QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#630873 | #9120. Huge Segment Tree | maspy | AC ✓ | 120ms | 26940kb | C++20 | 44.7kb | 2024-10-11 20:45:30 | 2024-10-11 20:45:36 |
Judging History
answer
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない?
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"
#line 2 "/home/maspy/compro/library/mod/modint_common.hpp"
struct has_mod_impl {
template <class T>
static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n %= mod;
while (len(dat) <= n) {
int k = len(dat);
int q = (mod + k - 1) / k;
dat.eb(dat[k * q - mod] * mint::raw(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
assert(0 <= n && n < mod);
static vector<mint> dat = {1, 1};
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static vector<mint> dat = {1, 1};
if (n < 0) return mint(0);
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}
template <typename mint>
mint C_dense(int n, int k) {
static vvc<mint> C;
static int H = 0, W = 0;
auto calc = [&](int i, int j) -> mint {
if (i == 0) return (j == 0 ? mint(1) : mint(0));
return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
};
if (W <= k) {
FOR(i, H) {
C[i].resize(k + 1);
FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
FOR(i, H, n + 1) {
C[i].resize(W);
FOR(j, W) { C[i][j] = calc(i, j); }
}
H = n + 1;
}
return C[n][k];
}
template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if constexpr (dense) return C_dense<mint>(n, k);
if constexpr (!large) return multinomial<mint>(n, k, n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) x *= mint(n - i);
return x * fact_inv<mint>(k);
}
template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
assert(n >= 0);
if (d < 0) return mint(0);
if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
return C<mint, large, dense>(n + d - 1, d);
}
#line 3 "/home/maspy/compro/library/mod/modint.hpp"
template <int mod>
struct modint {
static constexpr u32 umod = u32(mod);
static_assert(umod < u32(1) << 31);
u32 val;
static modint raw(u32 v) {
modint x;
x.val = v;
return x;
}
constexpr modint() : val(0) {}
constexpr modint(u32 x) : val(x % umod) {}
constexpr modint(u64 x) : val(x % umod) {}
constexpr modint(u128 x) : val(x % umod) {}
constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
bool operator<(const modint &other) const { return val < other.val; }
modint &operator+=(const modint &p) {
if ((val += p.val) >= umod) val -= umod;
return *this;
}
modint &operator-=(const modint &p) {
if ((val += umod - p.val) >= umod) val -= umod;
return *this;
}
modint &operator*=(const modint &p) {
val = u64(val) * p.val % umod;
return *this;
}
modint &operator/=(const modint &p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return val == p.val; }
bool operator!=(const modint &p) const { return val != p.val; }
modint inverse() const {
int a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint(u);
}
modint pow(ll n) const {
assert(n >= 0);
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
static constexpr int get_mod() { return mod; }
// (n, r), r は 1 の 2^n 乗根
static constexpr pair<int, int> ntt_info() {
if (mod == 120586241) return {20, 74066978};
if (mod == 167772161) return {25, 17};
if (mod == 469762049) return {26, 30};
if (mod == 754974721) return {24, 362};
if (mod == 880803841) return {23, 211};
if (mod == 943718401) return {22, 663003469};
if (mod == 998244353) return {23, 31};
if (mod == 1004535809) return {21, 836905998};
if (mod == 1045430273) return {20, 363};
if (mod == 1051721729) return {20, 330};
if (mod == 1053818881) return {20, 2789};
return {-1, -1};
}
static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};
#ifdef FASTIO
template <int mod>
void rd(modint<mod> &x) {
fastio::rd(x.val);
x.val %= mod;
// assert(0 <= x.val && x.val < mod);
}
template <int mod>
void wt(modint<mod> x) {
fastio::wt(x.val);
}
#endif
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 2 "/home/maspy/compro/library/poly/count_terms.hpp"
template<typename mint>
