結果
| 問題 |
No.2839 AND Constraint
|
| コンテスト | |
| ユーザー |
 t9unkubj
|
| 提出日時 | 2024-08-20 16:44:01 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 37 ms / 2,000 ms |
| コード長 | 20,686 bytes |
| コンパイル時間 | 4,638 ms |
| コンパイル使用メモリ | 278,992 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-08-20 16:44:07 |
| 合計ジャッジ時間 | 5,833 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 16 |
コンパイルメッセージ
main.cpp:156:9: warning: #pragma once in main file
156 | #pragma once
| ^~~~
ソースコード
#ifdef t9unkubj
#include"template.h"
//#include"template_no_debug.h"
#else
#undef _GLIBCXX_DEBUG
#pragma GCC optimize("O3")
#define dbg(...) 199958
using namespace std;
#include<bits/stdc++.h>
using uint=unsigned;
using ll=long long;
using ull=unsigned long long;
using ld=long double;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
template<class T>using vc=vector<T>;
template<class T>using vvc=vc<vc<T>>;
template<class T>using vvvc=vvc<vc<T>>;
using vi=vc<int>;
using vvi=vc<vi>;
using vvvi=vc<vvi>;
using vl=vc<ll>;
using vvl=vc<vl>;
using vvvl=vc<vvl>;
template<class T>using smpq=priority_queue<T,vector<T>,greater<T>>;
template<class T>using bipq=priority_queue<T>;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define REP(i,j,n) for(ll i=(j);i<(ll)(n);i++)
#define DREP(i,n,m) for(ll i=(n);i>=(m);i--)
#define drep(i,n) for(ll i=((n)-1);i>=0;i--)
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define is insert
#define bg begin()
#define ed end()
void scan(int&a) { cin >> a; }
void scan(ll&a) { cin >> a; }
void scan(string&a) { cin >> a; }
void scan(char&a) { cin >> a; }
void scan(uint&a) { cin >> a; }
void scan(ull&a) { cin >> a; }
void scan(bool&a) { cin >> a; }
void scan(ld&a){ cin>> a;}
template<class T> void scan(vector<T>&a) { for(auto&x:a) scan(x); }
void read() {}
template<class Head, class... Tail> void read(Head&head, Tail&... tail) { scan(head); read(tail...); }
#define INT(...) int __VA_ARGS__; read(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; read(__VA_ARGS__);
#define ULL(...) ull __VA_ARGS__; read(__VA_ARGS__);
#define STR(...) string __VA_ARGS__; read(__VA_ARGS__);
#define CHR(...) char __VA_ARGS__; read(__VA_ARGS__);
#define DBL(...) double __VA_ARGS__; read(__VA_ARGS__);
#define LD(...) ld __VA_ARGS__; read(__VA_ARGS__);
#define VC(type, name, ...) vector<type> name(__VA_ARGS__); read(name);
#define VVC(type, name, size, ...) vector<vector<type>> name(size, vector<type>(__VA_ARGS__)); read(name);
void print(int a) { cout << a; }
void print(ll a) { cout << a; }
void print(string a) { cout << a; }
void print(char a) { cout << a; }
void print(uint a) { cout << a; }
void print(bool a) { cout << a; }
void print(ull a) { cout << a; }
void print(double a) { cout << a; }
void print(ld a){ cout<< a; }
template<class T> void print(vector<T>a) { for(int i=0;i<(int)a.size();i++){if(i)cout<<" ";print(a[i]);}cout<<endl;}
void PRT() { cout <<endl; return ; }
template<class T> void PRT(T a) { print(a); cout <<endl; return; }
