結果

問題 No.1100 Boxes
ユーザー mugen_1337
提出日時 2020-09-27 23:51:59
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 136 ms / 2,000 ms
コード長 6,645 bytes
コンパイル時間 2,013 ms
コンパイル使用メモリ 199,212 KB
最終ジャッジ日時 2025-01-14 23:09:29
ジャッジサーバーID
(参考情報)
judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 36
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include<bits/stdc++.h>
using namespace std;
#define ALL(x) x.begin(),x.end()
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 998244353
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}
struct IOSetup{
IOSetup(){
cin.tie(0);
ios::sync_with_stdio(0);
cout<<fixed<<setprecision(12);
}
} iosetup;
template<typename T1,typename T2>
ostream &operator<<(ostream &os,const pair<T1,T2>&p){
os<<p.first<<" "<<p.second;
return os;
}
template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
return os;
}
template<typename T1,typename T2>
istream &operator>>(istream &is,pair<T1,T2>&p){
is>>p.first>>p.second;
return is;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
for(T &x:v)is>>x;
return is;
}
template<ll Mod>
struct ModInt{
long long x;
ModInt():x(0){}
ModInt(long long y):x(y>=0?y%Mod:(Mod-(-y)%Mod)%Mod){}
ModInt &operator+=(const ModInt &p){
if((x+=p.x)>=Mod) x-=Mod;
return *this;
}
ModInt &operator-=(const ModInt &p){
if((x+=Mod-p.x)>=Mod)x-=Mod;
return *this;
}
ModInt &operator*=(const ModInt &p){
x=(int)(1ll*x*p.x%Mod);
return *this;
}
ModInt &operator/=(const ModInt &p){
(*this)*=p.inverse();
return *this;
}
ModInt operator-()const{return ModInt(-x);}
ModInt operator+(const ModInt &p)const{return ModInt(*this)+=p;}
ModInt operator-(const ModInt &p)const{return ModInt(*this)-=p;}
ModInt operator*(const ModInt &p)const{return ModInt(*this)*=p;}
ModInt operator/(const ModInt &p)const{return ModInt(*this)/=p;}
ModInt operator==(const ModInt &p)const{return x==p.x;}
ModInt operator!=(const ModInt &p)const{return x!=p.x;}
ModInt inverse()const{
int a=x,b=Mod,u=1,v=0,t;
while(b>0){
t=a/b;
swap(a-=t*b,b);swap(u-=t*v,v);
}
return ModInt(u);
}
ModInt pow(long long n)const{
ModInt ret(1),mul(x);
while(n>0){
if(n&1) ret*=mul;
mul*=mul;n>>=1;
}
return ret;
}
friend ostream &operator<<(ostream &os,const ModInt &p){return os<<p.x;}
friend istream &operator>>(istream &is,ModInt &a){long long t;is>>t;a=ModInt<Mod>(t);return (is);}
static int get_mod(){return Mod;}
};
using mint=ModInt<mod>;
template<int MAX>
struct comcalc{
vector<mint> fact,finv,inv;
comcalc():fact(MAX),finv(MAX),inv(MAX){
fact[0]=mint(1),fact[1]=mint(1),finv[0]=mint(1),finv[1]=mint(1),inv[1]=mint(1);
for(int i=2;i<MAX;i++){
fact[i]=fact[i-1]*mint(i);
inv[i]=mint(0)-inv[mod%i]*(mint(mod/i));
finv[i]=finv[i-1]*inv[i];
}
}
mint com(int n,int k){
if(n<k) return mint(0);
if(n<0 or k<0) return mint(0);
return fact[n]*(finv[k]*finv[n-k]);
}
mint fac(int n){
return fact[n];
}
// :nk
mint nHk(int n,int k){
return com(n+k-1,k);
}
// nk1O(k)
mint F12_dis_dis_one(int n,int k){
if(n<k)return mint(0);
mint ret=0;
for(int i=0;i<=k;i++){
mint add=com(k,i)*(mint(i).pow(n));
if((k-i)%2) ret-=add;
else ret+=add;
}
return ret;
}
/* sum combination(n+x, x), x=l to r
https://www.wolframalpha.com/input/?i=sum+combination%28n%2Bx+%2Cx%29%2C+x%3Dl+to+r&lang=ja
check n+x < [COM_PRECALC_MAX] */
mint sum_of_comb(int n,int l,int r){
if(l>r)return mint(0);
mint ret=mint(r+1)*com(n+r+1,r+1)-mint(l)*com(l+n,l);
ret/=mint(n+1);
return ret;
}
};
mint pow_mod(mint x,ll n){
return x.pow(n);
}
mint inv_mod(mint x){
return x.inverse();
}
// O(n)
mint fact_mod(ll n){
mint ret=1;
for(int i=2;i<=n;i++) ret*=mint(i);
return ret;
}
// O(r)
mint comb_mod(ll n,ll r){
if(r>n-r) r=n-r;
if(r==0) return 1;
mint a=1,b=mint(fact_mod(r)).inverse();
for(int i=0;i<r;i++)a*=mint(n-i);
return a*b;
}
const int MAX=4010000;
using cominit=comcalc<MAX>;
struct NTTmodint{
vector<mint> dw,idw;
int max_base;
mint root;
NTTmodint(){
ll tmp=mod-1;
max_base=0;
while(tmp%2==0) tmp>>=1,max_base++;
root=2;
while(root.pow((mod-1)>>1).x==1) root+=1;
dw.resize(max_base);idw.resize(max_base);
for(int i=0;i<max_base;i++){
dw[i]=-root.pow((mod-1)>>(i+2));
idw[i]=mint(1)/dw[i];
}
}
void ntt(vector<mint> &a){
int n=(int)a.size();
for(int m=n;m>>=1;){
mint w=1;
for(int s=0,k=0;s<n;s+=2*m){
for(int i=s,j=s+m;i<s+m;i++,j++){
auto x=a[i],y=a[j]*w;
a[i]=x+y,a[j]=x-y;
}
w*=dw[__builtin_ctz(++k)];
}
}
}
void intt(vector<mint> &a,bool f=true){
int n=(int)a.size();
for(int m=1;m<n;m*=2){
mint w=1;
for(int s=0,k=0;s<n;s+=2*m){
for(int i=s,j=s+m;i<s+m;i++,j++){
auto x=a[i],y=a[j];
a[i]=x+y,a[j]=(x-y)*w;
}
w*=idw[__builtin_ctz(++k)];
}
}
if(f){
mint inv_sz=mint(1)/n;
for(int i=0;i<n;i++) a[i]*=inv_sz;
}
}
vector<mint> multiply(vector<mint> a,vector<mint> b){
int need=(int)a.size()+b.size()-1;
int nbase=1;
while((1<<nbase)<need) nbase++;
int sz=1<<nbase;
a.resize(sz,0);b.resize(sz,0);
ntt(a);ntt(b);
mint inv_sz=mint(1)/sz;
for(int i=0;i<sz;i++) a[i]*=b[i]*inv_sz;
intt(a,false);
a.resize(need);
return a;
}
};
signed main(){
cominit F;
int n,k;cin>>n>>k;
mint res=0;
for(int i=1;i<=k;i++){
mint tmp=F.com(k,i)*mint(k-i).pow(n);
tmp*=mint(2).pow(i-1);
if(i%2) res+=tmp;
else res-=tmp;
}
cout<<res<<endl;
return 0;
}
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