結果
| 問題 | No.3394 Big Binom |
| コンテスト | |
| ユーザー |
 Nachia
|
| 提出日時 | 2025-12-01 00:20:45 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 128 ms / 2,000 ms |
| コード長 | 26,333 bytes |
| 記録 | |
| コンパイル時間 | 1,755 ms |
| コンパイル使用メモリ | 111,748 KB |
| 実行使用メモリ | 7,848 KB |
| 最終ジャッジ日時 | 2025-12-14 19:57:48 |
| 合計ジャッジ時間 | 3,779 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / 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
#ifdef NACHIA
//#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;
using ll = long long;
const ll INF = 1ll << 60;
#define REP(i,n) for(ll i=0; i<ll(n); i++)
template <class T> using V = vector<T>;
template <class A, class B> void chmax(A& l, const B& r){ if(l < r) l = r; }
template <class A, class B> void chmin(A& l, const B& r){ if(r < l) l = r; }
#include <cassert>
namespace nachia{
template<unsigned int MOD>
struct PrimitiveRoot{
using u64 = unsigned long long;
static constexpr u64 powm(u64 a, u64 i) {
u64 res = 1, aa = a;
for( ; i; i /= 2){
if(i & 1) res = res * aa % MOD;
aa = aa * aa % MOD;
}
return res;
}
static constexpr bool ExamineVal(unsigned int g){
u64 t = MOD - 1;
for(u64 d=2; d*d<=t; d+=1+(d&1)) if(t % d == 0){
if(powm(g, (MOD - 1) / d) == 1) return false;
while(t % d == 0) t /= d;
}
if(t != 1) if(powm(g, (MOD - 1) / t) == 1) return false;
return true;
}
static constexpr unsigned int GetVal(){
for(u64 x=2; x<MOD; x++) if(ExamineVal(x)) return x;
return 0;
}
static const unsigned int val = GetVal();
};
} // namespace nachia
namespace nachia{
template<class Modint>
class Comb{
private:
std::vector<Modint> F;
std::vector<Modint> iF;
public:
void extend(int newN){
int prevN = (int)F.size() - 1;
if(prevN >= newN) return;
F.resize(newN+1);
iF.resize(newN+1);
for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i);
iF[newN] = F[newN].inv();
for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i);
}
Comb(int n = 1){
F.assign(2, Modint(1));
iF.assign(2, Modint(1));
extend(n);
}
Modint factorial(int n) const { return F[n]; }
Modint invFactorial(int n) const { return iF[n]; }
Modint invOf(int n) const { return iF[n] * F[n-1]; }
Modint comb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[r] * iF[n-r];
}
Modint invComb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[r] * F[n-r];
}
Modint perm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[n-r];
}
Modint invPerm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[n-r];
}
Modint operator()(int n, int r) const { return comb(n,r); }
Modint parityToSign(long long x) const {
return Modint(x%2 == 0 ? 1 : -1);
}
};
} // namespace nachia
namespace nachia{
int Popcount(unsigned long long c) noexcept {
#ifdef __GNUC__
return __builtin_popcountll(c);
#else
c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
c = (c * (~0ull/257)) >> 56;
return c;
#endif
}
// please ensure x != 0
int MsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
return 63 - __builtin_clzll(x);
#else
using u64 = unsigned long long;
int q = (x >> 32) ? 32 : 0;
auto m = x >> q;
constexpr u64 hi = 0x88888888;
constexpr u64 mi = 0x11111111;
m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35;
m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 31;