int count_terms(const vc<mint>& f){
int t = 0;
FOR(i, len(f)) if(f[i] != mint(0)) ++t;
return t;
}
#line 2 "/home/maspy/compro/library/mod/mod_inv.hpp"
// long でも大丈夫
// (val * x - 1) が mod の倍数になるようにする
// 特に mod=0 なら x=0 が満たす
ll mod_inv(ll val, ll mod) {
if (mod == 0) return 0;
mod = abs(mod);
val %= mod;
if (val < 0) val += mod;
ll a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
if (u < 0) u += mod;
return u;
}
#line 2 "/home/maspy/compro/library/mod/crt3.hpp"
constexpr u32 mod_pow_constexpr(u64 a, u64 n, u32 mod) {
a %= mod;
u64 res = 1;
FOR(32) {
if (n & 1) res = res * a % mod;
a = a * a % mod, n /= 2;
}
return res;
}
template <typename T, u32 p0, u32 p1>
T CRT2(u64 a0, u64 a1) {
static_assert(p0 < p1);
static constexpr u64 x0_1 = mod_pow_constexpr(p0, p1 - 2, p1);
u64 c = (a1 - a0 + p1) * x0_1 % p1;
return a0 + c * p0;
}
template <typename T, u32 p0, u32 p1, u32 p2>
T CRT3(u64 a0, u64 a1, u64 a2) {
static_assert(p0 < p1 && p1 < p2);
static constexpr u64 x1 = mod_pow_constexpr(p0, p1 - 2, p1);
static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
static constexpr u64 p01 = u64(p0) * p1;
u64 c = (a1 - a0 + p1) * x1 % p1;
u64 ans_1 = a0 + c * p0;
c = (a2 - ans_1 % p2 + p2) * x2 % p2;
return T(ans_1) + T(c) * T(p01);
}
template <typename T, u32 p0, u32 p1, u32 p2, u32 p3, u32 p4>
T CRT5(u64 a0, u64 a1, u64 a2, u64 a3, u64 a4) {
static_assert(p0 < p1 && p1 < p2 && p2 < p3 && p3 < p4);
static constexpr u64 x1 = mod_pow_constexpr(p0, p1 - 2, p1);
static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
static constexpr u64 x3
= mod_pow_constexpr(u64(p0) * p1 % p3 * p2 % p3, p3 - 2, p3);
static constexpr u64 x4
= mod_pow_constexpr(u64(p0) * p1 % p4 * p2 % p4 * p3 % p4, p4 - 2, p4);
static constexpr u64 p01 = u64(p0) * p1;
static constexpr u64 p23 = u64(p2) * p3;
u64 c = (a1 - a0 + p1) * x1 % p1;
u64 ans_1 = a0 + c * p0;
c = (a2 - ans_1 % p2 + p2) * x2 % p2;
u128 ans_2 = ans_1 + c * static_cast<u128>(p01);
c = static_cast<u64>(a3 - ans_2 % p3 + p3) * x3 % p3;
u128 ans_3 = ans_2 + static_cast<u128>(c * p2) * p01;
c = static_cast<u64>(a4 - ans_3 % p4 + p4) * x4 % p4;
return T(ans_3) + T(c) * T(p01) * T(p23);
}
#line 2 "/home/maspy/compro/library/poly/convolution_naive.hpp"
template <class T, typename enable_if<!has_mod<T>::value>::type* = nullptr>
vc<T> convolution_naive(const vc<T>& a, const vc<T>& b) {
int n = int(a.size()), m = int(b.size());
if (n > m) return convolution_naive<T>(b, a);
if (n == 0) return {};
vector<T> ans(n + m - 1);
FOR(i, n) FOR(j, m) ans[i + j] += a[i] * b[j];
return ans;
}
template <class T, typename enable_if<has_mod<T>::value>::type* = nullptr>
vc<T> convolution_naive(const vc<T>& a, const vc<T>& b) {
int n = int(a.size()), m = int(b.size());
if (n > m) return convolution_naive<T>(b, a);
if (n == 0) return {};
vc<T> ans(n + m - 1);
if (n <= 16 && (T::get_mod() < (1 << 30))) {
for (int k = 0; k < n + m - 1; ++k) {
int s = max(0, k - m + 1);
int t = min(n, k + 1);
u64 sm = 0;
for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }
ans[k] = sm;
}
} else {
for (int k = 0; k < n + m - 1; ++k) {
int s = max(0, k - m + 1);
int t = min(n, k + 1);
u128 sm = 0;
for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }
ans[k] = T::raw(sm % T::get_mod());
}
}
return ans;
}
#line 2 "/home/maspy/compro/library/poly/convolution_karatsuba.hpp"
// 任意の環でできる
template <typename T>
vc<T> convolution_karatsuba(const vc<T>& f, const vc<T>& g) {
const int thresh = 30;
if (min(len(f), len(g)) <= thresh) return convolution_naive(f, g);
int n = max(len(f), len(g));
int m = ceil(n, 2);
vc<T> f1, f2, g1, g2;
if (len(f) < m) f1 = f;
if (len(f) >= m) f1 = {f.begin(), f.begin() + m};
if (len(f) >= m) f2 = {f.begin() + m, f.end()};
if (len(g) < m) g1 = g;
if (len(g) >= m) g1 = {g.begin(), g.begin() + m};
if (len(g) >= m) g2 = {g.begin() + m, g.end()};
vc<T> a = convolution_karatsuba(f1, g1);
vc<T> b = convolution_karatsuba(f2, g2);
FOR(i, len(f2)) f1[i] += f2[i];
FOR(i, len(g2)) g1[i] += g2[i];
