結果
問題 | No.1100 Boxes |
ユーザー |
![]() |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 36 |
ソースコード
#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 998244353using 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];}// 重複組み合わせ:n種類の物から重複を許し,k個選ぶmint nHk(int n,int k){return com(n+k-1,k);}// 玉n区別,箱k区別,各箱1個以上O(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 rhttps://www.wolframalpha.com/input/?i=sum+combination%28n%2Bx+%2Cx%29%2C+x%3Dl+to+r&lang=jacheck 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;}