結果
| 問題 |
No.2763 Macaron Gift Box
|
| コンテスト | |
| ユーザー |
 aplysiaSheep
|
| 提出日時 | 2024-05-17 01:16:34 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 558 ms / 3,000 ms |
| コード長 | 40,087 bytes |
| コンパイル時間 | 7,557 ms |
| コンパイル使用メモリ | 341,804 KB |
| 実行使用メモリ | 12,468 KB |
| 最終ジャッジ日時 | 2024-12-20 11:25:56 |
| 合計ジャッジ時間 | 11,760 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 15 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;
#define int long long
// #define endl "\n"
#ifndef _LOCAL
#pragma GCC optimize("-O3")
// #pragma GCC target("avx2")
// #pragma GCC optimize("unroll-loops")
#endif
void solve();
typedef long long ll;
typedef __int128_t LL;
typedef unsigned long long ull;
typedef double db;
typedef long double ld;
typedef pair<int, int> pi;
typedef pair<int, pair<int, int>> pip;
typedef vector<int> vi;
typedef vector<double> vd;
typedef vector<bool> vb;
typedef vector<string> vs;
typedef vector<char> vc;
typedef vector<pair<int, int>> vp;
typedef vector<vector<int>> vvi;
typedef vector<vector<double>> vvd;
typedef vector<vector<bool>> vvb;
typedef vector<vector<string>> vvs;
typedef vector<vector<char>> vvc;
typedef vector<vector<pair<int, int>>> vvp;
typedef vector<vector<vector<int>>> vvvi;
typedef vector<vector<vector<vector<int>>>> vvvvi;
template <typename T>
using vec = vector<T>;
template <typename T>
using vv = vector<vector<T>>;
template <typename T>
using vvv = vector<vector<vector<T>>>;
template <typename T>
using vvvv = vector<vector<vector<vector<T>>>>;
template <typename T>
using pq = priority_queue<T>;
template <typename T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using mset = multiset<T>;
template <typename T>
using uset = unordered_set<T>;
template <typename T, typename U>
using umap = unordered_map<T, U>;
#define _PI 3.14159265358979323846
#define _E 2.7182818284590452354
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define bg begin()
#define ed end()
#define mt make_tuple
#define td typedef
#define elif else if
#define ifnot(x) if(!(x))
#define si(x) (int)((x).size())
#define all(obj) (obj).begin(), (obj).end()
#define rall(obj) (obj).rbegin(), (obj).rend()
#define lb(v, a) (lower_bound(begin(v), end(v), a) - begin(v))
#define ub(v, a) (upper_bound(begin(v), end(v), a) - begin(v))
#define inr(l, x, r) (l <= x && x < r)
#define cbit(x) __builtin_popcountll(x)
#define tbit(t) (t == 0 ? -1 : 63 - __builtin_clzll(t))
#define bbit(t) (t == 0 ? 64 : __builtin_ctzll(t))
#define gb(msk, i) ((msk) >> (i) & 1)
#define mask(x) ((1LL << (x)) - 1)
#define setbits(i, n) \
for(int j_ = (n), i = bbit(j_); j_; j_ ^= 1LL << i, i = bbit(j_))
#define rep1(a) \
for(int NEVER_USE_VARIABLE = 0; NEVER_USE_VARIABLE < (int)a; \
NEVER_USE_VARIABLE++)
#define rep2(i, a) for(int i = 0; i < (int)a; i++)
#define rep3(i, a, b) for(int i = a; i < (int)b; i++)
#define rep4(i, a, b, c) for(int i = a; i < (int)b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for(ll NEVER_USE_VARIABLE = n; NEVER_USE_VARIABLE--;)
#define rrep2(i, n) for(ll i = n; i--;)
#define rrep3(i, a, b) for(ll i = b; i-- > (a);)
#define rrep4(i, a, b, c) \
for(ll i = (a) + ((b) - (a) - 1) / (c) * (c); i >= (a); i -= c)
#define rrep(...) \
overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define reps(i, a) for(int i = 0; i < (int)a.size(); i++)
#define rreps(i, a) for(int i = (int)a.size() - 1; i >= 0; i--)
#define fore1(i, a) for(auto &&i : a)
#define fore2(x, y, a) for(auto &&[x, y] : a)
#define fore3(x, y, z, a) for(auto &&[x, y, z] : a)
#define fore(...) overload4(__VA_ARGS__, fore3, fore2, fore1)(__VA_ARGS__)
#define ryes return yes();
#define rno return no();
#define rerr return err();
istream &operator>>(istream &is, modint998244353 &a) {
long long v;
is >> v;
a = v;
return is;
}
ostream &operator<<(ostream &os, const modint998244353 &a) {
return os << a.val();
}
istream &operator>>(istream &is, modint1000000007 &a) {
long long v;
is >> v;
a = v;
return is;
}
ostream &operator<<(ostream &os, const modint1000000007 &a) {
return os << a.val();
}
// 十進数からb進数へ
template <class T>
string to_baseB(T x, int b = 10) {
string ans;
do {
int num = x % b;
ans = (char)((num <= 9) ? ('0' + num) : ('A' + num - 10)) + ans;
x /= b;
} while(x != 0);
return ans;
}
// b進数から十進数へ
long long to_base10(const string &x, int b = 10) {
long long ans = 0, base = 1;
for(int i = x.length() - 1; i >= 0; --i) {
int num =
('0' <= x[i] && x[i] <= '9') ? (x[i] - '0') : (x[i] - 'A' + 10);