vc<T> c = convolution_karatsuba(f1, g1);
vc<T> F(len(f) + len(g) - 1);
assert(2 * m + len(b) <= len(F));
FOR(i, len(a)) F[i] += a[i], c[i] -= a[i];
FOR(i, len(b)) F[2 * m + i] += b[i], c[i] -= b[i];
if (c.back() == T(0)) c.pop_back();
FOR(i, len(c)) if (c[i] != T(0)) F[m + i] += c[i];
return F;
}
#line 2 "/home/maspy/compro/library/poly/ntt.hpp"
template <class mint>
void ntt(vector<mint>& a, bool inverse) {
assert(mint::can_ntt());
const int rank2 = mint::ntt_info().fi;
const int mod = mint::get_mod();
static array<mint, 30> root, iroot;
static array<mint, 30> rate2, irate2;
static array<mint, 30> rate3, irate3;
assert(rank2 != -1 && len(a) <= (1 << max(0, rank2)));
static bool prepared = 0;
if (!prepared) {
prepared = 1;
root[rank2] = mint::ntt_info().se;
iroot[rank2] = mint(1) / root[rank2];
FOR_R(i, rank2) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
int n = int(a.size());
int h = topbit(n);
assert(n == 1 << h);
if (!inverse) {
int len = 0;
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
FOR(s, 1 << len) {
int offset = s << (h - len);
FOR(i, p) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
rot *= rate2[topbit(~s & -~s)];
}
len++;
} else {
int p = 1 << (h - len - 2);
mint rot = 1, imag = root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
u64 mod2 = u64(mod) * mod;
u64 a0 = a[i + offset].val;
u64 a1 = u64(a[i + offset + p].val) * rot.val;
u64 a2 = u64(a[i + offset + 2 * p].val) * rot2.val;
u64 a3 = u64(a[i + offset + 3 * p].val) * rot3.val;
u64 a1na3imag = (a1 + mod2 - a3) % mod * imag.val;
u64 na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
rot *= rate3[topbit(~s & -~s)];
}
len += 2;
}
}
} else {
mint coef = mint(1) / mint(len(a));
FOR(i, len(a)) a[i] *= coef;
int len = h;
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
FOR(s, 1 << (len - 1)) {
int offset = s << (h - len + 1);
FOR(i, p) {
u64 l = a[i + offset].val;
u64 r = a[i + offset + p].val;
a[i + offset] = l + r;
a[i + offset + p] = (mod + l - r) * irot.val;
}
irot *= irate2[topbit(~s & -~s)];
}
len--;
} else {
int p = 1 << (h - len);
mint irot = 1, iimag = iroot[2];
FOR(s, (1 << (len - 2))) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
u64 a0 = a[i + offset + 0 * p].val;
u64 a1 = a[i + offset + 1 * p].val;
u64 a2 = a[i + offset + 2 * p].val;
u64 a3 = a[i + offset + 3 * p].val;
u64 x = (mod + a2 - a3) * iimag.val % mod;
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] = (a0 + mod - a1 + x) * irot.val;
a[i + offset + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * irot2.val;
a[i + offset + 3 * p] = (a0 + 2 * mod - a1 - x) * irot3.val;
}
irot *= irate3[topbit(~s & -~s)];
}
len -= 2;
}
}
}
}
#line 1 "/home/maspy/compro/library/poly/fft.hpp"
namespace CFFT {
using real = double;
struct C {
real x, y;
C() : x(0), y(0) {}
C(real x, real y) : x(x), y(y) {}
inline C operator+(const C& c) const { return C(x + c.x, y + c.y); }
inline C operator-(const C& c) const { return C(x - c.x, y - c.y); }
inline C operator*(const C& c) const {
return C(x * c.x - y * c.y, x * c.y + y * c.x);
}
inline C conj() const { return C(x, -y); }
};
const real PI = acosl(-1);
int base = 1;
vector<C> rts = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
void ensure_base(int nbase) {
if (nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
while (base < nbase) {
real angle = PI * 2.0 / (1 << (base + 1));
for (int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
real angle_i = angle * (2 * i + 1 - (1 << base));
rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
}
++base;
}
}
void fft(vector<C>& a, int n) {
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++) {
if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); }
}
for (int k = 1; k < n; k <<= 1) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
C z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
} // namespace CFFT
#line 9 "/home/maspy/compro/library/poly/convolution.hpp"
template <class mint>
vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) {