template<class Head, class... Tail> void PRT(Head head, Tail ... tail) { print(head); cout << " "; PRT(tail...); return; }
template<class T,class F>
bool chmin(T &x, F y){
if(x>y){
x=y;
return true;
}
return false;
}
template<class T, class F>
bool chmax(T &x, F y){
if(x<y){
x=y;
return true;
}
return false;
}
void YesNo(bool b){
cout<<(b?"Yes":"No")<<endl;
}
void Yes(){
cout<<"Yes"<<endl;
}
void No(){
cout<<"No"<<endl;
}
template<class T>
int popcount(T n){
return __builtin_popcountll(n);
}
template<class T>
T sum(vc<T>&a){
return accumulate(all(a),T(0));
}
template<class T>
T max(vc<T>&a){
return *max_element(all(a));
}
template<class T>
T min(vc<T>&a){
return *min_element(all(a));
}
template<class T>
void unique(vc<T>&a){
a.erase(unique(all(a)),a.end());
}
vvi readgraph(int n,int m,int off = -1){
vvi g(n);
rep(i, m){
int u,v;
cin>>u>>v;
u+=off,v+=off;
g[u].push_back(v);
g[v].push_back(u);
}
return g;
}
vvi readtree(int n,int off=-1){
return readgraph(n,n-1,off);
}
template<class T>
vc<T> presum(vc<T> &a){
vc<T> ret(a.size()+1);
rep(i,a.size())ret[i+1]=ret[i]+a[i];
return ret;
}
template<class T, class F>
vc<T> &operator+=(vc<T> &a,F b){
for (auto&v:a)v += b;
return a;
}
template<class T, class F>
vc<T> &operator-=(vc<T>&a,F b){
for (auto&v:a)v-=b;
return a;
}
template<class T, class F>
vc<T> &operator*=(vc<T>&a,F b){
for (auto&v:a)v*=b;
return a;
}
#endif
double pass_time=0;
#pragma once
template<class T,class G,class F>
F modpow(T x,G p,F m){
T ret=1%m;
x%=m;
while(p){
if(p&1)ret=(1ll*ret*x)%m;
x=(1ll*x*x)%m;
p>>=1;
}
return ret;
}
template<class T>
T extgcd(T a,T b,T&x,T&y){//ax+by=gcd(a,b)となるようなもの
if(b==0){
x=1;
y=0;
return a;
}else{
T res=extgcd(b,a%b,y,x);
y-=(a/b)*x;
return res;
}
}
template<class T>
pair<T,T> inv(T x,T m){
T a1,a2;
T res=extgcd(x,m,a1,a2);
return {a1,m/res};
}
constexpr int mod=998244353;
struct mint{
long long val;
inline long long fast(long long x){
if(x<mod&&x>=0)return x;
x%=mod;
if(x<0)x+=mod;
return x;
}
mint():val(0){}
mint(long long val):val(fast(val)){}
mint power(long long m)const {
mint res(1);
mint ret(*this);
while(m){
if(m&1)res*=ret;
ret*=ret;
m>>=1;
}
return res;
}
mint& operator++() {
val++;
if (val == mod) val = 0;
return *this;
}
mint& operator--() {
if (val == 0)val=mod;
val--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint operator-() const {
return mint(-val);
}
friend mint operator +(const mint&a,const mint&b) noexcept{
return mint(a)+=b;
}
friend mint operator -(const mint&a,const mint&b) noexcept{
return mint(a)-=b;
}
friend mint operator *(const mint&a,const mint&b) noexcept{
return mint(a)*=b;
}
friend mint operator /(const mint&a,const mint&b) noexcept{
return mint(a)/=b;
}
mint& operator+=(const mint&a)noexcept{
val+=a.val;
if(val>=mod)val-=mod;
return *this;
}
mint& operator-=(const mint&a)noexcept{
val-=a.val;
if(val<0)val+=mod;
return *this;
}
mint& operator*=(const mint&a){
val*=a.val;
val=fast(val);