ans += base * num;
base *= b;
}
return ans;
}
ostream &operator<<(ostream &s, const __int128_t &p) {
s << to_baseB(p);
return s;
}
istream &operator>>(istream &is, __int128_t &v) {
string s;
is >> s;
v = 0;
for(int i = 0; i < (int)s.size(); i++) {
if(isdigit(s[i])) {
v = v * 10 + s[i] - '0';
}
}
if(s[0] == '-') {
v *= -1;
}
return is;
}
template <class T, class U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << "," << p.second;
return os;
}
template <class T>
ostream &operator<<(ostream &s, set<T> P) {
fore(it, P) {
s << it << " ";
}
return s;
}
template <class T1, class T2>
ostream &operator<<(ostream &s, map<T1, T2> P) {
fore(x, y, P) {
s << "<" << x << "->" << y << "> ";
}
return s;
}
template <class T>
ostream &operator<<(ostream &s, multiset<T> P) {
fore(it, P) {
s << it << " ";
}
return s;
}
template <class T>
ostream &operator<<(ostream &s, unordered_set<T> P) {
fore(it, P) {
s << it << " ";
}
return s;
}
template <class T1, class T2>
ostream &operator<<(ostream &s, unordered_map<T1, T2> P) {
fore(x, y, P) {
s << "<" << x << "->" << y << "> ";
}
return s;
}
template <class T>
istream &operator>>(istream &is, vector<T> &v) {
for(auto &e : v) is >> e;
return is;
}
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for(auto &e : v) os << e << ' ';
return os;
}
template <class T>
ostream &operator<<(ostream &os, const vector<vector<T>> &v) {
for(auto &e : v) {
for(auto &c : e) os << c << ' ';
os << endl;
}
return os;
}
template <class t, size_t n>
ostream &operator<<(ostream &os, const array<t, n> &a) {
return os << vector<t>(all(a));
}
template <int i, class T>
void print_tuple(ostream &, const T &) {}
template <int i, class T, class H, class... Args>
void print_tuple(ostream &os, const T &t) {
if(i) os << ",";
os << get<i>(t);
print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
print_tuple<0, tuple<Args...>, Args...>(os, t);
return os;
}
template <class T>
ostream &operator<<(ostream &os, queue<T> q) {
while(!q.empty()) {
os << q.front() << ' ';
q.pop();
}
return os;
}
template <class T>
ostream &operator<<(ostream &os, stack<T> q) {
while(!q.empty()) {
os << q.top() << ' ';
q.pop();
}
return os;
}
template <class T>
ostream &operator<<(ostream &os, deque<T> q) {
while(!q.empty()) {
os << q.front() << ' ';
q.pop_front();
}
return os;
}
template <class T>
ostream &operator<<(ostream &os, priority_queue<T> q) {
while(!q.empty()) {
os << q.top() << ' ';
q.pop();
}
return os;
}
template <class T>
ostream &operator<<(ostream &os, priority_queue<T, vector<T>, greater<T>> q) {
while(!q.empty()) {
os << q.top() << ' ';
q.pop();
}
return os;
}
template <class T>
vector<T> &operator++(vector<T> &v) {
for(auto &e : v) e++;
return v;
}
template <class T>
vector<T> operator++(vector<T> &v, signed) {
auto res = v;
for(auto &e : v) e++;
return res;
}
template <class T>
vector<T> &operator--(vector<T> &v) {
for(auto &e : v) e--;
return v;
}
template <class T>
vector<T> operator--(vector<T> &v, signed) {
auto res = v;
for(auto &e : v) e--;
return res;
}
template <class T, class U>
pair<T, U> &operator+=(pair<T, U> &a, pair<T, U> b) {
a.first += b.first;
a.second += b.second;
return a;
}
template <class T, class U>
pair<T, U> &operator-=(pair<T, U> &a, pair<T, U> b) {
a.first -= b.first;
a.second -= b.second;
return a;
}
template <class T, class U>
pair<T, U> operator+(pair<T, U> a, pair<T, U> b) {
return make_pair(a.first + b.first, a.second + b.second);
}
template <class T, class U>
pair<T, U> operator-(pair<T, U> a, pair<T, U> b) {
return make_pair(a.first - b.first, a.second - b.second);
}
// debug methods
// usage: debug(x,y);
#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0, a1, a2, a3, a4, x, ...) x
#define debug_1(x1) cout << #x1 << ": " << x1 << endl
#define debug_2(x1, x2) \
cout << #x1 << ": " << x1 << ", " #x2 << ": " << x2 << endl
#define debug_3(x1, x2, x3) \
cout << #x1 << ": " << x1 << ", " #x2 << ": " << x2 << ", " #x3 << ": " \
<< x3 << endl
#define debug_4(x1, x2, x3, x4) \
cout << #x1 << ": " << x1 << ", " #x2 << ": " << x2 << ", " #x3 << ": " \
<< x3 << ", " #x4 << ": " << x4 << endl
#define debug_5(x1, x2, x3, x4, x5) \
cout << #x1 << ": " << x1 << ", " #x2 << ": " << x2 << ", " #x3 << ": " \
<< x3 << ", " #x4 << ": " << x4 << ", " #x5 << ": " << x5 << endl
#ifdef _DEBUG
#define debug(...) \
CHOOSE((__VA_ARGS__, debug_5, debug_4, debug_3, debug_2, debug_1, ~)) \
(__VA_ARGS__)
#else
#define debug(...)
