeof(T) <= 4) {
memset(now_ib_ = int_bf_, 0, 11);
u32tostr(n, now_ib_);
return write(now_ib_);
}
now_ib_ = int_bf_ + INTBUF - 1;
do {
*(--(now_ib_)) = char(n % 10) | '0';
} while (n /= 10);
return write(now_ib_);
}
template <mint_c T>
fastout &write(T n) { return write(n.val()); }
fastout &write(strn CR str) { return write(str.c_str()); }
template <class T, class U>
fastout &write(std::pair<T, U> CR p) { return write(p.first).space().write(p.second); }
template <class... Ts>
fastout &write(std::tuple<Ts...> CR p) {
std::apply(
[&](Ts CR... targs) {
usz n{0};
((write(targs).space_if(++n != sizeof...(Ts))), ...);
},
p);
return *this;
}
template <container_c T>
fastout &write(T CR p) {
if (p.begin() == p.end()) return *this;
auto it = p.begin();
write(*it++);
for (; it != p.end(); ++it) space().write(*it);
return *this;
}
fastout &linebreak() { return write('\n'); }
fastout &linebreak_if(bool flag) { return flag ? linebreak() : *this; }
fastout &space() { return write(' '); }
fastout &space_if(bool flag) { return flag ? space() : *this; }
template <class T>
fastout &operator<<(T CR val) { return write(val); }
};
} // namespace fastio_impl_
inline fastio_impl_::fastin<0x200005> fin;
inline fastio_impl_::fastout<0x200005, 41> fout;
} // namespace tifa_libs
#line 1 "src/code/poly/exp_fps.hpp"
#line 1 "src/code/poly/ln_fps.hpp"
#line 1 "src/code/poly/deriv_fps.hpp"
#line 1 "src/code/poly/poly.hpp"
#line 5 "src/code/poly/poly.hpp"
namespace tifa_libs::math {
// clang-format off
enum ccore_t { ct_FFT, ct_3NTT, ct_NTT };
// clang-format on
template <class mint, class ccore>
requires requires(ccore cc, vec<mint> l, vec<mint> CR r, u32 sz) {
{ ccore::ct_cat } -> std::same_as<ccore_t CR>;
cc.conv(l, r);
cc.conv(l, r, sz);
}
class poly {
vec<mint> d;
public:
using value_type = mint;
using data_type = vec<value_type>;
using ccore_type = ccore;
static inline ccore_type conv_core;
explicit CEXP poly(u32 sz = 1, cT_(value_type) val = value_type{}) : d(sz, val) {}
CEXP poly(TPN data_type::const_iterator begin, TPN data_type::const_iterator end) : d(begin, end) {}
CEXP poly(std::initializer_list<value_type> v) : d(v) {}
template <class T>
explicit CEXP poly(vec<T> CR v) : d(v) {}
friend CEXP std::istream &operator>>(std::istream &is, poly &poly) {
for (auto &val : poly.d) is >> val;
return is;
}
friend CEXP std::ostream &operator<<(std::ostream &os, poly CR poly) {
if (!poly.size()) return os;
for (u32 i = 1; i < poly.size(); ++i) os << poly[i - 1] << ' ';
return os << poly.d.back();
}
CEXP u32 size() const { return (u32)d.size(); }
CEXP bool empty() const {
for (auto &&i : d)
if (i != 0) return 0;
return 1;
}
CEXP data_type &data() { return d; }
CEXP data_type CR data() const { return d; }
CEXP value_type &operator[](u32 x) { return d[x]; }
CEXP value_type CR operator[](u32 x) const { return d[x]; }
CEXP value_type operator()(value_type x) const {
value_type ans = 0;
for (u32 i = size() - 1; ~i; --i) ans = ans * x + d[i];
return ans;
}
template <class F>
requires requires(F f, u32 idx, mint &val) { f(idx, val); }
CEXP void apply_range(u32 l, u32 r, F &&f) {
assert(l < r && r <= size());
flt_ (u32, i, l, r) f(i, d[i]);
}
template <class F>
CEXP void apply(F &&f) { apply_range(0, size(), std::forward<F>(f)); }
CEXP void resize(u32 size) { d.resize(size); }
CEXP poly pre(u32 size) const {
poly _ = *this;
_.resize(size);
return _;
}
