結果
| 問題 | No.3394 Big Binom |
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2025-12-01 21:44:34 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 8 ms / 2,000 ms |
| コード長 | 36,233 bytes |
| 記録 | |
| コンパイル時間 | 2,248 ms |
| コンパイル使用メモリ | 229,076 KB |
| 実行使用メモリ | 7,848 KB |
| 最終ジャッジ日時 | 2025-12-14 20:01:25 |
| 合計ジャッジ時間 | 3,180 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 22 |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_CYAN = "\033[1;36m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
#include <cassert>
#include <iostream>
#include <set>
#include <vector>
template <int md> struct ModInt {
static_assert(md > 1);
using lint = long long;
constexpr static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val_;
int val() const noexcept { return val_; }
constexpr ModInt() : val_(0) {}
constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
constexpr ModInt(lint v) { _setval(v % md + md); }
constexpr explicit operator bool() const { return val_ != 0; }
constexpr ModInt operator+(const ModInt &x) const {
return ModInt()._setval((lint)val_ + x.val_);
}
constexpr ModInt operator-(const ModInt &x) const {
return ModInt()._setval((lint)val_ - x.val_ + md);
}
constexpr ModInt operator*(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.val_ % md);
}
constexpr ModInt operator/(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.inv().val() % md);
}
constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }
constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
constexpr bool operator<(const ModInt &x) const {
return val_ < x.val_;
} // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
return os << x.val_;
}
constexpr ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static constexpr int cache_limit = std::min(md, 1 << 21);
static std::vector<ModInt> facs, facinvs, invs;
constexpr static void _precalculation(int N) {
const int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
constexpr ModInt inv() const {
if (this->val_ < cache_limit) {
if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val_];
} else {
return this->pow(md - 2);
}
}
constexpr static ModInt fac(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
while (n >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[n];
}
constexpr static ModInt facinv(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
while (n >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[n];
}
constexpr static ModInt doublefac(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
long long k = (n + 1) / 2;
return (n & 1) ? ModInt::fac(k * 2) / (ModInt(2).pow(k) * ModInt::fac(k))
: ModInt::fac(k) * ModInt(2).pow(k);
}
constexpr static ModInt nCr(int n, int r) {
assert(n >= 0);
if (r < 0 or n < r) return ModInt(0);
return ModInt::fac(n) * ModInt::facinv(r) * ModInt::facinv(n - r);
}
constexpr static ModInt nPr(int n, int r) {
assert(n >= 0);
if (r < 0 or n < r) return ModInt(0);
return ModInt::fac(n) * ModInt::facinv(n - r);
}
static ModInt binom(long long n, long long r) {
static long long bruteforce_times = 0;
if (r < 0 or n < r) return ModInt(0);
if (n <= bruteforce_times or n < (int)facs.size()) return ModInt::nCr(n, r);
r = std::min(r, n - r);
assert((int)r == r);
ModInt ret = ModInt::facinv(r);
for (int i = 0; i < r; ++i) ret *= n - i;
bruteforce_times += r;
return ret;
}
// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
// Complexity: O(sum(ks))
// Verify: https://yukicoder.me/problems/no/3178
template <class Vec> static ModInt multinomial(const Vec &ks) {
ModInt ret{1};
int sum = 0;
for (int k : ks) {
assert(k >= 0);
ret *= ModInt::facinv(k), sum += k;
}
return ret * ModInt::fac(sum);
}
template <class... Args> static ModInt multinomial(Args... args) {
int sum = (0 + ... + args);
ModInt result = (1 * ... * ModInt::facinv(args));