#endif
void out() {
cout << endl;
}
template <class T>
void out(const T &a) {
cout << a;
cout << endl;
}
template <class T, class... Ts>
void out(const T &a, const Ts &...b) {
cout << a;
(cout << ... << (cout << ' ', b));
cout << endl;
}
void ofs_in(ostream &ofs) {
ofs << endl;
}
template <class T>
void ofs_in(ostream &ofs, const T &a) {
ofs << a;
ofs << endl;
}
template <class T, class... Ts>
void ofs_in(ostream &ofs, const T &a, const Ts &...b) {
ofs << a;
(ofs << ... << (ofs << ' ', b));
ofs << endl;
}
#define rout_1(x1) return out(x1)
#define rout_2(x1, x2) return out(x1, x2)
#define rout_3(x1, x2, x3) return out(x1, x2, x3)
#define rout_4(x1, x2, x3, x4) return out(x1, x2, x3, x4)
#define rout_5(x1, x2, x3, x4, x5) return out(x1, x2, x3, x4, x5)
#define rout(...) \
CHOOSE((__VA_ARGS__, rout_5, rout_4, rout_3, rout_2, rout_1, ~)) \
(__VA_ARGS__)
struct fast_ios {
fast_ios() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(12);
};
} fast_ios_;
template <class T = long long>
struct Binomial {
int p;
int MAX;
vector<long long> fac, finv, inv;
// テーブルを作る前処理
Binomial(int p_, int n = 1) : p(p_), MAX(1), fac(2), finv(2), inv(2) {
fac[0] = fac[1] = 1;
finv[0] = finv[1] = 1;
inv[1] = 1;
if(n != 1) build(n);
}
void build(int new_max) {
MAX++;
fac.resize(new_max + 1);
inv.resize(new_max + 1);
finv.resize(new_max + 1);
for(; MAX <= new_max; MAX++) {
fac[MAX] = fac[MAX - 1] * MAX % p;
inv[MAX] = p - inv[p % MAX] * (p / MAX) % p;
finv[MAX] = finv[MAX - 1] * inv[MAX] % p;
}
MAX--;
}
// nCk
T mod_comb(int n, int k) {
if(n < k) return 0;
if(n < 0 || k < 0) return 0;
if(n > MAX) build(n);
return fac[n] * (finv[k] * finv[n - k] % p) % p;
}
T operator()(int n, int k) {
return mod_comb(n, k);
}
// nPk
T mod_perm(int n, int k) {
if(n < k) return 0;
if(n < 0 || k < 0) return 0;
if(n > MAX) build(n);
return fac[n] * finv[n - k] % p;
}
// n!
T operator[](int n) {
if(n > MAX) build(n);
return fac[n];
}
// 1/n!
T operator()(int n) {
if(n > MAX) build(n);
return finv[n];
}
};
template <typename T = long long>
struct modpow {
long long x, m;
int n;
vector<T> d;
modpow(long long x) : x(x), n(1), d(1, 1) {}
T operator[](int i) {
while(n <= i) d.push_back(d.back() * x), ++n;
return d[i];
}
};
modpow two(2), ten(10);
/*
座標圧縮
https://youtu.be/fR3W5IcBGLQ?t=8550
を参考に
(T x):xが何番目か
[T i]:i番目の値
*/
template <typename T = int>
struct CC {
bool initialized;
vector<T> xs;
CC() : initialized(false) {}
CC(vector<T> v) : initialized(false) {
for(auto x : v) xs.push_back(x);
}
void add(T x) {
xs.push_back(x);
}
void add(vector<T> v) {
for(auto x : v) xs.push_back(x);
}
void init() {
sort(xs.begin(), xs.end());
xs.erase(unique(xs.begin(), xs.end()), xs.end());
initialized = true;
}
int operator()(T x) {
if(!initialized) init();
return upper_bound(xs.begin(), xs.end(), x) - xs.begin() - 1;
}
T operator[](int i) {
if(!initialized) init();
return xs[i];
}
int size() {
if(!initialized) init();
return xs.size();
}
friend ostream &operator<<(ostream &os, const CC &cc) {
for(int i = 0; i < (int)cc.xs.size(); i++) {
os << cc.xs[i] << " ";
}
os << endl;
return (os);
}
};
struct RandomNumberGenerator {
mt19937 engine;
RandomNumberGenerator(int seed = -1) {
if(seed == -1)
engine =
mt19937(chrono::steady_clock::now().time_since_epoch().count());
else
engine = mt19937(seed);
}
long long operator()(long long a, long long b) { // [a, b)
uniform_int_distribution<long long> dist(a, b - 1);
return dist(engine);
}
long long operator()(long long b) { // [0, b)
return (*this)(0, b);
}
long long operator()() {
return (*this)(0, 1LL << 60);
}
double operator[](double a) {
return (double)(*this)(0, 1LL << 60) / (1LL << 60) * a;
}
double normal_dist(double sigma, double mean = 0) {
std::normal_distribution<> dist(mean, sigma);
return dist(engine);
}
} rnd;
clock_t start_time = clock();
double now_time() {
clock_t end_time = clock();
return (double)(end_time - start_time) / CLOCKS_PER_SEC;
}
template <class T = int, size_t n, size_t idx = 0>