CEXP void strip() {
auto it = std::find_if(d.rbegin(), d.rend(), [](cT_(mint) x) { return x.val() != 0; });
d.resize(usz(d.rend() - it));
if (d.empty()) d.push_back(value_type(0));
}
friend poly stripped(poly p) {
p.strip();
return p;
}
CEXP void reverse(u32 n = 0) { std::reverse(d.begin(), d.begin() + (n ? n : size())); }
CEXP void conv(poly CR r, u32 ans_size = 0) { conv_core.conv(d, r.d, ans_size); }
CEXP poly operator-() const {
poly ret = *this;
ret.apply([](u32, auto &v) { v = -v; });
return ret;
}
friend CEXP poly operator+(poly p, value_type c) {
p[0] += c;
return p;
}
friend CEXP poly operator+(value_type c, poly CR p) { return p + c; }
friend CEXP poly operator-(poly p, value_type c) {
p[0] -= c;
return p;
}
friend CEXP poly operator-(value_type c, poly CR p) { return p - c; }
CEXP poly &operator*=(value_type c) {
apply([&c](u32, auto &v) { v *= c; });
return *this;
}
friend CEXP poly operator*(poly p, value_type c) { return p *= c; }
friend CEXP poly operator*(value_type c, poly p) { return p *= c; }
CEXP poly &operator+=(poly CR r) {
if (!r.size()) return *this;
resize(max(size(), r.size()));
apply_range(0, r.size(), [&r](u32 i, auto &v) { v += r[i]; });
return *this;
}
friend CEXP poly operator+(poly l, poly CR r) { return l += r; }
CEXP poly &operator-=(poly CR r) {
if (!r.size()) return *this;
resize(max(size(), r.size()));
apply_range(0, r.size(), [&r](u32 i, auto &v) { v -= r[i]; });
return *this;
}
friend CEXP poly operator-(poly l, poly CR r) { return l -= r; }
CEXP poly &operator*=(poly CR r) {
if (!r.size()) {
resize(1);
d[0] = 0;
return *this;
}
conv(r);
return *this;
}
friend CEXP poly operator*(poly l, poly CR r) { return l *= r; }
CEXP auto operator<=>(poly CR r) const { return stripped(*this).d <=> stripped(r).d; }
CEXP bool operator==(poly CR r) const { return stripped(*this).d == stripped(r).d; }
};
} // namespace tifa_libs::math
#line 5 "src/code/poly/deriv_fps.hpp"
namespace tifa_libs::math {
template <class mint, class ccore>
CEXP poly<mint, ccore> deriv_fps(poly<mint, ccore> CR p) {
auto _ = p;
for (u32 i = 1; i < _.size(); ++i) _[i - 1] = _[i] * i;
_.data().back() = 0;
return _;
}
} // namespace tifa_libs::math
#line 1 "src/code/poly/int_fps.hpp"
#line 5 "src/code/poly/int_fps.hpp"
namespace tifa_libs::math {
template <class mint, class ccore>
CEXP poly<mint, ccore> int_fps(poly<mint, ccore> CR p) {
auto _ = p;
for (u32 i = _.size() - 1; i; --i) _[i] = _[i - 1] * mint(i).inv();
_[0] = 0;
return _;
}
} // namespace tifa_libs::math
#line 1 "src/code/poly/inv_fps.hpp"
#line 5 "src/code/poly/inv_fps.hpp"
namespace tifa_libs::math {
template <class mint, class ccore>
CEXP poly<mint, ccore> inv_fps(poly<mint, ccore> CR p, u32 n = 0) {
assert(p[0] != 0);
if (!n) n = p.size();
poly<mint, ccore> 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::math
#line 7 "src/code/poly/ln_fps.hpp"
namespace tifa_libs::math {
template <class mint, class ccore>
CEXP poly<mint, ccore> ln_fps(poly<mint, ccore> CR p, u32 n = 0) {
assert(p[0] == 1);
if (!n) n = p.size();
auto _ = deriv_fps(p).pre(n);
_.conv(inv_fps(p, n));
return int_fps(_).pre(n);
}
} // namespace tifa_libs::math
#line 5 "src/code/poly/exp_fps.hpp"
namespace tifa_libs::math {
template <class mint, class ccore>
CEXP poly<mint, ccore> exp_fps(poly<mint, ccore> p, u32 n = 0) {
assert(p[0] == 0);
if (!n) n = p.size();
p[0] += 1;
poly<mint, ccore> a{1};