return *this;
}
mint& operator/=(const mint&a){
val*=inv<long long>(a.val,mod).first;
val=fast(val);
return *this;
}
bool operator == (const mint&x)const noexcept{
return this->val==x.val;
}
bool operator != (const mint&x)const noexcept{
return this->val!=x.val;
}
friend ostream& operator << (ostream &os, const mint &x) noexcept {
return os << x.val;
}
friend istream& operator >> (istream &is, mint &x) noexcept {
long long v;
is >> v;
x=mint(v);
return is;
}
};
vector<mint>fact(1,1),invfact(1,1);
void build(int n){
if(n<(int)fact.size())return;
fact=invfact=vector<mint>(n+1);
fact[0]=1;
for(int i=1;i<=n;i++)fact[i]=fact[i-1]*i;
invfact[n]=(1/fact[n]);
for(int i=n-1;i>=0;i--)invfact[i]=invfact[i+1]*(i+1);
}
mint C(int a,int b){//aCb
if(a<0||b<0||a-b<0)return mint(0);
while((int)fact.size()<=a){
fact.push_back(fact.back()*(fact.size()));
}
while((int)invfact.size()<=a){
invfact.push_back(invfact.back()/invfact.size());
}
return fact[a]*invfact[b]*invfact[a-b];
}
mint P(int a,int b){
if(a<b||b<0)return 0;
return fact[a]*invfact[a-b];
}
//a個のものからb個を重複を許して選ぶ
mint H(int a,int b){
return C(a+b-1,b);
}
void print(mint a) { cout << a; }
template<class T>
pair<T,T> mod_solve(T a,T b,T m){//ax=b mod mとなるxを返す
a%=m,b%=m;if(a<0)a+=m;if(b<0)b+=m;
T g=gcd(gcd(a,b),m);
a/=g,b/=g,m/=g;
if(gcd(a,m)>1)return {-1,-1};
return {(inv(a,m).first*b)%m,inv(a,m).second};
}
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mod>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = internal::bsf(mod - 1);
mint e = mint(g).power((mod - 1) >> cnt2), ie = 1/e;
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[internal::bsf(~(unsigned int)(s))];
}
}
}
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mod>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = internal::bsf(mod - 1);
mint e = mint(g).power((mod - 1) >> cnt2), ie = 1/e;
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mod + l.val - r.val) *
inow.val;
}
inow *= sum_ie[internal::bsf(~(unsigned int)(s))];
}
}
}
vector<mint>ntt(const vector<mint>&A,const vector<mint>&B){
auto a=A,b=B;
int alen=a.size();
int blen=b.size();
int clen=alen+blen-1;
int n=1;
while(n<=clen)n*=2;
int log=1;
while((1<<log)<n)log++;
a.resize(n);
b.resize(n);
butterfly(a);
butterfly(b);
for(int i=0;i<n;i++)a[i]*=b[i];
butterfly_inv(a);
mint invn=1/mint(n);
for(int i=0;i<clen;i++){
a[i]*=invn;
}
a.resize(clen);
return a;
}
struct FPS{
using poly=vector<mint>;
poly p;
FPS():p(){}
explicit FPS(mint a):p(1,a){}
FPS(poly p):p(p){}
explicit FPS(int size,mint val):p(size,val){}
int size() const {
return int(p.size());
}
mint&operator[](int i) {
return p[i];
}
FPS operator-() const {
auto res=p;
for(auto&x:res)x=-x;
return res;
}
FPS&operator+=(const FPS& a) noexcept {
if(p.size()<a.size())p.resize(a.size());
for(int i=0;i<int(a.size());i++){
p[i]+=a.p[i];
}
return *this;
}
FPS&operator-=(const FPS& a) noexcept {
return (*this)+=(-a);
}
FPS&operator*=(const FPS& a) noexcept {