auto mv(const size_t (&d)[n], const T &init) noexcept {
if constexpr(idx < n)
return std::vector(d[idx], mv<T, n, idx + 1>(d, init));
else
return init;
}
template <class T = int, size_t n>
auto mv(const size_t (&d)[n]) noexcept {
return mv(d, T{});
}
template <class T>
void rnd_shuffle(vector<T> &v) {
shuffle(v.begin(), v.end(), rnd.engine);
}
template <class T>
T sample(T v, int n) {
T res;
sample(v.begin(), v.end(), back_inserter(res), n, rnd.engine);
return res;
}
template <class F>
long long bin_search(long long ok, long long ng, const F &f) {
while(abs(ok - ng) > 1) {
long long mid = (ok + ng) >> 1;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
template <class T, class F>
T bin_search_double(T ok, T ng, const F &f, int iter = 90) {
while(iter--) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
void read_edges(vector<vector<int>> &g, int m = -1, int bidirected = true) {
if(m == -1) m = g.size() - 1;
for(int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
u--;
v--;
g[u].push_back(v);
if(bidirected) g[v].push_back(u);
}
}
vector<int> counter(vector<int> &v, int mx = -1) {
if(mx == -1) mx = *max_element(v.begin(), v.end());
vector<int> res(mx + 1);
for(auto x : v) res[x]++;
return res;
}
template <class T = int, class U = vector<T>>
map<T, int> map_counter(U &v) {
map<T, int> res;
for(auto x : v) res[x]++;
return res;
}
vector<int> iota(int n, int s = 0) {
vi a(n);
iota(a.begin(), a.end(), s);
return a;
}
template <class T>
void sort(T &v) {
sort(all(v));
}
template <class T>
void rsort(T &v) {
sort(rall(v));
}
template <class T>
void reverse(T &v) {
reverse(all(v));
}
template <class T>
auto max(const T &a) {
return *max_element(a.begin(), a.end());
}
template <class T>
auto min(const T &a) {
return *min_element(a.begin(), a.end());
}
template <class T>
int argmax(const T &a) {
return max_element(a.begin(), a.end()) - a.begin();
}
template <class T>
int argmin(const T &a) {
return min_element(a.begin(), a.end()) - a.begin();
}
long long max(signed x, long long y) {
return max((long long)x, y);
}
long long max(long long x, signed y) {
return max(x, (long long)y);
}
long long min(signed x, long long y) {
return min((long long)x, y);
}
long long min(long long x, signed y) {
return min(x, (long long)y);
}
template <class T, class S>
bool chmax(T &a, const S &b) {
if(a < (T)b) {
a = (T)b;
return 1;
}
return 0;
}
template <class T, class S>
bool chmin(T &a, const S &b) {
if((T)b < a) {
a = (T)b;
return 1;
}
return 0;
}
template <class T>
vector<int> argsort(vector<T> v, bool ascending_order = true) {
vector<int> res(v.size());
iota(res.begin(), res.end(), 0);
if(ascending_order)
sort(res.begin(), res.end(), [&](int i, int j) { return v[i] < v[j]; });
else
sort(res.begin(), res.end(), [&](int i, int j) { return v[i] > v[j]; });
return res;
}
template <class T>
T sumv(vector<T> &v) {
T res = 0;
int n = v.size();
for(int i = 0; i < n; i++) res += v[i];
return res;
}
template <class T>
vector<T> uniq(vector<T> v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
return v;
}
template <class T>
vector<T> compress(vector<T> v) {
vector<T> v2(v.size());
v2 = v;
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
for(int i = 0; i < (int)v2.size(); i++) {
v2[i] = lower_bound(v.begin(), v.end(), v2[i]) - v.begin();
}
return v2;
}
vector<int> inverse(vector<int> &p) {
int n = p.size();
vector<int> inv(n);
for(int i = 0; i < n; i++) inv[p[i]] = i;
return inv;
}
template <typename T>
vector<pair<T, int>> idx_pair(vector<T> &a) {
int n = a.size();
vector<pair<T, int>> res(n);
for(int i = 0; i < n; i++) res[i] = {a[i], i};
return res;
}
template <typename T>
vector<T> acc0(vector<T> &v) {
vector<T> res(v.size());
if((int)v.size() == 0) return res;
res[0] = v[0];
for(int i = 1; i < (int)v.size(); i++) {
res[i] = res[i - 1] + v[i];
}
return res;
}
template <typename T>
vector<T> acc1(vector<T> &v) {
vector<T> res(v.size() + 1);
for(int i = 0; i < (int)v.size(); i++) {
res[i + 1] = res[i] + v[i];
}
return res;
}