for (u32 i = 1; i < n; i *= 2) a = (a * (p.pre(i * 2) - ln_fps(a, i * 2))).pre(i * 2);
return a.pre(n);
}
} // namespace tifa_libs::math
#line 6 "src/test_cpverifier/library-checker-math/exp_of_formal_power_series.pmtt-s30.test.cpp"
CEXP u32 MOD = 998244353;
#line 1 "src/code/math/mint_s30.hpp"
#line 1 "src/code/math/mint.hpp"
#line 1 "src/code/nt/inverse.hpp"
#line 1 "src/code/nt/inv_gcd.hpp"
#line 1 "src/code/math/safe_mod.hpp"
#line 5 "src/code/math/safe_mod.hpp"
namespace tifa_libs::math {
template <sint_c T>
CEXP T safe_mod(T x, to_uint_t<T> mod) { return ((x %= (T)mod) < 0 ? x + (T)mod : x); }
} // namespace tifa_libs::math
#line 1 "src/code/nt/exgcd.hpp"
#line 5 "src/code/nt/exgcd.hpp"
namespace tifa_libs::math {
// Binary exgcd
template <uint_c U, bool only_x = false>
CEXP auto exgcd_b(U a, U b) {
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;
T s = 1, t = 0, u = 0, v = 1;
while (x) {
while (!(x & 1)) {
x /= 2;
if (!((s | t) & 1)) s /= 2, t /= 2;
else s = (s + (T)b) / 2, t = (t - (T)a) / 2;
}
while (!(y & 1)) {
y /= 2;
if (!((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) {
T _ = v / (T)a;
v -= _ * (T)a, u += _ * (T)b;
}
if (b && (U)abs(u) >= b) {
T _ = u / (T)b;
u -= _ * (T)b, v += _ * (T)a;
}
if (T u_ = u + (T)b, v_ = v - (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
if (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) {
using U = to_uint_t<T>;
if (auto [x, y] = std::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::math
#line 6 "src/code/nt/inv_gcd.hpp"
namespace tifa_libs::math {
template <uint_c T>
CEXP ptt<T> inv_gcd(T n, T mod) {
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::math
#line 5 "src/code/nt/inverse.hpp"
namespace tifa_libs::math {
template <uint_c T, uint_c U>
CEXP U inverse(T n, U mod) {
auto [g, x] = inv_gcd(U(n % mod), mod);
assert(g == 1);
return x;
}
} // namespace tifa_libs::math
#line 6 "src/code/math/mint.hpp"
namespace tifa_libs::math {
template <class D, uint_c Rt>
class mint {
CEXP D CR d() const { return static_cast<D CR>(*this); }
CEXP D &d() { return static_cast<D &>(*this); }
protected:
Rt v_{};
public:
CEXP mint() {}
template <int_c T>
CEXP mint(T v) : v_(D::mod_(v)) {}
CEXP operator D() { return d(); }
using raw_type = Rt;
using sraw_type = to_sint_t<Rt>;
static CEXP raw_type mod() { return D::mod_(); }
static CEXP sraw_type smod() { return (sraw_type)D::mod_(); }
CEXP raw_type val() const { return d().val_(); }
CEXP sraw_type sval() const { return (sraw_type)d().val_(); }
CEXP raw_type &data() { return d().data_(); }
template <int_c T>
explicit CEXP operator T() const { return (T)val(); }
CEXP mint &operator+=(mint CR r) { return d().adde_(r.d()); }
CEXP mint &operator-=(mint CR r) { return d().sube_(r.d()); }
CEXP mint &operator*=(mint CR r) { return d().mule_(r.d()); }
CEXP mint &operator/=(mint CR r) { return *this = *this * r.inv(); }
CEXP mint CR operator+() const { return *this; }
CEXP mint operator-() const { return d().neg_(); }
CEXP mint inv() const { return inverse(val(), mod()); }
friend CEXP mint operator+(mint l, mint CR r) { return l += r; }
friend CEXP mint operator-(mint l, mint CR r) { return l -= r; }
friend CEXP mint operator*(mint l, mint CR r) { return l *= r; }
friend CEXP mint operator/(mint l, mint CR r) { return l /= r; }
friend CEXP bool operator==(mint CR l, mint CR r) { return l.val() == r.val(); }