return ModInt::fac(sum) * result;
}
// Catalan number, C_n = binom(2n, n) / (n + 1) = # of Dyck words of length 2n
// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
// https://oeis.org/A000108
// Complexity: O(n)
static ModInt catalan(int n) {
if (n < 0) return ModInt(0);
return ModInt::fac(n * 2) * ModInt::facinv(n + 1) * ModInt::facinv(n);
}
ModInt sqrt() const {
if (val_ == 0) return 0;
if (md == 2) return val_;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val_, md - x.val_));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using ModInt998244353 = ModInt<998244353>;
// using mint = ModInt<998244353>;
// using mint = ModInt<1000000007>;
#include <cassert>
#include <fstream>
#include <vector>
// 結合法則が成立する要素の列について連続部分列の積を前計算を利用し高速に求める
template <class S, S (*op)(S, S), S (*e)(), S (*getter)(long long), int Bucket>
struct product_embedding {
std::vector<S> pre_; // pre_[i] = S[i * Bucket] * ... * S[(i + 1) * Bucket - 1]
product_embedding(std::vector<S> pre) : pre_(pre) {}
S prod(long long l, long long r) { // S[l] * ... * S[r - 1]
assert(0 <= l);
assert(l <= r);
assert(r <= (long long)Bucket * (long long)pre_.size());
if (r - l <= Bucket) {
S ret = e();
while (l < r) ret = op(ret, getter(l++));
return ret;
}
long long lb = (l + Bucket - 1) / Bucket, rb = r / Bucket;
S ret = e();
for (long long i = l; i < lb * Bucket; ++i) ret = op(ret, getter(i));
for (int i = lb; i < rb; ++i) ret = op(ret, pre_[i]);
for (long long i = rb * Bucket; i < r; ++i) ret = op(ret, getter(i));
return ret;
}
static void prerun(std::string filename, long long upper_lim) {
std::ofstream ofs(filename);
long long cur = 0;
long long num_bucket = (upper_lim + Bucket - 1) / Bucket;
ofs << "({";
while (num_bucket--) {
S p = e();
for (int t = 0; t < Bucket; ++t) { p = op(p, getter(cur++)); }
ofs << p;
if (num_bucket) ofs << ",";
}
ofs << "});";
}
};
// /* Usage:
using S = int;
constexpr S md = 998244353;
S op(S l, S r) { return (long long)l * r % md; }
S e() { return 1; }
S getter(long long i) { return i + 1 >= md ? (i + 1) % md : i + 1; }
using PE = product_embedding<S, op, e, getter, 500000>;
// int main() {
// PE::prerun("tmp.txt", md); // -> copy & paste the content of dumped file
// }
// */
using mint = ModInt998244353;
int main() {
PE pe({832944090,704684917,615706648,847294252,88352218,907186201,691150420,913840185,615963223,855364605,119871024,260484657,859947701,746803828,757605891,90252390,303168424,458692733,447902118,519044747,337902171,527262360,806954223,278433728,371945574,802657446,33796109,479029221,13074962,263679799,637034850,968665616,191551499,17396452,627009992,772903324,570222470,206900285,819076745,27672112,241549436,692501166,560987504,452030081,798290073,486395423,289596666,373492135,488937237,104582136,702664424,722130811,867669096,953433936,525925834,547831392,810191792,259515457,646462939,87520491,45130800,872439232,854509412,546905493,416913780,370009844,215906029,270663392,633518868,353660403,9557444,137174105,113142527,530062995,558370997,969283332,686746504,389907830,185278447,2425097,216737352,899793077,357571905,270870373,314893045,911840177,444906080,381832665,401470410,692839732,98864994,541679223,616224683,267140709,104124053,511029824,635050637,706453173,285939194,200357740,510478137,185885637,397669445,443607993,554478339,46750669,139176254,538999618,459494109,733260799,617176936,512018697,746780475,667740900,537479303,86146177,662071180,518101865,134794267,754404967,955634140,820294170,889803075,352952586,848590919,563568811,795071441,695639765,262777923,924356134,335545297,709511822,241813913,923488656,693947185,996767921,229966252,669350019,990409291,615776680,665912266,234328009,79764676,457436288,761000715,581509788,882807186,500352747,445576519,424358603,329380611,766526