if (a.empty() || b.empty()) return {};
int n = int(a.size()), m = int(b.size());
int sz = 1;
while (sz < n + m - 1) sz *= 2;
// sz = 2^k のときの高速化。分割統治的なやつで損しまくるので。
if ((n + m - 3) <= sz / 2) {
auto a_last = a.back(), b_last = b.back();
a.pop_back(), b.pop_back();
auto c = convolution(a, b);
c.resize(n + m - 1);
c[n + m - 2] = a_last * b_last;
FOR(i, len(a)) c[i + len(b)] += a[i] * b_last;
FOR(i, len(b)) c[i + len(a)] += b[i] * a_last;
return c;
}
a.resize(sz), b.resize(sz);
bool same = a == b;
ntt(a, 0);
if (same) {
b = a;
} else {
ntt(b, 0);
}
FOR(i, sz) a[i] *= b[i];
ntt(a, 1);
a.resize(n + m - 1);
return a;
}
template <typename mint>
vector<mint> convolution_garner(const vector<mint>& a, const vector<mint>& b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
static constexpr int p0 = 167772161;
static constexpr int p1 = 469762049;
static constexpr int p2 = 754974721;
using mint0 = modint<p0>;
using mint1 = modint<p1>;
using mint2 = modint<p2>;
vc<mint0> a0(n), b0(m);
vc<mint1> a1(n), b1(m);
vc<mint2> a2(n), b2(m);
FOR(i, n) a0[i] = a[i].val, a1[i] = a[i].val, a2[i] = a[i].val;
FOR(i, m) b0[i] = b[i].val, b1[i] = b[i].val, b2[i] = b[i].val;
auto c0 = convolution_ntt<mint0>(a0, b0);
auto c1 = convolution_ntt<mint1>(a1, b1);
auto c2 = convolution_ntt<mint2>(a2, b2);
vc<mint> c(len(c0));
FOR(i, n + m - 1) { c[i] = CRT3<mint, p0, p1, p2>(c0[i].val, c1[i].val, c2[i].val); }
return c;
}
template <typename R>
vc<double> convolution_fft(const vc<R>& a, const vc<R>& b) {
using C = CFFT::C;
int need = (int)a.size() + (int)b.size() - 1;
int nbase = 1;
while ((1 << nbase) < need) nbase++;
CFFT::ensure_base(nbase);
int sz = 1 << nbase;
vector<C> fa(sz);
for (int i = 0; i < sz; i++) {
double x = (i < (int)a.size() ? a[i] : 0);
double y = (i < (int)b.size() ? b[i] : 0);
fa[i] = C(x, y);
}
CFFT::fft(fa, sz);
C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
for (int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
fa[i] = z;
}
for (int i = 0; i < (sz >> 1); i++) {
C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * CFFT::rts[(sz >> 1) + i];
fa[i] = A0 + A1 * s;
}
CFFT::fft(fa, sz >> 1);
vector<double> ret(need);
for (int i = 0; i < need; i++) { ret[i] = (i & 1 ? fa[i >> 1].y : fa[i >> 1].x); }
return ret;
}
vector<ll> convolution(const vector<ll>& a, const vector<ll>& b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
if (min(n, m) <= 2500) return convolution_naive(a, b);
ll abs_sum_a = 0, abs_sum_b = 0;
ll LIM = 1e15;
FOR(i, n) abs_sum_a = min(LIM, abs_sum_a + abs(a[i]));
FOR(i, m) abs_sum_b = min(LIM, abs_sum_b + abs(b[i]));
if (i128(abs_sum_a) * abs_sum_b < 1e15) {
vc<double> c = convolution_fft<ll>(a, b);
vc<ll> res(len(c));
FOR(i, len(c)) res[i] = ll(floor(c[i] + .5));
return res;
}
static constexpr u32 MOD1 = 167772161; // 2^25
static constexpr u32 MOD2 = 469762049; // 2^26
static constexpr u32 MOD3 = 754974721; // 2^24
using mint1 = modint<MOD1>;
using mint2 = modint<MOD2>;
using mint3 = modint<MOD3>;
vc<mint1> a1(n), b1(m);
vc<mint2> a2(n), b2(m);
vc<mint3> a3(n), b3(m);
FOR(i, n) a1[i] = a[i], a2[i] = a[i], a3[i] = a[i];
FOR(i, m) b1[i] = b[i], b2[i] = b[i], b3[i] = b[i];
auto c1 = convolution_ntt<mint1>(a1, b1);
auto c2 = convolution_ntt<mint2>(a2, b2);
auto c3 = convolution_ntt<mint3>(a3, b3);
u128 prod = u128(MOD1) * MOD2 * MOD3;
vc<ll> res(n + m - 1);
FOR(i, n + m - 1) {
u128 x = CRT3<u128, MOD1, MOD2, MOD3>(c1[i].val, c2[i].val, c3[i].val);
res[i] = (x < prod / 2 ? ll(x) : -ll(prod - x));
}
return res;
}
template <typename mint>
vc<mint> convolution(const vc<mint>& a, const vc<mint>& b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
if (mint::can_ntt()) {
if (min(n, m) <= 50) return convolution_karatsuba<mint>(a, b);
return convolution_ntt(a, b);
}
if (min(n, m) <= 200) return convolution_karatsuba<mint>(a, b);
return convolution_garner(a, b);
}
#line 2 "/home/maspy/compro/library/poly/integrate.hpp"
// 不定積分:integrate(f)
// 定積分:integrate(f, L, R)
template <typename mint>
