結果

問題 No.1321 塗るめた
ユーザー tko919tko919
提出日時 2020-12-18 00:57:29
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 180 ms / 2,000 ms
コード長 9,618 bytes
コンパイル時間 2,281 ms
コンパイル使用メモリ 188,852 KB
実行使用メモリ 33,048 KB
最終ジャッジ日時 2024-09-21 08:45:57
合計ジャッジ時間 8,068 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 34 ms
26,880 KB
testcase_01 AC 37 ms
27,008 KB
testcase_02 AC 33 ms
26,880 KB
testcase_03 AC 33 ms
26,880 KB
testcase_04 AC 34 ms
26,752 KB
testcase_05 AC 34 ms
26,864 KB
testcase_06 AC 34 ms
26,880 KB
testcase_07 AC 33 ms
26,880 KB
testcase_08 AC 33 ms
26,732 KB
testcase_09 AC 33 ms
26,724 KB
testcase_10 AC 35 ms
26,752 KB
testcase_11 AC 34 ms
26,872 KB
testcase_12 AC 105 ms
30,072 KB
testcase_13 AC 73 ms
29,796 KB
testcase_14 AC 74 ms
28,504 KB
testcase_15 AC 109 ms
29,892 KB
testcase_16 AC 104 ms
30,084 KB
testcase_17 AC 36 ms
27,008 KB
testcase_18 AC 180 ms
32,404 KB
testcase_19 AC 68 ms
28,572 KB
testcase_20 AC 103 ms
29,804 KB
testcase_21 AC 118 ms
30,324 KB
testcase_22 AC 178 ms
32,252 KB
testcase_23 AC 177 ms
32,396 KB
testcase_24 AC 178 ms
33,000 KB
testcase_25 AC 175 ms
32,376 KB
testcase_26 AC 179 ms
32,468 KB
testcase_27 AC 177 ms
33,048 KB
testcase_28 AC 173 ms
32,908 KB
testcase_29 AC 174 ms
32,964 KB
testcase_30 AC 174 ms
32,388 KB
testcase_31 AC 115 ms
30,636 KB
testcase_32 AC 102 ms
30,156 KB
testcase_33 AC 103 ms
29,828 KB
testcase_34 AC 105 ms
30,204 KB
testcase_35 AC 104 ms
29,760 KB
testcase_36 AC 60 ms
29,664 KB
testcase_37 AC 118 ms
30,704 KB
testcase_38 AC 118 ms
30,572 KB
testcase_39 AC 119 ms
30,572 KB
testcase_40 AC 117 ms
30,704 KB
testcase_41 AC 118 ms
30,708 KB
testcase_42 AC 33 ms
26,880 KB
testcase_43 AC 104 ms
30,020 KB
testcase_44 AC 103 ms
29,704 KB
testcase_45 AC 105 ms
30,076 KB
testcase_46 AC 50 ms
27,776 KB
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 # 

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

//template
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll;
const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
//end

template<unsigned mod=998244353>struct fp {
   using uint=unsigned; uint v;
   static uint get_mod(){return mod;}
   int inv() const{
      int tmp,a=v,b=mod,x=1,y=0;
      while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);
      if(x<0){x+=mod;} return x;
   }
   fp(ll x=0){init(x%mod+mod);}
   fp& init(uint x){v=(x<mod?x:x-mod); return *this;}
   fp operator-()const{return fp()-*this;}
   fp pow(ll t){fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}
   fp& operator+=(const fp& x){return init(v+x.v);}
   fp& operator-=(const fp& x){return init(v+mod-x.v);}
   fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}
   fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}
   fp operator+(const fp& x)const{return fp(*this)+=x;}
   fp operator-(const fp& x)const{return fp(*this)-=x;}
   fp operator*(const fp& x)const{return fp(*this)*=x;}
   fp operator/(const fp& x)const{return fp(*this)/=x;}
   bool operator==(const fp& x)const{return v==x.v;}
   bool operator!=(const fp& x)const{return v!=x.v;}
   friend istream& operator>>(istream& is,fp& x){is>>x.v; return is;}
   friend ostream& operator<<(ostream& os,fp x){os<<x.v; return os;}
}; using Fp=fp<>;
template<typename T>struct factorial {
   vector<T> Fact,Finv,Inv;
   factorial(int maxx){
      Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx);
      Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1;
      rep(i,2,maxx){Fact[i]=Fact[i-1]*i;} Finv[maxx-1]=Fact[maxx-1].inv();
      for(int i=maxx-1;i>=2;i--){Finv[i-1]=Finv[i]*i; Inv[i]=Finv[i]*Fact[i-1];}
   }
   T fact(int n,bool inv=0){if(inv)return Finv[n];else return Fact[n];}
   T inv(int n){return Inv[n];}
   T nPr(int n,int r){if(n<0||n<r||r<0)return Fp(0);else return Fact[n]*Finv[n-r];}
   T nCr(int n,int r){if(n<0||n<r||r<0)return Fp(0);else return Fact[n]*Finv[r]*Finv[n-r];}
};