template <typename T>
vector<vector<T>> acc0(vector<vector<T>> v) {
int h = v.size(), w = v[0].size();
for(int i = 0; i < h; i++) {
for(int j = 1; j < w; j++) {
v[i][j] += v[i][j - 1];
}
}
for(int i = 1; i < h; i++) {
for(int j = 0; j < w; j++) {
v[i][j] += v[i - 1][j];
}
}
return v;
}
template <typename T>
vector<vector<T>> acc1(vector<vector<T>> &v) {
int h = v.size(), w = v[0].size();
vector<vector<T>> res(h + 1, vector<T>(w + 1));
for(int i = 0; i < h; i++) {
for(int j = 0; j < w; j++) {
res[i + 1][j + 1] = v[i][j] + res[i + 1][j];
}
}
for(int i = 0; i < h; i++) {
for(int j = 0; j < w; j++) {
res[i + 1][j + 1] += res[i][j + 1];
}
}
return res;
}
template <class T>
void erase1(multiset<T> &st, int x) {
auto it = st.find(x);
assert(it != st.end());
st.erase(it);
}
long long exp(long long x, int n) {
long long res = 1;
while(n > 0) {
if(n & 1) res = res * x;
x = x * x;
n >>= 1;
}
return res;
}
__int128_t absl(const __int128_t &x) {
return x > 0 ? x : -x;
}
bool ispow2(int i) {
return i && (i & -i) == i;
}
int countDigits(long long n) {
string tmp = to_string(n);
return (int)tmp.size();
}
template <class T>
T sq(T n) {
return n * n;
}
long long ceil(long long x, long long y) {
return (x + y - 1) / y;
}
long long floor(long long x, long long y) {
return (y < 0 ? floor(-x, -y)
: (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1)));
}
constexpr long long tri(long long n) {
return n * (n + 1) / 2;
}
// l + ... + r
constexpr long long tri(long long l, long long r) {
return (l + r) * (r - l + 1) / 2;
}
template <typename T>
T modulo(T n, T d) {
return (n % d + d) % d;
}
int ctoi(const char &c, const char start = '0') {
return c - start;
}
int atoi(const char &c, const char start = 'a') {
return c - start;
}
vector<int> ctoi(string &s, const char start = '0') {
vector<int> res;
for(auto &c : s) {
int x = c - start;
if(x < 0 || x >= 10) x = -1;
res.push_back(x);
}
return res;
}
vector<int> atoi(string &s, const char start = 'a') {
vector<int> res;
for(auto &c : s) {
int x = c - start;
if(x < 0 || x >= 26) x = -1;
res.push_back(x);
}
return res;
}
vector<vector<int>> ctoi(vector<string> &s, const char start = '0') {
int n = s.size();
vector<vector<int>> res(n);
for(int i = 0; i < n; i++) res[i] = ctoi(s[i], start);
return res;
}
vector<vector<int>> atoi(vector<string> &s, const char start = 'a') {
int n = s.size();
vector<vector<int>> res(n);
for(int i = 0; i < n; i++) res[i] = atoi(s[i], start);
return res;
}
string itoc(vector<int> &v, const char start = '0') {
int n = v.size();
string res;
for(int i = 0; i < n; i++) {
res.push_back(start + v[i]);
}
return res;
}
string itoa(vector<int> &v, const char start = 'a') {
return itoc(v, start);
}
vector<string> itoc(vector<vector<int>> &v, const char start = '0') {
int n = v.size();
vector<string> res(n);
for(int i = 0; i < n; i++) {
int m = v[i].size();
for(int j = 0; j < m; j++) {
res[i] = itoc(v[i], start);
}
}
return res;
}
vector<string> itoa(vector<vector<int>> &v, const char start = 'a') {
return itoc(v, start);
}
template <class T>
int mex(T &a) {
int n = a.size();
vector<int> cnt(n + 1);
for(auto x : a) {
if(x > n) continue;
cnt[x]++;
}
int res = 0;
while(cnt[res]) res++;
return res;
}
void yes() {
cout << "Yes" << endl;
// cout << "Alice" << endl;
// cout << "Takahashi" << endl;
}
void no() {
cout << "No" << endl;
// cout << "Bob" << endl;
// cout << "Aoki" << endl;
}
void yesno(bool x) {
if(x)
yes();
else
no();
}
void err() {
cout << -1 << endl;
}
int dx[] = {1, 0, -1, 0, 1, 1, -1, -1};
int dy[] = {0, 1, 0, -1, -1, 1, 1, -1};
long long inf = (1 << 30) + (1LL << 60) - 2;
double eps = 1e-9;
// long long mod = 67280421310721;
// using mint = static_modint<1000000009>;
// using mint = dynamic_modint<1000000009>;
// long long mod = 1000000007;
// using mint = modint1000000007;
long long mod = 998244353;
using mint = modint998244353;
typedef vector<mint> vm;
typedef vector<vector<mint>> vvm;
typedef vector<vector<vector<mint>>> vvvm;