q += (m & 0xf) << 2;
q += 0x3333333322221100 >> (((x >> q) & 0xf) << 2) & 0xf;
return q;
#endif
}
// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
return __builtin_ctzll(x);
#else
return MsbIndex(x & -x);
#endif
}
}
namespace nachia {
template<class mint>
struct NttInterface{
template<class Iter>
void Butterfly(Iter, int) const {}
template<class Iter>
void IButterfly(Iter, int) const {}
template<class Iter>
void BitReversal(Iter a, int N) const {
for(int i=0, j=0; j<N; j++){
if(i < j) std::swap(a[i], a[j]);
for(int k = N>>1; k > (i^=k); k>>=1);
}
}
};
} // namespace nachia
#include <iterator>
#include <array>
namespace nachia{
template <class mint>
struct Ntt : NttInterface<mint> {
using u32 = unsigned int;
using u64 = unsigned long long;
static int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (u32)(n)) x++;
return x;
}
static constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
struct fft_info {
static constexpr u32 g = nachia::PrimitiveRoot<mint::mod()>::val;
static constexpr int rank2 = bsf_constexpr(mint::mod()-1);
using RootTable = std::array<mint, rank2+1>;
RootTable root, iroot, rate3, irate3;
fft_info(){
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for(int i=rank2-1; i>=0; i--){
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<=rank2-3; i++){
rate3[i] = root[i+3] * prod;
irate3[i] = iroot[i+3] * iprod;
prod *= iroot[i+3];
iprod *= root[i+3];
}
}
};
template<class RandomAccessIterator>
void ButterflyLayered(RandomAccessIterator a, int n, int stride, int repeat) const {
static const fft_info info;
int h = n * stride;
while(repeat--){
int len = 1;
int p = h;
if(ceil_pow2(n)%2 == 1){
p >>= 1;
for(int i=0; i<p; i++){
mint l = a[i], r = a[i+p];
a[i] = l+r; a[i+p] = l-r;
}
len <<= 1;
}
for( ; p > stride; ){
p >>= 2;
mint rot = 1, imag = info.root[2];
u64 mod2 = u64(mint::mod()) * mint::mod();
int offset = p;
for(int s=0; s<len; s++){
if(s) rot *= info.rate3[LsbIndex(~(u32)(s-1))];
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
for(int i=offset-p; i<offset; i++){
u64 a0 = u64(a[i].val());
u64 a1 = u64(a[i+p].val()) * rot.val();
u64 a2 = u64(a[i+2*p].val()) * rot2.val();
u64 a3 = u64(a[i+3*p].val()) * rot3.val();
u64 a1na3imag = u64(mint(a1 + mod2 - a3).val()) * imag.val();
u64 na2 = mod2 - a2;
a[i] = a0 + a2 + a1 + a3;
a[i+1*p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i+2*p] = a0 + na2 + a1na3imag;
a[i+3*p] = a0 + na2 + (mod2 - a1na3imag);
}
offset += p << 2;
}
len <<= 2;
}
a += h;
}
}
template<class RandomAccessIterator>
void Butterfly(RandomAccessIterator a, int n) const {
ButterflyLayered(a, n, 1, 1);
}
template<class RandomAccessIterator>
void IButterflyLayered(RandomAccessIterator a, int n, int stride, int repeat) const {
static const fft_info info;
constexpr int MOD = mint::mod();
while(repeat--){
int len = n;
int p = stride;
for( ; 2 < len; ){
len >>= 2;
mint irot = 1, iimag = info.iroot[2];
int offset = p;
for(int s=0; s<len; s++){
if(s) irot *= info.irate3[LsbIndex(~(u32)(s-1))];
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
for(int i=offset-p; i<offset; i++){
u64 a0 = a[i].val();
u64 a1 = a[i+p].val();
u64 a2 = a[i+2*p].val();
u64 a3 = a[i+3*p].val();