template<typename T=Fp,unsigned p=3>struct NTT{
   vector<T> rt,irt;
   NTT(int lg=21){
      unsigned m=T::get_mod()-1; T prt=p;
      rt.resize(lg); irt.resize(lg);
      rep(k,0,lg){
         rt[k]=-prt.pow(m>>(k+2));
         irt[k]=rt[k].inv();
      }
   }
   void ntt(vector<T>& f,bool inv=0){
      int n=f.size();
      if(inv){
         for(int m=1;m<n;m<<=1){ T w=1;
            for(int s=0,t=0;s<n;s+=m*2){
               for(int i=s,j=s+m;i<s+m;i++,j++){
                  auto x=f[i],y=f[j];
                  f[i]=x+y; f[j]=(x-y)*w;
               } w*=irt[__builtin_ctz(++t)];
            }
         } T mul=T(n).inv(); rep(i,0,n)f[i]*=mul;
      }else{
         for(int m=n;m>>=1;){ T w=1;
            for(int s=0,t=0;s<n;s+=m*2){
               for(int i=s,j=s+m;i<s+m;i++,j++){
                  auto x=f[i],y=f[j]*w;
                  f[i]=x+y; f[j]=x-y;
               } w*=rt[__builtin_ctz(++t)];
            }
         }
      }
   }
   vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0){
      if(a.empty() or b.empty())return vector<T>();
      int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
      vector<T> res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res);
      if(same)rep(i,0,m)res[i]*=res[i];
      else{
         vector<T> c(m); rep(i,0,b.size())c[i]=b[i];
         ntt(c); rep(i,0,m)res[i]*=c[i];
      } ntt(res,1); return res;
   }
};