// Binomial<mint> C(mod);
// modpow<mint> mtwo(2), mten(10);
////////////////////////////////////////////////////////////////////////////////////////////
/*
https:opt-cp.com/fps-implementation/
https:judge.yosupo.jp/submission/42413
を参考に
以下、d:サイズdにresizeする
+,-,*,/,>>,<<
inv(d):逆数
multiply(g,d):gをconvolution
divide(g,d):gで割る
eval(a):f(a)
log(d):log(f)
exp(d):exp(f)
pow(k,d):f^k
MOD = 998244353（NTT-friendry）の時はfastが使える。
MOD =1000000007などの他の時は使えないので、
define fastをコメントアウトして、その下のnaiveを使う。
（*fpsや/fpsに関わる部分。）
*/
#define fast
#define rep_(i, a_, b_, a, b, ...) \
for(int i = (a), lim##i = (b); i < lim##i; ++i)
#define rep2_(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define drep_(i, a_, b_, a, b, ...) \
for(int i = (a) - 1, lim##i = (b); i >= lim##i; --i)
#define drep(i, ...) drep_(i, __VA_ARGS__, __VA_ARGS__, __VA_ARGS__, 0)
template <typename T>
struct Factorial {
int MAX;
vector<T> fac, finv;
Factorial(int m = 0) : MAX(m), fac(m + 1, 1), finv(m + 1, 1) {
rep2_(i, 2, MAX + 1) fac[i] = fac[i - 1] * i;
finv[MAX] /= fac[MAX];
drep(i, MAX + 1, 3) finv[i - 1] = finv[i] * i;
}
T binom(int n, int k) {
if(k < 0 || n < k) return 0;
return fac[n] * finv[k] * finv[n - k];
}
T perm(int n, int k) {
if(k < 0 || n < k) return 0;
return fac[n] * finv[n - k];
}
};
Factorial<mint> fc;
template <class T>
struct FormalPowerSeries : vector<T> {
using vector<T>::vector;
using vector<T>::operator=;
using F = FormalPowerSeries;
F operator-() const {
F res(*this);
for(auto &e : res) e = -e;
return res;
}
F &operator*=(const T &g) {
for(auto &e : *this) e *= g;
return *this;
}
F &operator/=(const T &g) {
assert(g != T(0));
*this *= g.inv();
return *this;
}
F &operator+=(const F &g) {
int n = this->size(), m = g.size();
rep2_(i, min(n, m))(*this)[i] += g[i];
return *this;
}
F &operator-=(const F &g) {
int n = this->size(), m = g.size();
rep2_(i, min(n, m))(*this)[i] -= g[i];
return *this;
}
F &operator<<=(const int d) {
int n = this->size();
if(d >= n) *this = F(n);
this->insert(this->begin(), d, 0);
this->resize(n);
return *this;
}
F &operator>>=(const int d) {
int n = this->size();
this->erase(this->begin(), this->begin() + min(n, d));
this->resize(n);
return *this;
}
// O(n log n)
F inv(int d = -1) const {
int n = this->size();
assert(n != 0 && (*this)[0] != 0);
if(d == -1) d = n;
assert(d >= 0);
F res{(*this)[0].inv()};
for(int m = 1; m < d; m *= 2) {
F f(this->begin(), this->begin() + min(n, 2 * m));
F g(res);
f.resize(2 * m), internal::butterfly(f);
g.resize(2 * m), internal::butterfly(g);
rep2_(i, 2 * m) f[i] *= g[i];
internal::butterfly_inv(f);
f.erase(f.begin(), f.begin() + m);
f.resize(2 * m), internal::butterfly(f);
rep2_(i, 2 * m) f[i] *= g[i];
internal::butterfly_inv(f);
T iz = T(2 * m).inv();
iz *= -iz;
rep2_(i, m) f[i] *= iz;
res.insert(res.end(), f.begin(), f.begin() + m);
}
res.resize(d);
return res;
}
#ifdef fast
// fast: FMT-friendly modulus only
// O(n log n)
F &multiply_inplace(const F &g, int d = -1) {
int n = this->size();
if(d == -1) d = n;
assert(d >= 0);
*this = convolution(move(*this), g);
this->resize(d);
return *this;
}
F multiply(const F &g, const int d = -1) const {
return F(*this).multiply_inplace(g, d);
}
F &operator*=(const F &g) {
int n = this->size();
*this = convolution(move(*this), g);
this->resize(n);
return *this;
}
// O(n log n)
F ÷_inplace(const F &g, int d = -1) {
int n = this->size();
if(d == -1) d = n;
assert(d >= 0);
*this = convolution(move(*this), g.inv(d));
this->resize(d);
return *this;
}
F divide(const F &g, const int d = -1) const {
return F(*this).divide_inplace(g, d);
}
F &operator/=(const F &g) {
int n = (*this).size();
*this = convolution(*this, g.inv(n));
(*this).resize(n);
return *this;
}
#else
// naive
// // O(n^2)
F &multiply_inplace(const F &g) {
int n = this->size(), m = g.size();
drep(i, n) {
(*this)[i] *= g[0];
rep2_(j, 1, min(i + 1, m))(*this)[i] += (*this)[i - j] * g[j];
}
return *this;
}
F multiply(const F &g) const {
return F(*this).multiply_inplace(g);
}
// O(n^2)