u64 a2na3iimag = mint((a2 + MOD - a3) * iimag.val()).val();
a[i] = a0 + a1 + a2 + a3;
a[i+p] = (a0 + (MOD - a1) + a2na3iimag) * irot.val();
a[i+2*p] = (a0 + a1 + (MOD - a2) + (MOD - a3)) * irot2.val();
a[i+3*p] = (a0 + (MOD - a1) + (MOD - a2na3iimag)) * irot3.val();
}
offset += p << 2;
}
p <<= 2;
}
if(len == 2){
for(int i=0; i<p; i++){
mint l = a[i], r = a[i+p];
a[i] = l+r; a[i+p] = l-r;
}
p <<= 1;
}
a += p;
}
}
template<class RandomAccessIterator>
void IButterfly(RandomAccessIterator a, int n) const {
IButterflyLayered(a, n, 1, 1);
}
};
} // namespace nachia
namespace nachia {
template<class Elem, class NttInst = Ntt<Elem>>
struct FpsNtt {
public:
using Fps = FpsNtt;
using ElemTy = Elem;
static constexpr unsigned int MOD = Elem::mod();
static constexpr int CONV_THRES = 30;
static const NttInst nttInst;
static const unsigned int zeta = nachia::PrimitiveRoot<MOD>::GetVal();
private:
using u32 = unsigned int;
static Elem ZeroElem() noexcept { return Elem(0); }
static Elem OneElem() noexcept { return Elem(1); }
static Comb<Elem> comb;
std::vector<Elem> a;
int RSZ(int& sz) const { return sz = (sz < 0 ? size() : sz); }
public:
void push_back(Elem e){ a.push_back(e); }
int size() const noexcept { return a.size(); }
Elem& operator[](int x) noexcept { return a[x]; }
const Elem& operator[](int x) const noexcept { return a[x]; }
Elem getCoeff(int x) const noexcept { return (0 <= x && x < size()) ? a[x] : ZeroElem(); }
static Comb<Elem>& GetComb() { return comb; }
static int BestNttSize(int x) noexcept { assert(x); return 1 << MsbIndex(x*2-1); }
Fps move(){ return std::move(*this); }
Fps& set(int i, Elem c){ a[i] = c; return *this; }
Fps& removeLeadingZeros(){
int newsz = size();
while(newsz && a[newsz-1].val() == 0) newsz--;
a.resize(newsz);
if((int)a.capacity() / 4 > newsz) a.shrink_to_fit();
return *this;
}
FpsNtt(){}
FpsNtt(int sz) : a(sz, ZeroElem()) {}
FpsNtt(int sz, Elem e) : a(sz, e) {}
FpsNtt(std::vector<Elem>&& src) : a(std::move(src)) {}
FpsNtt(const std::vector<Elem>& src) : a(src) {}
Fps& ntt() {
capSize(BestNttSize(size()));
nttInst.Butterfly(a.begin(), size());
return *this;
}
Fps& intt() {
nttInst.IButterfly(a.begin(), a.size());
return times(Elem::raw(size()).inv());
}
Fps nttDouble(Fps vanilla) const {
int n = size();
assert(n != 0 && n == (n&-n)); // n is a power of 2
Elem q = Elem::raw(zeta).pow((Elem::mod() - 1) / (n*2));
Elem qq = OneElem();
for(int i=0; i<n; i++){ vanilla[i] *= qq; qq *= q; }
vanilla.ntt();
Fps res = clip(0, n*2);
for(int i=0; i<n; i++) res[n+i] = vanilla[i];
return res;
}
Fps nttDouble() const { return nttDouble(clip().intt().move()); }
// Fps res(resSz);
// for(int j=0; j<resSz-destL && j+srcL < srcR; j++) res[j+destL] = a.getCoeff(j+srcL)
// if srcR is unspecified -> srcR = max(srcL, size());
// if resSz is unspecified -> resSz = destL + srcR - srcL
Fps clip(int srcL, int srcR = -1, int destL = 0, int resSz = -1) const {
srcR = std::max(srcL, RSZ(srcR));
if(resSz < 0) resSz = destL + srcR - srcL;
int rj = std::min(std::min(srcR, size()) - srcL, resSz - destL);
Fps res(resSz);
for(int j=std::max(0, -srcL); j<rj; j++) res[j+destL] = a[j+srcL];
return res;
}