vc<mint> integrate(const vc<mint>& f) {
vc<mint> g(len(f) + 1);
FOR3(i, 1, len(g)) g[i] = f[i - 1] * inv<mint>(i);
return g;
}
// 不定積分:integrate(f)
// 定積分:integrate(f, L, R)
template <typename mint>
mint integrate(const vc<mint>& f, mint L, mint R) {
mint I = 0;
mint pow_L = 1, pow_R = 1;
FOR(i, len(f)) {
pow_L *= L, pow_R *= R;
I += inv<mint>(i + 1) * f[i] * (pow_R - pow_L);
}
return I;
}
#line 2 "/home/maspy/compro/library/poly/differentiate.hpp"
template <typename mint>
vc<mint> differentiate(const vc<mint>& f) {
if (len(f) <= 1) return {};
vc<mint> g(len(f) - 1);
FOR(i, len(g)) g[i] = f[i + 1] * mint(i + 1);
return g;
}
#line 6 "/home/maspy/compro/library/poly/fps_exp.hpp"
template <typename mint>
vc<mint> fps_exp_sparse(vc<mint>& f) {
if (len(f) == 0) return {mint(1)};
assert(f[0] == 0);
int N = len(f);
// df を持たせる
vc<pair<int, mint>> dat;
FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i - 1, mint(i) * f[i]);
vc<mint> F(N);
F[0] = 1;
FOR(n, 1, N) {
mint rhs = 0;
for (auto&& [k, fk]: dat) {
if (k > n - 1) break;
rhs += fk * F[n - 1 - k];
}
F[n] = rhs * inv<mint>(n);
}
return F;
}
template <typename mint>
vc<mint> fps_exp_dense(vc<mint>& h) {
const int n = len(h);
assert(n > 0 && h[0] == mint(0));
if (mint::can_ntt()) {
vc<mint>& f = h;
vc<mint> b = {1, (1 < n ? f[1] : 0)};
vc<mint> c = {1}, z1, z2 = {1, 1};
while (len(b) < n) {
int m = len(b);
auto y = b;
y.resize(2 * m);
ntt(y, 0);
z1 = z2;
vc<mint> z(m);
FOR(i, m) z[i] = y[i] * z1[i];
ntt(z, 1);
FOR(i, m / 2) z[i] = 0;
ntt(z, 0);
FOR(i, m) z[i] *= -z1[i];
ntt(z, 1);
c.insert(c.end(), z.begin() + m / 2, z.end());
z2 = c;
z2.resize(2 * m);
ntt(z2, 0);
vc<mint> x(f.begin(), f.begin() + m);
FOR(i, len(x) - 1) x[i] = x[i + 1] * mint(i + 1);
x.back() = 0;
ntt(x, 0);
FOR(i, m) x[i] *= y[i];
ntt(x, 1);
FOR(i, m - 1) x[i] -= b[i + 1] * mint(i + 1);
x.resize(m + m);
FOR(i, m - 1) x[m + i] = x[i], x[i] = 0;
ntt(x, 0);
FOR(i, m + m) x[i] *= z2[i];
ntt(x, 1);
FOR_R(i, len(x) - 1) x[i + 1] = x[i] * inv<mint>(i + 1);
x[0] = 0;
FOR3(i, m, min(n, m + m)) x[i] += f[i];
FOR(i, m) x[i] = 0;
ntt(x, 0);
FOR(i, m + m) x[i] *= y[i];
ntt(x, 1);
b.insert(b.end(), x.begin() + m, x.end());
}
b.resize(n);
return b;
}
const int L = len(h);
assert(L > 0 && h[0] == mint(0));
int LOG = 0;
while (1 << LOG < L) ++LOG;
h.resize(1 << LOG);
auto dh = differentiate(h);
vc<mint> f = {1}, g = {1};
int m = 1;
vc<mint> p;
FOR(LOG) {
p = convolution(f, g);
p.resize(m);
p = convolution(p, g);
p.resize(m);
g.resize(m);
FOR(i, m) g[i] += g[i] - p[i];
p = {dh.begin(), dh.begin() + m - 1};
p = convolution(f, p);
p.resize(m + m - 1);
FOR(i, m + m - 1) p[i] = -p[i];
FOR(i, m - 1) p[i] += mint(i + 1) * f[i + 1];
p = convolution(p, g);
p.resize(m + m - 1);
FOR(i, m - 1) p[i] += dh[i];
p = integrate(p);
FOR(i, m + m) p[i] = h[i] - p[i];
p[0] += mint(1);
f = convolution(f, p);
f.resize(m + m);
m += m;
}
f.resize(L);
return f;
}
template <typename mint>
vc<mint> fps_exp(vc<mint>& f) {
int n = count_terms(f);
int t = (mint::can_ntt() ? 320 : 3000);
return (n <= t ? fps_exp_sparse<mint>(f) : fps_exp_dense<mint>(f));
}
#line 2 "/home/maspy/compro/library/poly/fps_log.hpp"
#line 4 "/home/maspy/compro/library/poly/fps_inv.hpp"
template <typename mint>
vc<mint> fps_inv_sparse(const vc<mint>& f) {
int N = len(f);
vc<pair<int, mint>> dat;
FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i, f[i]);
vc<mint> g(N);
mint g0 = mint(1) / f[0];
g[0] = g0;
FOR(n, 1, N) {
mint rhs = 0;
for (auto&& [k, fk]: dat) {
if (k > n) break;
rhs -= fk * g[n - k];
}
g[n] = rhs * g0;
}
return g;
}
template <typename mint>
vc<mint> fps_inv_dense_ntt(const vc<mint>& F) {
vc<mint> G = {mint(1) / F[0]};
ll N = len(F), n = 1;
G.reserve(N);
while (n < N) {
vc<mint> f(2 * n), g(2 * n);
FOR(i, min(N, 2 * n)) f[i] = F[i];
FOR(i, n) g[i] = G[i];
ntt(f, false), ntt(g, false);
FOR(i, 2 * n) f[i] *= g[i];
ntt(f, true);
FOR(i, n) f[i] = 0;
ntt(f, false);
FOR(i, 2 * n) f[i] *= g[i];
ntt(f, true);
FOR(i, n, min(N, 2 * n)) G.eb(-f[i]);