824,392121440,484087487,945403082,661078349,361486608,418779645,2047908,790121293,717319608,181370889,246321649,264130035,593914025,501011429,888792043,726043686,543471483,558121411,25320611,380791470,864178613,322869975,75052465,671375132,934470063,681356552,731820230,540562934,246250337,898548852,501435722,645211462,984306599,603512249,10173564,103142919,483320083,77477420,504125401,871282714,893685842,442026845,172237327,462737473,305280106,236641044,130159734,127411991,450000803,748338626,662543565,468110724,132498639,291021318,545257818,551546108,701726537,313606148,297564719,382416160,67102615,279512928,78638017,448448905,756688280,593997502,312588959,290832776,129707390,624650235,557355897,238261927,121925590,362083384,234875527,425833339,480539233,106030094,172218364,952925093,635704320,635763376,943293808,664757555,535325704,160913233,342146476,610171684,349280028,532241258,647283895,785956119,487557452,875742751,329524131,939160764,470188386,727473676,865816474,153612065,285604631,606994152,96707086,146082330,131276205,694526979,795908785,574669965,68297241,310263879,981026205,682536036,382231137,475872984,295877903,451223167,876264010,708776818,696873077,23468719,6656113,772393476,648660683,452073171,702772465,655566941,660259716,845914532,171812887,170722369,429075375,638795268,129509320,470723034,681826522,61667818,426797734,717004532,416360058,225664875,290024229,918559157,188631059,422932338,759185298,513413011,796306384,267387829,520944657,522529672,489563204,732763088,169165050,917393532,645351691,829660260,34801306,400284161,79943282,940469822,870134687,32915287,179372351,117987380,534980592,472079946,120654283,369256017,12840367,220843777,987347928,531915924,454678057,473647442,908234924,93612215,354346483,244447478,902987399,374480738,391608870,16717414,383590348,562466602,287498834,548484934,223919319,105791239,733705025,653133119,920458406,926100928,541250239,917374201,476441488,876170735,210115868,257550453,88859392,208330688,28766939,559304604,617055733,384236027,920029552,297649547,582781732,162607781,925103418,10535319,494631007,113663680,982682735,28164542,847728321,667610886,341090839,935561939,179913956,177548070,765619720,268917887,747391931,808473081,414391352,396867630,268971031,577589482,844186883,899701547,926976231,742075664,382014807,123049443,78097534,240479098,960060331,597901213,358197202,944743545,794008581,796488938,122198933,532051694,855497454,212107682,550619009,655108052,980800940,322905946,641588402,571533601,240943570,902228965,394730555,880954325,30654933,831081844,365432633,129673244,943766468,243363382,892539880,481048296,299162179,692900032,323398505,996843507,597243714,458077362,191032769,405281429,969138036,931305831,572728483,402096153,376617212,165408216,868339148,748866282,592619490,669915230,613204348,472216681,23106973,308027574,128618720,887545879,377040748,406795107,60356254,374078096,560583986,13507308,37108919,390026819,103131865,893733906,425718096,503242327,546689046,896034414,322730412,830016747,233676778,755669800,333658230,900914110,557355351,659554106,824580104,610352358,842181708,697570971,457633454,859557456,436699936,228365152,487929223,318447092,36520112,676609456,869218838,945078316,358762590,115086076,487078887,105140302,414903418,369303270,723079185,781996045,35010079,332207777,980330188,346113692,875293652,394264892,452282275,683269960,646642323,765688763,496251030,162639942,768347695,76245924,379013965,431439069,740925481,127244598,72274088,159283742,715440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int N, K;
cin >> N >> K;
K = min(K, N - K);
if (N - K < mint::mod() and N >= mint::mod()) {
puts("0");
} else if (K == 0) {
puts("1");
} else {
N %= mint::mod();
cout << mint(pe.prod(N - K, N)) / mint(pe.prod(0, K)) << '\n';
}
}