p=ntt(p,a.p);
return *this;
}
FPS&operator/=(const FPS& a) noexcept {
return (*this)*=a.inv();
}
FPS&operator+=(const mint& a) noexcept {
p[0]+=a;
return *this;
}
FPS&operator-=(const mint& a) noexcept {
return (*this)+=(-a);
}
FPS&operator*=(const mint& a) noexcept {
for(auto&x:p)x*=a;
return *this;
}
FPS&operator/=(const mint& a) noexcept {
mint inv=1/a;
for(auto&x:p)x*=inv;
return *this;
}
FPS&operator<<=(int i) noexcept {
reverse(p.begin(),p.end());
while(i--)p.push_back(0);
reverse(p.begin(),p.end());
return *this;
}
FPS&operator>>=(int i) noexcept {
reverse(p.begin(),p.end());
while(i--)p.pop_back();
reverse(p.begin(),p.end());
return *this;
}
friend FPS operator +(const FPS&a,const FPS&b) noexcept{return FPS(a)+=b;}
friend FPS operator -(const FPS&a,const FPS&b) noexcept{return FPS(a)-=b;}
friend FPS operator *(const FPS&a,const FPS&b) noexcept{return FPS(a)*=b;}
friend FPS operator /(const FPS&a,const FPS&b) noexcept{return FPS(a)/=b;}
friend FPS operator +(const FPS&a,const mint&b) noexcept{return FPS(a)+=b;}
friend FPS operator -(const FPS&a,const mint&b) noexcept{return FPS(a)-=b;}
friend FPS operator *(const FPS&a,const mint&b) noexcept{return FPS(a)*=b;}
friend FPS operator /(const FPS&a,const mint&b) noexcept{return FPS(a)/=b;}
friend FPS operator <<(const FPS&a,const int i) noexcept{return FPS(a)<<=i;}
friend FPS operator >>(const FPS&a,const int i) noexcept{return FPS(a)>>=i;}
//前N項を抜き出す
FPS&shrink(int n){
p.resize(n);
return *this;
}
FPS shrinked(const FPS&a,int n) const {
return FPS(a).shrink(n);
}
void push_back(const mint&a){
p.emplace_back(a);
}
void push_back(const FPS&a){
for(const auto&x:a.p)p.emplace_back(x);
}
void emplace_back(const mint&a){
p.emplace_back(a);
}
void emplace_back(const FPS&a){
for(const auto&x:a.p)p.emplace_back(x);
}
FPS inv(long long a=-1) const {
if(a==-1)a=p.size();
assert(p[0]!=0);
FPS res(1/p[0]);
for(int i=1;;i++){
if((1<<(i-1))>a)break;
auto f=shrinked(*this,1<<i);
auto h=f*res;
h>>=(1<<(i-1));
h=-h*res;
for(int j=0;j<(1<<(i-1));j++)res.p.emplace_back(h[j]);
}
res.shrink(a);
return FPS(res);
}
FPS diff() const {
auto res=*this;
for(int i=0;i<size();i++){
res[i]*=i;
}
res>>=1;
return res;
}
FPS integral() const {
int n=size();
FPS ret(n+1,0);
if(n>0)ret[1]=1;
for(int i=2;i<=n;i++)ret[i]=-ret[mod%i]*(mod/i);
for(int i=0;i<n;i++)ret[i+1]*=p[i];
return ret;
}
FPS log(int n=-1) const {
if(n==-1)n=size();
auto res=shrinked(diff()/(*this),n-1).integral();
return res;
}
//i*2+1をi*2にするとだめらしい
//todo なんで？
FPS exp(int a=-1) const {
if(a==-1)a=size();
assert(p.empty()||p[0]==0);
FPS ret(mint{1});
for(int i=1;i<a;i*=2){
ret=ret*(shrinked(*this,i*2+1)+mint(1)-ret.log(i<<1));
}
return shrinked(ret,a);
}
};
void solve(){
INT(n,m);
FPS ft(1);
rep(i,n){
ft=((ft*ft)<<=1)+ft;
ft.shrink(m+1);
}
PRT(ft[m]);
}
signed main(){
cin.tie(0)->sync_with_stdio(0);
pass_time=clock();
int t=1;
//cin>>t;
while(t--)solve();
pass_time=clock()-pass_time;
dbg(pass_time/CLOCKS_PER_SEC);
}