Fps clip() const { return *this; }
Fps& capSize(int l, int r) {
if(r <= (int)size()) a.resize(r);
if(size() <= l) a.resize(l, ZeroElem());
return *this;
}
Fps& capSize(int z){ a.resize(RSZ(z), ZeroElem()); return *this; }
Fps& times(Elem x){ for(int i=0; i<size(); i++){ a[i] *= x; } return *this; }
Fps& timesFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.factorial(i); } return *this; }
Fps& timesInvFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.invFactorial(i); } return *this; }
Fps& clrRange(int l, int r){ for(int i=l; i<r; i++){ a[i] = ZeroElem(); } return *this; }
Fps& negate(){ for(auto& e : a){ e = -e; } return *this; }
Fps& mulEach(const Fps& other, int maxi = -1){
maxi = std::min(RSZ(maxi), std::min(size(), other.size()));
for(int i=0; i<maxi; i++) a[i] *= other[i];
return *this;
}
Fps& reverse(int sz = -1){ RSZ(sz); std::reverse(a.begin(), a.begin() + sz); return *this; }
Fps& revRange(int l, int r = -1){ RSZ(r); std::reverse(a.begin() + l, a.begin() + r); return *this; }
static Fps convolution(const Fps& a, const Fps& b, int sz = -1){
if(std::min(a.size(), b.size()) <= CONV_THRES){
if(a.size() > b.size()) return convolution(b, a, sz);
if(sz < 0) sz = std::max(0, a.size() + b.size() - 1);
std::vector<Elem> res(sz);
for(int i=0; i<a.size(); i++) for(int j=0; j<b.size() && i+j<sz; j++) res[i+j] += a[i] * b[j];
return res;
}
int Z = BestNttSize(a.size() + b.size() - 1);
return a.clip(0, Z).ntt().mulEach(b.clip(0, Z).ntt()).intt().capSize(sz).move();
}
Fps convolve(const Fps& r, int sz = -1) const { return convolution(*this, r, sz); }
// 1
// ----- = 1 + f + f^2 + f^3 + ...
// 1-f
Fps powerSum(int sz) const {
RSZ(sz);
if(sz == 0) return {};
int q = std::min(sz, 32);
Fps x = Fps(q).set(0, OneElem()).move();
for(int i=1; i<q; i++) for(int j=1; j<=std::min(i,(int)a.size()-1); j++) x[i] += x[i-j] * a[j];
while(x.size() < sz){
int hN = x.size(), N = hN*2;
Fps a = x.clip(0, N).ntt().move();
Fps b = clip(0, N).ntt().mulEach(a).intt().clrRange(0,hN).ntt().mulEach(a).intt().move();
for(int i=0; i<hN; i++) b[i] = x[i];
std::swap(b, x);
}
return x.capSize(sz).move();
}
Fps inv(int sz = -1) const {
RSZ(sz);
Elem iA0 = a[0].inv();
return clip(0, std::min(sz, size())).times(-iA0).set(0, ZeroElem()).powerSum(sz).times(iA0).move();
}
Fps& difference(){
if(size() == 0) return *this;
for(int i=0; i+1<size(); i++) a[i] = a[i+1] * Elem::raw(i+1);
return capSize(size()-1);
}
Fps& integral(){
if(size() == 0) return capSize(1);
capSize(size()+1);
comb.extend(size());
for(int i=size()-1; i>=1; i--) a[i] = a[i-1] * comb.invOf(i);
return set(0, ZeroElem());
}
Fps log(int sz = -1){
RSZ(sz);
assert(sz != 0);
assert(a[0].val() == 1);
return convolution(inv(sz), clip().difference(), sz-1).integral();
}
Fps exp(int sz = -1){
RSZ(sz);
Fps res = Fps(1).set(0, OneElem());
while(res.size() < sz){
auto z = res.size();
auto tmp = res.capSize(z*2).log().set(0, -OneElem()).move();
for(int i=0; i<z*2 && i<size(); i++) tmp[i] -= a[i];
auto resntt = res.clip().ntt().mulEach(tmp.ntt()).intt().move();
for(int i=z; i<z*2; i++) res[i] = -resntt[i];
}
return res.capSize(0, sz).move();
}
Fps pow(unsigned long long k, int sz = -1){
int n = RSZ(sz);