friend CEXP auto operator<=>(mint CR l, mint CR r) { return l.sval() - r.sval(); }
friend std::istream &operator>>(std::istream &is, mint &x) {
i64 _;
is >> _;
x = mint(_);
return is;
}
friend std::ostream &operator<<(std::ostream &os, mint CR x) { return os << x.val(); }
friend CEXP mint abs(mint CR x) { return x.val(); }
};
} // namespace tifa_libs::math
#line 5 "src/code/math/mint_s30.hpp"
namespace tifa_libs::math {
template <u32 MOD>
class mint_s30 : public mint<mint_s30<MOD>, u32> {
using base = mint<mint_s30<MOD>, u32>;
friend base;
static CEXP u32 MOD2 = MOD << 1;
static CEXP u32 R = []() {
u32 t = 2, iv = MOD * (t - MOD * MOD);
iv *= t - MOD * iv, iv *= t - MOD * iv;
return iv * (MOD * iv - t);
}();
static CEXP u32 R2 = -(u64)(MOD) % MOD;
static_assert(MOD & 1);
static_assert(-R * MOD == 1);
static_assert((MOD >> 30) == 0);
static_assert(MOD != 1);
static CEXP u32 reduce(u64 x) { return u32((x + u64((u32)x * R) * MOD) >> 32); }
static CEXP u32 norm(u32 x) { return x - (MOD & -((MOD - 1 - x) >> 31)); }
public:
static CEXP bool FIXED_MOD = true;
CEXP mint_s30() {}
template <int_c T>
CEXP mint_s30(T v) { this->v_ = mod_(v); }
private:
using raw_t = TPN base::raw_type;
using sraw_t = TPN base::sraw_type;
template <sint_c T>
static CEXP raw_t mod_(T v) { return reduce(u64(v % (i32)mod_() + (i32)mod_()) * R2); }
template <uint_c T>
static CEXP raw_t mod_(T v) { return reduce(u64(v % mod_()) * R2); }
static CEXP raw_t mod_() { return MOD; }
CEXP raw_t val_() const { return norm(reduce(this->v_)); }
CEXP raw_t &data_() { return this->v_; }
CEXP mint_s30 neg_() const {
mint_s30 res;
res.v_ = (MOD2 & -(this->v_ != 0)) - this->v_;
return res;
}
CEXP mint_s30 &adde_(mint_s30 CR r) {
this->v_ += r.v_ - MOD2, this->v_ += MOD2 & -(this->v_ >> 31);
return *this;
}
CEXP mint_s30 &sube_(mint_s30 CR r) {
this->v_ -= r.v_, this->v_ += MOD2 & -(this->v_ >> 31);
return *this;
}
CEXP mint_s30 &mule_(mint_s30 CR r) {
this->v_ = reduce(u64(this->v_) * r.v_);
return *this;
}
};
} // namespace tifa_libs::math
#line 1 "src/code/poly/polymtt.hpp"
#line 1 "src/code/conv/conv_mtt.hpp"
#line 1 "src/code/conv/conv_naive.hpp"
#line 5 "src/code/conv/conv_naive.hpp"
namespace tifa_libs::math {
template <class U, class T = U>
requires(sizeof(U) <= sizeof(T))
CEXP vec<T> conv_naive(vec<U> CR l, vec<U> CR r, u32 ans_size = 0) {
if (l.empty() || r.empty()) return {};
if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
u32 n = (u32)l.size(), m = (u32)r.size();
vec<T> ans(ans_size);
if (n < m)
flt_ (u32, j, 0, m)
flt_ (u32, i, 0, n) {
if (i + j >= ans_size) break;
ans[i + j] += (T)l[i] * (T)r[j];
}
else
flt_ (u32, i, 0, n)
flt_ (u32, j, 0, m) {
if (i + j >= ans_size) break;
ans[i + j] += (T)l[i] * (T)r[j];
}
return ans;
}
} // namespace tifa_libs::math
#line 1 "src/code/conv/fft.hpp"
#line 5 "src/code/conv/fft.hpp"
namespace tifa_libs::math {
template <std::floating_point FP>
struct FFT {
using C = std::complex<FP>;
using data_t = C;
explicit CEXP FFT() : rev(), w() {}
CEXP u32 size() const { return (u32)rev.size(); }
CEXP void bzr(u32 len) {
u32 n = max<u32>(std::bit_ceil(len), 2);
if (n == size()) return;
rev.resize(n, 0);
u32 k = (u32)(std::bit_width(n) - 1);
flt_ (u32, i, 0, n) rev[i] = (rev[i / 2] / 2) | ((i & 1) << (k - 1));
w.resize(n);
w[0].real(1);
flt_ (u32, i, 1, n) w[i] = {std::cos(TAU * (FP)i / (FP)n), std::sin(TAU * (FP)i / (FP)n)};
}