F ÷_inplace(const F &g) {
assert(g[0] != T(0));
T ig0 = g[0].inv();
int n = this->size(), m = g.size();
rep(i, n) {
rep2_(j, 1, min(i + 1, m))(*this)[i] -= (*this)[i - j] * g[j];
(*this)[i] *= ig0;
}
return *this;
}
F divide(const F &g) const {
return F(*this).divide_inplace(g);
}
F &operator*=(const F &g) {
int n = (*this).size(), m = g.size();
drep(i, n) {
(*this)[i] *= g[0];
rep2_(j, 1, min(i + 1, m))(*this)[i] += (*this)[i - j] * g[j];
}
return *this;
}
F &operator/=(const F &g) {
assert(g[0] != T(0));
T ig0 = g[0].inv();
int n = (*this).size(), m = g.size();
rep(i, n) {
rep2_(j, 1, min(i + 1, m))(*this)[i] -= (*this)[i - j] * g[j];
(*this)[i] *= ig0;
}
return *this;
}
#endif
// sparse
// O(nk)
F &multiply_inplace(vector<pair<int, T>> g) {
int n = this->size();
auto [d, c] = g.front();
if(d == 0)
g.erase(g.begin());
else
c = 0;
drep(i, n) {
(*this)[i] *= c;
for(auto &[j, b] : g) {
if(j > i) break;
(*this)[i] += (*this)[i - j] * b;
}
}
return *this;
}
F multiply(const vector<pair<int, T>> &g) const {
return F(*this).multiply_inplace(g);
}
F &operator*=(vector<pair<int, T>> g) {
int n = (*this).size();
auto [d, c] = g.front();
if(d == 0)
g.erase(g.begin());
else
c = 0;
drep(i, n) {
(*this)[i] *= c;
for(auto &[j, b] : g) {
if(j > i) break;
(*this)[i] += (*this)[i - j] * b;
}
}
return *this;
}
// O(nk)
F ÷_inplace(vector<pair<int, T>> g) {
int n = this->size();
auto [d, c] = g.front();
assert(d == 0 && c != T(0));
T ic = c.inv();
g.erase(g.begin());
rep2_(i, n) {
for(auto &[j, b] : g) {
if(j > i) break;
(*this)[i] -= (*this)[i - j] * b;
}
(*this)[i] *= ic;
}
return *this;
}
F divide(const vector<pair<int, T>> &g) const {
return F(*this).divide_inplace(g);
}
F &operator/=(vector<pair<int, T>> g) {
int n = (*this).size();
auto [d, c] = g.front();
assert(d == 0 && c != T(0));
T ic = c.inv();
g.erase(g.begin());
rep2_(i, n) {
for(auto &[j, b] : g) {
if(j > i) break;
(*this)[i] -= (*this)[i - j] * b;
}
(*this)[i] *= ic;
}
return *this;
}
// multiply and divide (1 + cz^d)
// O(n)
void multiply_inplace(const int d, const T c) {
int n = this->size();
if(c == T(1))
drep(i, n - d)(*this)[i + d] += (*this)[i];
else if(c == T(-1))
drep(i, n - d)(*this)[i + d] -= (*this)[i];
else
drep(i, n - d)(*this)[i + d] += (*this)[i] * c;
}
// O(n)
void divide_inplace(const int d, const T c) {
int n = this->size();
if(c == T(1))
rep2_(i, n - d)(*this)[i + d] -= (*this)[i];
else if(c == T(-1))
rep2_(i, n - d)(*this)[i + d] += (*this)[i];
else
rep2_(i, n - d)(*this)[i + d] -= (*this)[i] * c;
}
// O(n)
T eval(const T &a) const {
T x(1), res(0);
for(auto e : *this) res += e * x, x *= a;
return res;
}
// O(n)
F &integral_inplace() {
int n = this->size();
assert(n > 0);
if(n == 1) return *this = F{0};
this->insert(this->begin(), 0);
this->pop_back();
vector<T> inv(n);
inv[1] = 1;
int p = T::mod();
rep2_(i, 2, n) inv[i] = -inv[p % i] * (p / i);
rep2_(i, 2, n)(*this)[i] *= inv[i];
return *this;
}
F integral() const {
return F(*this).integral_inplace();
}
// O(n)
F &derivative_inplace() {
int n = this->size();
assert(n > 0);
rep2_(i, 2, n)(*this)[i] *= i;
this->erase(this->begin());
this->push_back(0);
return *this;
}
F derivative() const {
return F(*this).derivative_inplace();
}
// O(n log n)
F &log_inplace(int d = -1) {
int n = this->size();
assert(n > 0 && (*this)[0] == 1);
if(d == -1) d = n;
assert(d >= 0);
if(d < n) this->resize(d);
F f_inv = this->inv();
this->derivative_inplace();
this->multiply_inplace(f_inv);
this->integral_inplace();
return *this;
}
F log(const int d = -1) const {
return F(*this).log_inplace(d);
}
// O(n log n)
// https://arxiv.org/abs/1301.5804 (Figure 1, right)
F &exp_inplace(int d = -1) {
int n = this->size();
assert(n > 0 && (*this)[0] == 0);
if(d == -1) d = n;
assert(d >= 0);
F g{1}, g_fft{1, 1};
(*this)[0] = 1;
this->resize(d);
F h_drv(this->derivative());
for(int m = 2; m < d; m *= 2) {
// prepare
F f_fft(this->begin(), this->begin() + m);
f_fft.resize(2 * m), internal::butterfly(f_fft);