n *= 2;
}
return G;
}
template <typename mint>
vc<mint> fps_inv_dense(const vc<mint>& F) {
if (mint::can_ntt()) return fps_inv_dense_ntt(F);
const int N = len(F);
vc<mint> R = {mint(1) / F[0]};
vc<mint> p;
int m = 1;
while (m < N) {
p = convolution(R, R);
p.resize(m + m);
vc<mint> f = {F.begin(), F.begin() + min(m + m, N)};
p = convolution(p, f);
R.resize(m + m);
FOR(i, m + m) R[i] = R[i] + R[i] - p[i];
m += m;
}
R.resize(N);
return R;
}
template <typename mint>
vc<mint> fps_inv(const vc<mint>& f) {
assert(f[0] != mint(0));
int n = count_terms(f);
int t = (mint::can_ntt() ? 160 : 820);
return (n <= t ? fps_inv_sparse<mint>(f) : fps_inv_dense<mint>(f));
}
#line 5 "/home/maspy/compro/library/poly/fps_log.hpp"
template <typename mint>
vc<mint> fps_log_dense(const vc<mint>& f) {
assert(f[0] == mint(1));
ll N = len(f);
vc<mint> df = f;
FOR(i, N) df[i] *= mint(i);
df.erase(df.begin());
auto f_inv = fps_inv(f);
auto g = convolution(df, f_inv);
g.resize(N - 1);
g.insert(g.begin(), 0);
FOR(i, N) g[i] *= inv<mint>(i);
return g;
}
template <typename mint>
vc<mint> fps_log_sparse(const vc<mint>& f) {
int N = f.size();
vc<pair<int, mint>> dat;
FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i, f[i]);
vc<mint> F(N);
vc<mint> g(N - 1);
for (int n = 0; n < N - 1; ++n) {
mint rhs = mint(n + 1) * f[n + 1];
for (auto&& [i, fi]: dat) {
if (i > n) break;
rhs -= fi * g[n - i];
}
g[n] = rhs;
F[n + 1] = rhs * inv<mint>(n + 1);
}
return F;
}
template <typename mint>
vc<mint> fps_log(const vc<mint>& f) {
assert(f[0] == mint(1));
int n = count_terms(f);
int t = (mint::can_ntt() ? 200 : 1200);
return (n <= t ? fps_log_sparse<mint>(f) : fps_log_dense<mint>(f));
}
#line 5 "/home/maspy/compro/library/poly/fps_pow.hpp"
// fps の k 乗を求める。k >= 0 の前提である。
// 定数項が 1 で、k が mint の場合には、fps_pow_1 を使うこと。
// ・dense な場合: log, exp を使う O(NlogN)
// ・sparse な場合: O(NK)
template <typename mint>
vc<mint> fps_pow(const vc<mint>& f, ll k) {
assert(0 <= k);
int n = len(f);
if (k == 0) {
vc<mint> g(n);
g[0] = mint(1);
return g;
}
int d = n;
FOR_R(i, n) if (f[i] != 0) d = i;
// d * k >= n
if (d >= ceil<ll>(n, k)) {
vc<mint> g(n);
return g;
}
ll off = d * k;
mint c = f[d];
mint c_inv = mint(1) / mint(c);
vc<mint> g(n - off);
FOR(i, n - off) g[i] = f[d + i] * c_inv;
g = fps_pow_1(g, mint(k));
vc<mint> h(n);
c = c.pow(k);
FOR(i, len(g)) h[off + i] = g[i] * c;
return h;
}
template <typename mint>
vc<mint> fps_pow_1_sparse(const vc<mint>& f, mint K) {
int N = len(f);
assert(N == 0 || f[0] == mint(1));
vc<pair<int, mint>> dat;
FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i, f[i]);
vc<mint> g(N);
g[0] = 1;
FOR(n, N - 1) {
mint& x = g[n + 1];
for (auto&& [d, cf]: dat) {
if (d > n + 1) break;
mint t = cf * g[n - d + 1];
x += t * (K * mint(d) - mint(n - d + 1));
}
x *= inv<mint>(n + 1);
}
return g;
}
template <typename mint>
vc<mint> fps_pow_1_dense(const vc<mint>& f, mint K) {
assert(f[0] == mint(1));
auto log_f = fps_log(f);
FOR(i, len(f)) log_f[i] *= K;
return fps_exp_dense(log_f);
}
template <typename mint>
vc<mint> fps_pow_1(const vc<mint>& f, mint K) {
int n = count_terms(f);
int t = (mint::can_ntt() ? 100 : 1300);
return (n <= t ? fps_pow_1_sparse(f, K) : fps_pow_1_dense(f, K));
}
// f^e, sparse, O(NMK)
template <typename mint>
vvc<mint> fps_pow_1_sparse_2d(vvc<mint> f, mint n) {
assert(f[0][0] == mint(1));
int N = len(f), M = len(f[0]);
vv(mint, dp, N, M);
dp[0] = fps_pow_1_sparse<mint>(f[0], n);
vc<tuple<int, int, mint>> dat;
FOR(i, N) FOR(j, M) {
if ((i > 0 || j > 0) && f[i][j] != mint(0)) dat.eb(i, j, f[i][j]);
}
FOR(i, 1, N) {
FOR(j, M) {
// F = f^n, f dF = n df F
// [x^{i-1}y^j]
mint lhs = 0, rhs = 0;
for (auto&& [a, b, c]: dat) {
if (a < i && b <= j) lhs += dp[i - a][j - b] * mint(i - a);
if (a <= i && b <= j) rhs += dp[i - a][j - b] * c * mint(a);
}
dp[i][j] = (n * rhs - lhs) * inv<mint>(i);
}
}
return dp;
}
#line 2 "/home/maspy/compro/library/poly/fps_div.hpp"
#line 5 "/home/maspy/compro/library/poly/fps_div.hpp"
// f/g. f の長さで出力される.