NTT<Fp,3> ntt;
vector<Fp> mult(const vector<Fp>& a,const vector<Fp>& b,bool same){
   return ntt.mult(a,b,same);
}
factorial<Fp> fact(2010101);
template<typename T=Fp>struct Poly:vector<T>{
   Poly(int n=0){this->assign(n,T());}
   Poly(const vector<T>& f){this->assign(ALL(f));}
   T eval(const T& x){T res; for(auto& v:*this)res*=x,res+=v; return res;}
   Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;}
   void shrink(){while(!this->empty() and this->back()==0)this->pop_back();}
   Poly inv()const{
      assert(this->front()!=0); const int n=this->size();
      Poly res(1); res.front()=T(1)/this->front();
      for(int k=1;k<n;k<<=1){
         Poly g=res,h=*this; h.resize(k*2); res.resize(k*2);
         g=(g.square()*h); g.resize(k*2);
         rep(i,k,min(k*2,n))res[i]-=g[i];
      }
      res.resize(n); return res;
   }
   Poly square()const{return Poly(mult(*this,*this,1));}
   Poly operator+(const Poly& g)const{return Poly(*this)+=g;}
   Poly operator-(const Poly& g)const{return Poly(*this)-=g;}
   Poly operator*(const Poly& g)const{return Poly(*this)*=g;}
   Poly operator/(const Poly& g)const{return Poly(*this)/=g;}
   Poly operator%(const Poly& g)const{return Poly(*this)%=g;}
   Poly& operator+=(const Poly& g){
      if(g.size()>this->size())this->resize(g.size());
      rep(i,0,g.size()){(*this)[i]+=g[i];} shrink(); return *this;
   }
   Poly& operator-=(const Poly& g){
      if(g.size()>this->size())this->resize(g.size());
      rep(i,0,g.size()){(*this)[i]-=g[i];} shrink(); return *this;
   }
   Poly& operator*=(const Poly& g){
      *this=mult(*this,g,0);
      shrink(); return *this;
   }
   Poly& operator/=(const Poly& g){
      if(g.size()>this->size()){
         this->clear(); return *this;
      }
      *this=this->rev(); g=g.rev();
      int n=this->size()-g.size()+1;
      this->resize(n); g.resize(n);
      *this*=g.inv_fast(); this->resize(n); //
      *this=this->rev(); shrink(); return *this;
   }
   Poly& operator%=(Poly& g){*this-=*this/g*g; shrink(); return *this;}
   Poly diff()const{
      Poly res(this->size()-1);
      rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1);
      return res;
   }
   Poly inte()const{
      Poly res(this->size()+1);
      for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]*fact.inv(i);
      return res;
   }
   Poly log()const{
      assert(this->front()==1); const int n=this->size();
      Poly res=diff()*inv_fast(); res=res.inte(); //
      res.resize(n); return res;
   }
   Poly exp()const{
      assert(this->front()==0); const int n=this->size();
      Poly res(1),g(1); res.front()=g.front()=1;
      for(int k=1;k<n;k<<=1){
         g=(g+g-g.square()*res); g.resize(k);
         Poly q=*this; q.resize(k); q=q.diff();
         Poly w=(q+g*(res.diff()-res*q)),t=*this;
         w.resize(k*2-1); t.resize(k*2);
         res=(res+res*(t-w.inte())); res.resize(k*2);
      } res.resize(n); return res;
   }
   Poly shift(const int& c)const{
      const int n=this->size();
      Poly res=*this,g(n); g[1]=c; g=g.exp();
      rep(i,0,n){res[i]*=fact.fact(i);} res=res.rev();
      res*=g; res.resize(n); res=res.rev();
      rep(i,0,n){res[i]*=fact.fact(i,1);} return res;
   }
   Poly inv_fast()const{
      const int n=this->size();
      Poly res(1); res.front()=T(1)/this->front();
      for(int k=1;k<n;k<<=1){
         Poly f(k*2),g(k*2);
         rep(i,0,min(n,k*2))f[i]=(*this)[i];
         rep(i,0,k)g[i]=res[i];
         ntt.ntt(f); ntt.ntt(g);
         rep(i,0,k*2)f[i]*=g[i];
         ntt.ntt(f,1);
         rep(i,0,k){f[i]=0; f[i+k]=-f[i+k];}
         ntt.ntt(f); rep(i,0,k*2)f[i]*=g[i]; ntt.ntt(f,1);
         rep(i,0,k)f[i]=res[i];
         swap(res,f);
      } res.resize(n); return res;
   }
   Poly exp_fast()const{
      const int n=this->size();
      if(n==1)return Poly({T(1)});
      Poly b(2),c(1),z1,z2(2);
      b[0]=c[0]=z2[0]=z2[1]=1; b[1]=(*this)[1];
      for(int k=2;k<n;k<<=1){
         Poly y=b; y.resize(k*2);
         ntt.ntt(y); z1=z2;
         Poly z(k);
         rep(i,0,k)z[i]=y[i]*z1[i];
         ntt.ntt(z,1);
         rep(i,0,k>>1)z[i]=0;
         ntt.ntt(z);
         rep(i,0,k)z[i]*=-z1[i];
         ntt.ntt(z,1);
         c.insert(c.end(),z.begin()+(k>>1),z.end());
         z2=c; z2.resize(k*2);
         ntt.ntt(z2);
         Poly x=*this; x.resize(k); x=x.diff(); x.resize(k);
         ntt.ntt(x);
         rep(i,0,k)x[i]*=y[i];
         ntt.ntt(x,1);
         Poly bb=b.diff();
         rep(i,0,k-1)x[i]-=bb[i];
         x.resize(k*2);
         rep(i,0,k-1){x[k+i]=x[i]; x[i]=0;}
         ntt.ntt(x);
         rep(i,0,k*2)x[i]*=z2[i];
         ntt.ntt(x,1);
         x.pop_back(); x=x.inte();
         rep(i,k,min(n,k*2))x[i]+=(*this)[i];
         rep(i,0,k)x[i]=0;
         ntt.ntt(x);
         rep(i,0,k*2)x[i]*=y[i];
         ntt.ntt(x,1);
         b.insert(b.end(),x.begin()+k,x.end());
      } b.resize(n); return b;
   }
   Poly pow(ll t){
      int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;
      Poly res(n); if(t*k>=n)return res;
      n-=t*k; Poly g(n); T c=(*this)[k],ic=T(1)/c;
      rep(i,0,n)g[i]=(*this)[i+k]*ic;
      g=g.log(); for(auto& x:g)x*=t; g=g.exp_fast(); //
      c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;
   }
};
Fp nth(Poly<Fp> p,Poly<Fp> q,ll n){
   while(n){
      Poly<Fp> ref(q),np,nq;
      for(int i=1;i<(int)q.size();i+=2)ref[i]*=-1;
      p*=ref; q*=ref;
      for(int i=n&1;i<(int)p.size();i+=2)np.emplace_back(p[i]);
      for(int i=0;i<(int)q.size();i+=2)nq.emplace_back(q[i]);
      swap(p,np); swap(q,nq);
      n>>=1;
   }
   return p[0]/q[0];
}

/*
[x^N*y^K] N! * e^{Mx}((e^x-1)y+1)^M
=N!*nCr(M,K)* [x^N] e^{Mx}(e^x-1)^K
*/

int main(){
   int n,m,k; cin>>n>>m>>k;
   Poly<Fp> f(n+1),g(n+1);
   Fp pw=1;
   rep(i,0,n+1){
      f[i]=pw*fact.fact(i,1);
      g[i]=fact.fact(i,1);
      pw*=m;
   }
   g[0]=0;
   g=g.pow(k);
   f*=g;
   Fp res=fact.fact(n)*fact.nCr(m,k)*f[n];
   cout<<res<<endl;
   return 0;
}
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