CEXP void dif(vec<C> &f, u32 n = 0) const {
if (!n) n = size();
if (f.size() < n) f.resize(n);
assert(n <= size());
flt_ (u32, i, 0, n)
if (i < rev[i]) swap(f[rev[i]], f[i]);
#pragma GCC diagnostic ignored "-Wsign-conversion"
for (u32 i = 2, d = n / 2; i <= n; i *= 2, d /= 2)
for (u32 j = 0; j < n; j += i) {
auto l = f.begin() + j, r = f.begin() + j + i / 2;
auto p = w.begin();
for (u32 k = 0; k < i / 2; ++k, ++l, ++r, p += d) {
C tmp = *r * *p;
*r = *l - tmp;
*l = *l + tmp;
}
}
#pragma GCC diagnostic warning "-Wsign-conversion"
}
CEXP void dit(vec<C> &f, u32 n = 0) const {
if (!n) n = size();
dif(f, n);
flt_ (u32, i, 0, n) f[i] /= (FP)n;
}
private:
const FP TAU = std::acos((FP)-1.) * 2;
vecu rev;
vec<C> w;
};
} // namespace tifa_libs::math
#line 6 "src/code/conv/conv_mtt.hpp"
namespace tifa_libs::math {
template <class mint, class FP>
CEXP vec<mint> conv_mtt(FFT<FP> &fft, vec<mint> CR l, vec<mint> CR r, u32 ans_size = 0) {
if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
if (ans_size < 32) return conv_naive(l, r, ans_size);
using C = TPN FFT<FP>::C;
if (l.size() == 1) {
vec<mint> ans = r;
ans.resize(ans_size);
for (auto &i : ans) i *= l[0];
return ans;
}
if (r.size() == 1) {
vec<mint> ans = l;
ans.resize(ans_size);
for (auto &i : ans) i *= r[0];
return ans;
}
fft.bzr(max({(u32)l.size(), (u32)r.size(), min(u32(l.size() + r.size() - 1), ans_size)}));
u32 n = fft.size();
const int OFS = ((int)sizeof(decltype(mint::mod())) * 8 - std::countl_zero(mint::mod() - 1) + 1) / 2;
const u32 MSK = ((1u << OFS) - 1);
vec<mint> ans(ans_size);
vec<C> a(n), b(n);
for (u32 i = 0; i < l.size(); ++i) a[i] = {(FP)(l[i].val() & MSK), (FP)(l[i].val() >> OFS)};
for (u32 i = 0; i < r.size(); ++i) b[i] = {(FP)(r[i].val() & MSK), (FP)(r[i].val() >> OFS)};
fft.dif(a);
fft.dif(b);
{
vec<C> p(n), q(n);
for (u32 i = 0, j; i < n; ++i) {
j = (n - i) & (n - 1);
C da = (a[i] + std::conj(a[j])) * C(.5, 0), db = (a[i] - std::conj(a[j])) * C(0, -.5), dc = (b[i] + std::conj(b[j])) * C(.5, 0), dd = (b[i] - std::conj(b[j])) * C(.5, 0);
p[j] = da * dc + da * dd;
q[j] = db * dc + db * dd;
}
a = p;
b = q;
}
fft.dif(a);
fft.dif(b);
flt_ (u32, i, 0, ans_size) {
i64 da = (i64)(a[i].real() / (FP)n + .5) % mint::smod(), db = (i64)(a[i].imag() / (FP)n + .5) % mint::smod(), dc = (i64)(b[i].real() / (FP)n + .5) % mint::smod(), dd = (i64)(b[i].imag() / (FP)n + .5) % mint::smod();
ans[i] = da + ((db + dc) << OFS) % mint::smod() + (dd << (OFS * 2)) % mint::smod();
}
return ans;
}
} // namespace tifa_libs::math
#line 6 "src/code/poly/polymtt.hpp"
namespace tifa_libs::math {
namespace polymtt_impl_ {
template <class FP = f64>
struct cconv_mtt : public FFT<FP> {
static CEXP auto ct_cat = ct_FFT;
template <class mint>
CEXP void conv(vec<mint>& l, vec<mint> CR r, u32 sz = 0) { l = conv_mtt(*this, l, r, sz); }
};
} // namespace polymtt_impl_
template <class mint, class FP = f64>
using polymtt = poly<mint, polymtt_impl_::cconv_mtt<FP>>;
} // namespace tifa_libs::math
#line 11 "src/test_cpverifier/library-checker-math/exp_of_formal_power_series.pmtt-s30.test.cpp"
using mint = tifa_libs::math::mint_s30<MOD>;
using poly = tifa_libs::math::polymtt<mint>;
int main() {
u32 n;
tifa_libs::fin >> n;
poly p(n);
tifa_libs::fin >> p.data();
tifa_libs::fout << tifa_libs::math::exp_fps(p).data();
return 0;
}
src/test_cpverifier/library-checker-math/exp_of_formal_power_series.pmtt-s30.test.cpp