template <typename mint, bool SPARSE = false>
vc<mint> fps_div(vc<mint> f, vc<mint> g) {
if (SPARSE || count_terms(g) < 200) return fps_div_sparse(f, g);
int n = len(f);
g.resize(n);
g = fps_inv<mint>(g);
f = convolution(f, g);
f.resize(n);
return f;
}
// f/g ただし g は sparse
template <typename mint>
vc<mint> fps_div_sparse(vc<mint> f, vc<mint>& g) {
if (g[0] != mint(1)) {
mint cf = g[0].inverse();
for (auto&& x: f) x *= cf;
for (auto&& x: g) x *= cf;
}
vc<pair<int, mint>> dat;
FOR(i, 1, len(g)) if (g[i] != mint(0)) dat.eb(i, -g[i]);
FOR(i, len(f)) {
for (auto&& [j, x]: dat) {
if (i >= j) f[i] += x * f[i - j];
}
}
return f;
}
#line 7 "main.cpp"
// ((1+x)^K-1+x)^2 - x^2 + x
// これを 2 べき重みで足す
// [x^1] 最後に
using mint = modint998;
void solve() {
LL(K);
ll L = 2 * K - 1;
vc<mint> F;
F.eb(inv<mint>(2));
F.eb(1);
F.eb(inv<mint>(2));
F.resize(L);
vc<mint> den = F;
F = fps_pow<mint>(F, K);
F[0] -= 1;
den[0] -= 1;
F = fps_div<mint>(F, den);
FOR(i, L) F[i] *= mint(2).pow(K - 1);
FOR(i, L) F[i] += mint(2) * C<mint>(K, i);
F[0] = 0;
mint n = mint(2).pow(K);
n = n * (n + 1) * inv<mint>(2);
F[1] += n - SUM<mint>(F);
F.erase(F.begin());
print(F);
}
signed main() {
solve();
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 4040kb
input:
2
output:
7 3
result:
ok 2 tokens
Test #2:
score: 0
Accepted
time: 0ms
memory: 3888kb
input:
3
output:
15 14 6 1
result:
ok 4 tokens
Test #3:
score: 0
Accepted
time: 0ms
memory: 3812kb
input:
4
output:
31 43 36 19 6 1
result:
ok 6 tokens
Test #4:
score: 0
Accepted
time: 0ms
memory: 3812kb
input:
5
output:
63 110 132 114 70 30 8 1
result:
ok 8 tokens
Test #5:
score: 0
Accepted
time: 0ms
memory: 3872kb
input:
6
output:
127 255 384 448 400 272 136 47 10 1
result:
ok 10 tokens
Test #6:
score: 0
Accepted
time: 0ms
memory: 4024kb
input:
7
output:
255 558 978 1401 1610 1478 1066 589 240 68 12 1
result:
ok 12 tokens
Test #7:
score: 0
Accepted
time: 0ms
memory: 3900kb
input:
8
output:
511 1179 2292 3803 5250 5987 5576 4183 2482 1137 388 93 14 1
result:
ok 14 tokens
Test #8:
score: 0
Accepted
time: 0ms
memory: 4024kb
input:
9
output:
1023 2438 5088 9398 14896 20038 22632 21250 16406 10282 5144 2006 588 122 16 1
result:
ok 16 tokens
Test #9:
score: 0
Accepted
time: 0ms
memory: 4024kb
input:
10
output:
2047 4975 10896 21772 38360 58724 77184 86312 81448 64324 42112 22576 9744 3304 848 155 18 1
result:
ok 18 tokens
Test #10:
score: 0
Accepted
time: 0ms
memory: 4024kb
input:
11
output:
4095 10070 22782 48209 92140 156292 232068 298744 330926 313422 252186 171122 97008 45368 17200 5155 1176 192 20 1
result:
ok 20 tokens
Test #11:
score: 0
Accepted
time: 111ms
memory: 26868kb
input:
500000
output:
390220183 534638705 182393715 303662724 176884209 76063846 314206329 970463075 138271132 869076105 902568877 121426660 599330372 720576343 535733058 609095360 499854676 427738345 789967637 850801793 767689169 103101879 573005863 597231280 725469375 299015007 178535851 966708332 305629 940093777 7830...
result:
ok 999998 tokens
Test #12:
score: 0
Accepted
time: 18ms
memory: 7552kb
input:
72787
output:
863191949 852718765 363831665 964981186 487891193 263854743 37522806 18985671 265243835 698211861 413341848 452649596 684165069 41891590 781946347 633808644 213891845 90859042 654886506 681500079 853399752 536402628 160278411 189221861 144879826 449123001 395247186 477700669 245829076 740028721 3991...
result:
ok 145572 tokens
Test #13:
score: 0
Accepted
time: 7ms
memory: 5024kb
input:
29621
output:
625188972 186328126 837166229 677006047 662339899 556164288 627678499 464879587 574719635 860749906 37224574 952205162 612486418 67731480 127518779 222659320 311864904 739493528 441208728 656349279 675863661 193365665 871786422 429030382 542544944 65332274 279132780 886986640 23673291 260179258 1458...
result:
ok 59240 tokens
Test #14:
score: 0
Accepted
time: 68ms
memory: 19096kb
input:
287834
output:
839249597 106353691 541743754 176289649 331709790 90695814 581166563 660013633 12148749 777570497 239549256 50822832 928845641 783688014 527134794 967565837 8829067 728890387 532021836 723133136 271356603 442733913 109610442 872231778 997519892 627636901 942495046 612005045 480787271 380535891 31598...