if(k == 0) return Fps(n).set(0, OneElem()).move();
int ctz = 0;
while(ctz<n && a[ctz].val() == 0) ctz++;
if((unsigned long long)ctz >= (n-1) / k + 1) return Fps(n);
Elem a0 = a[ctz];
return clip(ctz, ctz+n-ctz*k).times(a0.inv()).log().times(Elem(k)).exp().times(a0.pow(k)).clip(0, -1, ctz*k);
}
auto begin(){ return a.begin(); }
auto end(){ return a.end(); }
auto begin() const { return a.begin(); }
auto end() const { return a.end(); }
std::string toString(std::string beg = "[ ", std::string delim = " ", std::string en = " ]") const {
std::string res = beg;
bool f = false;
for(auto x : a){ if(f){ res += delim; } f = true; res += std::to_string(x.val()); }
res += en;
return res;
}
std::vector<Elem> getVectorMoved(){ return std::move(a); }
std::vector<Elem> get() const { return a; }
Fps& operator+=(const Fps& r){
capSize(std::max(size(), r.size()));
for(int i=0; i<r.size(); i++) a[i] += r[i];
return *this;
}
Fps& operator-=(const Fps& r){
capSize(std::max(size(), r.size()));
for(int i=0; i<r.size(); i++) a[i] -= r[i];
return *this;
}
Fps operator+(const Fps& r) const { return (clip(0, std::max(size(), r.size())) += r).move(); }
Fps operator-(const Fps& r) const { return (clip(0, std::max(size(), r.size())) -= r).move(); }
Fps operator-() const { return (clip().negate()).move(); }
Fps operator*(const Fps& r) const { return convolve(r).removeLeadingZeros().move(); }
Fps& operator*=(const Fps& r){ return (*this) = operator*(r); }
Fps& operator*=(Elem m){ return times(m); }
Fps operator*(Elem m) const { return (clip() *= m).move(); }
Elem eval(Elem x) const {
Elem res = 0;
for(int i=size()-1; i>=0; i--) res = res * x + a[i];
return res;
}
};
template<class Elem, class NttInst> Comb<Elem> FpsNtt<Elem, NttInst>::comb;
template<class Elem, class NttInst> const NttInst FpsNtt<Elem, NttInst>::nttInst;
} // namespace nachia
#include <utility>
namespace nachia{
template<class Elem>
struct MatrixOnRing{
private:
int h;
int w;
std::vector<Elem> elems;
public:
MatrixOnRing(int new_h=0, int new_w=0){ h = new_h; w = new_w; elems.resize(h * w); }
MatrixOnRing(MatrixOnRing const&) = default;
int numRow() const { return h; }
int numColumn() const { return w; }
int height() const { return numRow(); }
int width() const { return numColumn(); }
typename std::vector<Elem>::iterator operator[](int y){ return elems.begin() + (y*w); }
typename std::vector<Elem>::const_iterator operator[](int y) const { return elems.begin() + (y*w); }
static MatrixOnRing Identity(int idx, Elem One){ auto res = MatrixOnRing(idx, idx); for(int i=0; i<idx; i++) res[i][i] = One; return res; }
void swapColumns(int x1, int x2){
assert(0 <= x1 && x1 < numColumn());
assert(0 <= x2 && x2 < numColumn());
if(x1 == x2) return;
for(int y=0; y<numRow(); y++) std::swap((*this)[y][x1], (*this)[y][x2]);
}
void swapRows(int y1, int y2){
assert(0 <= y1 && y1 < numRow());
assert(0 <= y2 && y2 < numRow());
if(y1 == y2) return;
for(int x=0; x<numColumn(); x++) std::swap((*this)[y1][x], (*this)[y2][x]);
}
MatrixOnRing operator*(const MatrixOnRing& r) const {
assert(width() == r.height());
auto res = MatrixOnRing(h, r.w);
for(int i=0; i<h; i++) for(int j=0; j<w; j++) for(int k=0; k<r.w; k++) res[i][k] = res[i][k] + (*this)[i][j] * r[j][k];