// Step 2.a'
{
F _g(m);
rep2_(i, m) _g[i] = f_fft[i] * g_fft[i];
internal::butterfly_inv(_g);
_g.erase(_g.begin(), _g.begin() + m / 2);
_g.resize(m), internal::butterfly(_g);
rep2_(i, m) _g[i] *= g_fft[i];
internal::butterfly_inv(_g);
_g.resize(m / 2);
_g /= T(-m) * m;
g.insert(g.end(), _g.begin(), _g.begin() + m / 2);
}
// Step 2.b'--d'
F t(this->begin(), this->begin() + m);
t.derivative_inplace();
{
// Step 2.b'
F r{h_drv.begin(), h_drv.begin() + m - 1};
// Step 2.c'
r.resize(m);
internal::butterfly(r);
rep2_(i, m) r[i] *= f_fft[i];
internal::butterfly_inv(r);
r /= -m;
// Step 2.d'
t += r;
t.insert(t.begin(), t.back());
t.pop_back();
}
// Step 2.e'
if(2 * m < d) {
t.resize(2 * m);
internal::butterfly(t);
g_fft = g;
g_fft.resize(2 * m);
internal::butterfly(g_fft);
rep2_(i, 2 * m) t[i] *= g_fft[i];
internal::butterfly_inv(t);
t.resize(m);
t /= 2 * m;
} else { // この場合分けをしても数パーセントしか速くならない
F g1(g.begin() + m / 2, g.end());
F s1(t.begin() + m / 2, t.end());
t.resize(m / 2);
g1.resize(m), internal::butterfly(g1);
t.resize(m), internal::butterfly(t);
s1.resize(m), internal::butterfly(s1);
rep2_(i, m) s1[i] = g_fft[i] * s1[i] + g1[i] * t[i];
rep2_(i, m) t[i] *= g_fft[i];
internal::butterfly_inv(t);
internal::butterfly_inv(s1);
rep2_(i, m / 2) t[i + m / 2] += s1[i];
t /= m;
}
// Step 2.f'
F v(this->begin() + m, this->begin() + min<int>(d, 2 * m));
v.resize(m);
t.insert(t.begin(), m - 1, 0);
t.push_back(0);
t.integral_inplace();
rep2_(i, m) v[i] -= t[m + i];
// Step 2.g'
v.resize(2 * m);
internal::butterfly(v);
rep2_(i, 2 * m) v[i] *= f_fft[i];
internal::butterfly_inv(v);
v.resize(m);
v /= 2 * m;
// Step 2.h'
rep2_(i, min(d - m, m))(*this)[m + i] = v[i];
}
return *this;
}
F exp(const int d = -1) const {
return F(*this).exp_inplace(d);
}
// O(n log n)
F &pow_inplace(const ll k, int d = -1) {
int n = this->size();
if(d == -1) d = n;
assert(d >= 0 && k >= 0);
if(d == 0) return *this = F(0);
if(k == 0) {
*this = F(d);
(*this)[0] = 1;
return *this;
}
int l = 0;
while(l < n && (*this)[l] == 0) ++l;
if(l == n || l > (d - 1) / k) return *this = F(d);
T c{(*this)[l]};
this->erase(this->begin(), this->begin() + l);
*this /= c;
this->log_inplace(d - l * k);
*this *= k;
this->exp_inplace();
*this *= c.pow(k);
this->insert(this->begin(), l * k, 0);
return *this;
}
F pow(const ll k, const int d = -1) const {
return F(*this).pow_inplace(k, d);
}
// O(n log n)
F &shift_inplace(const T c) {
int n = this->size();
fc = Factorial<T>(n);
rep2_(i, n)(*this)[i] *= fc.fac[i];
reverse(this->begin(), this->end());
F g(n);
T cp = 1;
rep2_(i, n) g[i] = cp * fc.finv[i], cp *= c;
this->multiply_inplace(g, n);
reverse(this->begin(), this->end());
rep2_(i, n)(*this)[i] *= fc.finv[i];
return *this;
}
F shift(const T c) const {
return F(*this).shift_inplace(c);
}
F operator*(const T &g) const {
return F(*this) *= g;
}
F operator/(const T &g) const {
return F(*this) /= g;
}
F operator+(const F &g) const {
return F(*this) += g;
}
F operator-(const F &g) const {
return F(*this) -= g;
}
F operator<<(const int d) const {
return F(*this) <<= d;
}
F operator>>(const int d) const {
return F(*this) >>= d;
}
F operator*(const F &g) const {
return F(*this) *= g;
}
F operator/(const F &g) const {
return F(*this) /= g;
}
F operator*(vector<pair<int, T>> g) const {
return F(*this) *= g;
}
F operator/(vector<pair<int, T>> g) const {
return F(*this) /= g;
}
};
using fps = FormalPowerSeries<mint>;
using sfps = vector<pair<int, mint>>;
////////////////////////////////////////////////////////////////////////////////////////////
signed main() {
int testcase = 1;
// cin >> testcase;
for(int i = 0; i < testcase; i++) {
solve();
}
debug(now_time());
}
void solve() {
int n, k;
cin >> n >> k;
fps f(n + 1);
rep(i, 1, n + 1) {
rep(k, 1, n + 1) {
if(k * i > n) break;
f[k * i] -= mint{1} / k;
}
}
f = f.exp(n + 1);
debug(f);
fps g(n + 1);
rep(i, n) {
if(i * (k + 1) > n) break;
g[i * (k + 1)] = f[i];
}
f = g / f;
vm ans(n);
rep(i, 1, n + 1) ans[i - 1] = f[i];
out(ans);
}