result:
ok 575666 tokens
Test #15:
score: 0
Accepted
time: 84ms
memory: 23968kb
input:
372458
output:
238073678 125575487 257781224 432208434 926232022 985032784 972531646 156874450 242230869 958239072 623209641 963804956 760997596 492384034 248852029 480721426 727545366 871518883 526580215 340703419 119254798 894452847 503218079 466661994 21196998 64609258 607451189 866020376 472431142 833623174 95...
result:
ok 744914 tokens
Test #16:
score: 0
Accepted
time: 75ms
memory: 22936kb
input:
326174
output:
182767154 379158505 976650370 950752234 730142912 199366602 217176449 58415818 942059311 29041812 600728528 238722381 35842882 619426938 166582941 887411034 365366704 226747213 653768421 675658473 198607105 971515601 49241364 300610682 741576498 580333820 788122734 812899883 506754294 906735361 8477...
result:
ok 652346 tokens
Test #17:
score: 0
Accepted
time: 91ms
memory: 23232kb
input:
414785
output:
119371452 447324155 812098442 674259707 906095700 995739643 507821850 144836991 944844465 417859866 526136325 446179637 841143258 71594396 600687837 115917880 869472132 733304409 785178785 942797825 461532099 569481220 498200557 562246854 231360418 806781417 603555993 817444062 8765767 415391941 188...
result:
ok 829568 tokens
Test #18:
score: 0
Accepted
time: 13ms
memory: 5968kb
input:
52410
output:
109025791 520279794 997868526 544815757 1210333 262602454 444694081 215482612 359518123 630972106 469202475 93255040 356550496 552798085 978002390 758808807 872405738 26538225 591804454 180245449 487598812 486435998 100463040 636978431 131160375 54547501 21577758 600993423 54379208 278755072 3851668...
result:
ok 104818 tokens
Test #19:
score: 0
Accepted
time: 58ms
memory: 18492kb
input:
266488
output:
670591955 536664499 834582667 435202901 981715449 216606476 24885754 288060317 473842053 728197980 859018006 359189535 188879878 589394421 415307716 612098332 697672094 255330112 873094951 829240529 612715926 251238400 811393752 657428602 471660768 508314629 890321558 248471292 52873644 528909339 36...
result:
ok 532974 tokens
Test #20:
score: 0
Accepted
time: 49ms
memory: 14532kb
input:
235412
output:
838376130 82261816 749813798 853852768 548463514 590159263 767906723 873538508 681808483 793716931 81414518 387819437 489838184 649414809 971267048 518919507 299233671 402683441 670109161 673246099 315748962 982292160 524024775 990312514 930875705 394644470 79309906 651862394 296416662 949936814 511...
result:
ok 470822 tokens
Test #21:
score: 0
Accepted
time: 77ms
memory: 22344kb
input:
335028
output:
412572542 90575816 592590793 134956941 681546461 84123901 23797401 287575357 580630562 822219941 496015371 798714568 996561274 228437956 38964111 210338108 447304705 455001788 541599590 15999929 531678296 86106708 417035208 77019361 258493500 3295255 609295926 388289340 12082287 479955282 13536114 5...
result:
ok 670054 tokens
Test #22:
score: 0
Accepted
time: 116ms
memory: 26332kb
input:
490193
output:
89108812 9400903 759083927 482137918 881472778 819325246 469847190 224397125 941016878 318853318 823063910 192963094 253539854 195834928 305679610 177655853 744021959 486473727 952943524 80929181 726898580 419500987 86904978 500273473 864375683 752394278 447105311 649043680 568500692 716331790 79426...
result:
ok 980384 tokens
Test #23:
score: 0
Accepted
time: 116ms
memory: 26848kb
input:
494427
output:
224396630 171699844 874970651 366738496 188097388 20105024 923005591 475213547 862579354 219327984 402729610 343802472 824016768 274735056 606982614 720737421 379273500 527635893 326566225 588809571 892479263 956818966 119334763 921549067 728518606 341094293 734579914 96978341 54880988 441706555 375...
result:
ok 988852 tokens
Test #24:
score: 0
Accepted
time: 109ms
memory: 26940kb
input:
495456
output:
176309560 31132799 871206936 191727597 372664218 912078745 128667682 749015357 783582110 969205654 792240671 185634038 963924594 739384852 286035580 546230295 777033259 473035706 331715612 919733935 140740960 188303720 108317267 957369642 570466063 215525809 161735173 289750332 41787886 592639789 24...
result:
ok 990910 tokens
Test #25:
score: 0
Accepted
time: 120ms
memory: 26848kb
input:
499498
output:
10762491 87744479 29345176 330762125 67139471 859322674 517319159 444257903 287766504 323230886 614147692 179153449 789116746 632670050 42290946 845385229 648164696 260416611 791349068 162962424 446055973 201137312 796950696 787484329 797523547 634752612 675290933 712512594 448869911 573190874 93885...
result:
ok 998994 tokens
Test #26:
score: 0
Accepted
time: 111ms
memory: 26592kb
input:
493812
output:
613558532 754129691 624537960 491192546 52587972 335888580 918154485 412643191 632432095 756789608 652622556 498719566 684849283 923391920 735537543 543746954 46908287 213544787 692082087 977892286 329586609 673904401 701415241 768595797 918191698 628376968 628786912 839407278 263562545 942236399 70...
result:
ok 987622 tokens
Extra Test:
score: 0
Extra Test Passed