return res;
}
MatrixOnRing pow(unsigned long long i){
if(i == 1) return *this;
auto a = *this;
auto res = a; i--;
while(i){
if(i % 2 == 1) res = res * a;
a = a * a;
i /= 2;
}
return res;
}
};
} // namespace nachia
namespace nachia{
template<class Elem>
MatrixOnRing<Elem> PRecursiveMatrixProduct(
MatrixOnRing<FpsNtt<Elem>> p,
unsigned long long idx
){
struct PolynomialSamplingPointsShiftUpdate{
using Fps = FpsNtt<Elem>;
int n;
int N2;
Fps iF, F, iFI, iFIntt1, iFntt;
std::vector<Fps> iFIntt2s;
PolynomialSamplingPointsShiftUpdate(int n, std::vector<Elem> sh){
auto& comb = Fps::GetComb();
comb.extend(n);
this->n = n;
N2 = Fps::BestNttSize(n*2);
iF = F = iFI = Fps(n);
for(int i=0; i<n; i++) F[i] = comb.factorial(i);
for(int i=0; i<n; i++) iF[i] = comb.invFactorial(i);
for(int i=0; i<n; i++) iFI[i] = (i%2) ? -iF[i] : iF[i];
iFIntt1 = iFI.clip(0, N2); iFIntt1.ntt();
iFntt = iF.clip(0, N2); iFntt.ntt();
for(size_t shi=0; shi<sh.size(); shi++){
Elem q = 1;
Fps T(N2); T[0] = Elem(1);
for(int i=1; i<n; i++) T[i] = iF[i] * (q *= (sh[shi] - Elem::raw(i-1)));
iFIntt2s.push_back(T.ntt().move());
}
}
std::vector<std::vector<Elem>> calc(const std::vector<Elem>& points){
Fps P(N2);
for(int i=0; i<n; i++) P[i] = points[i] * iF[i];
P.ntt().mulEach(iFIntt1).intt().clrRange(n, N2).mulEach(F, n).reverse().ntt();
std::vector<std::vector<Elem>> res2(iFIntt2s.size());
for(size_t shi=0; shi<iFIntt2s.size(); shi++){
res2[shi] = P.clip().mulEach(iFIntt2s[shi]).intt()
.reverse().clrRange(n, N2).mulEach(iF, n).ntt()
.mulEach(iFntt).intt().mulEach(F, n).clip(0, n).getVectorMoved();
}
return res2;
}
};
using u64 = unsigned long long;
int h = p.height();
std::vector<std::vector<Elem>> res;
res.resize(h*h);
for(auto& a : res) a.resize(h);
u64 a = 1, b = 1;
for(int i=0; i<h; i++) for(int j=0; j<h; j++) while(b < (u64)p[i][j].size()) b <<= 1;
u64 maxA = 1, maxB = b;
while(maxA * maxB <= idx){ maxB <<= 1; maxA <<= 1; }
for(int i=0; i<h; i++) for(int j=0; j<h; j++){
res[i*h+j].resize(b);
for(u64 k=0; k<b; k++) res[i*h+j][k] = p[i][j].eval(Elem(maxA) * Elem(k));
}
auto EvalP = [p, h](Elem val) -> MatrixOnRing<Elem> {
MatrixOnRing<Elem> res(h, h);
for(int y=0; y<h; y++) for(int x=0; x<h; x++) res[y][x] = p[y][x].eval(val);
return res;
};
auto EvalL = [&res, h](u64 idx) -> MatrixOnRing<Elem> {
MatrixOnRing<Elem> g(h, h);
for(int y=0; y<h; y++) for(int x=0; x<h; x++) g[y][x] = res[y*h+x][idx];
return g;
};
while(b < maxB){
std::vector<Elem> sh(3);
sh[0] = Elem(b);
sh[1] = Elem(a) / Elem(maxA);
sh[2] = sh[0] + sh[1];
std::vector<std::vector<std::vector<Elem>>> shbuf(h*h);
auto shman = PolynomialSamplingPointsShiftUpdate(b, sh);
for(int i=0; i<h*h; i++) shbuf[i] = shman.calc(res[i]);
std::vector<std::vector<Elem>> resbuf;
resbuf.assign(h*h, std::vector<Elem>(b*2));
for(int i=0; i<h; i++) for(int j=0; j<h; j++) for(int k=0; k<h; k++){
auto Lbeg1 = shbuf[i*h+j][1].begin();
auto Rbeg1 = res[j*h+k].begin();
auto destbeg1 = resbuf[i*h+k].begin();
for(u64 id=0; id<b; id++) destbeg1[id] += Lbeg1[id] * Rbeg1[id];
auto Lbeg2 = shbuf[i*h+j][2].begin();
auto Rbeg2 = shbuf[j*h+k][0].begin();
auto destbeg2 = resbuf[i*h+k].begin() + b;
for(u64 id=0; id<b; id++) destbeg2[id] += Lbeg2[id] * Rbeg2[id];
}
std::swap(res, resbuf);
a *= 2;
b *= 2;
}
u64 pos = 0;
MatrixOnRing<Elem> ans = MatrixOnRing<Elem>::Identity(h, Elem::raw(1));
while(pos + maxA <= idx){ ans = EvalL(pos / maxA) * ans; pos += maxA; }
while(pos < idx){ ans = EvalP(pos++) * ans; }
return ans;
}
} // namespace nachia
namespace nachia{
template<class Modint>
Modint Factorial(long long N){
using Fps = nachia::FpsNtt<Modint>;
using Matrix = nachia::MatrixOnRing<Fps>;
Matrix A(1,1);
A[0][0] = Fps(2).set(1,Modint(1)).set(0,Modint(1));
auto ans = nachia::PRecursiveMatrixProduct(A, N);
return ans[0][0];
}
}
namespace nachia{
// ax + by = gcd(a,b)
// return ( x, - )
std::pair<long long, long long> ExtGcd(long long a, long long b){
long long x = 1, y = 0;
while(b){
long long u = a / b;
std::swap(a-=b*u, b);
std::swap(x-=y*u, y);
}
return std::make_pair(x, a);
}
} // namespace nachia
namespace nachia{
template<unsigned int MOD>
struct StaticModint{
private:
using u64 = unsigned long long;
unsigned int x;
public:
using my_type = StaticModint;
template< class Elem >
static Elem safe_mod(Elem x){
if(x < 0){
if(0 <= x+MOD) return x + MOD;
return MOD - ((-(x+MOD)-1) % MOD + 1);
}
return x % MOD;
}
StaticModint() : x(0){}
StaticModint(const my_type& a) : x(a.x){}
StaticModint& operator=(const my_type&) = default;
template< class Elem >
StaticModint(Elem v) : x(safe_mod(v)){}
unsigned int operator*() const { return x; }
my_type& operator+=(const my_type& r) { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
my_type operator+(const my_type& r) const { my_type res = *this; return res += r; }
my_type& operator-=(const my_type& r) { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
my_type operator-(const my_type& r) const { my_type res = *this; return res -= r; }
my_type operator-() const noexcept { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; }
my_type& operator*=(const my_type& r){ x = (u64)x * r.x % MOD; return *this; }
my_type operator*(const my_type& r) const { my_type res = *this; return res *= r; }
bool operator==(const my_type& r) const { return x == r.x; }
my_type pow(unsigned long long i) const {
my_type a = *this, res = 1;
while(i){ if(i & 1){ res *= a; } a *= a; i >>= 1; }
return res;
}
my_type inv() const { return my_type(ExtGcd(x, MOD).first); }
unsigned int val() const { return x; }
int hval() const { return int(x > MOD/2 ? x - MOD : x); }
static constexpr unsigned int mod() { return MOD; }
static my_type raw(unsigned int val) { auto res = my_type(); res.x = val; return res; }
my_type& operator/=(const my_type& r){ return operator*=(r.inv()); }
my_type operator/(const my_type& r) const { return operator*(r.inv()); }
};
} // namespace nachia
using Mint = nachia::StaticModint<998244353>;
void testcase(){
ll N, K; cin >> N >> K;
Mint ans = 1;
while(N > 0 && K > 0){
ll n = Mint(N).val();
ll k = Mint(K).val();
if(n < k) ans = 0;
else {
ans *= nachia::Factorial<Mint>(n);
ans /= nachia::Factorial<Mint>(k);
ans /= nachia::Factorial<Mint>(n-k);
}
N /= Mint::mod();
K /= Mint::mod();
}
cout << ans.val() << "\n";
}
int main(){
cin.tie(0)->sync_with_stdio(0);
testcase();
return 0;
}