#if !defined(MYLOCAL)//提出時用テンプレート #pragma GCC optimize("Ofast") #if defined(NDEBUG) #undef NDEBUG #endif #include "bits/stdc++.h" #if !defined(_MSC_VER) && __has_include() #include using namespace atcoder; #endif using namespace std; using ll=long long; using dd=double; using vll=vector< ll>; using vdd=vector< dd>; using vvll=vector< vll>; using vvdd=vector; using vvvll=vector< vvll>; using vvvdd=vector; using vvvvll=vector; using pll=pair; using tll=tuple; using qll=tuple; using vpll=vector< pll>; using vtll=vector< tll>; using vqll=vector< qll>; using vvpll=vector; using vvtll=vector; using vvqll=vector; using namespace chrono; constexpr ll INF = 1001001001001001001; struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<::max_digits10); } } fast; #define REPS(i, S, E) for (ll i = (S); i <= (E); i++) #define REP(i, N) REPS(i, 0, (N)-1) #define DEPS(i, S, E) for (ll i = (E); i >= (S); i--) #define DEP(i, N) DEPS(i, 0, (N)-1) #define EXPAND( x ) x//VS用おまじない #define overload3(_1,_2,_3,name,...) name #define overload4(_1,_2,_3,_4,name,...) name #define overload5(_1,_2,_3,_4,_5,name,...) name #define rep3(i, S, E) for (ll i = (S); i <= (E); i++) #define rep4(i, S, E, t) for (ll i = (S); i <= (E); i+=(t)) #define rep(...) EXPAND(overload4(__VA_ARGS__,rep4,rep3,_,_)(__VA_ARGS__)) #define dep3(i, E, S) for (ll i = (E); i >= (S); i--) #define dep4(i, E, S, t) for (ll i = (E); i >= (S); i-=(t)) #define dep(...) EXPAND(overload4(__VA_ARGS__, dep4, dep3,_,_)(__VA_ARGS__)) #define each2(e,v) for (auto && e:v) #define each3(a,b,v) for (auto &&[a,b]:v) #define each4(a,b,c,v) for (auto &&[a,b,c]:v) #define each5(a,b,c,d,v) for (auto &&[a,b,c,d]:v) #define each(...) EXPAND(overload5(__VA_ARGS__,each5,each4,each3,each2,_)(__VA_ARGS__)) #define ALL1(v) (v).begin(), (v).end() #define ALL2(v,E) (v).begin(), (v).begin()+((E)+1) #define ALL3(v,S,E) (v).begin()+(S), (v).begin()+((E)+1) #define ALL(...) EXPAND(overload3(__VA_ARGS__, ALL3, ALL2, ALL1)(__VA_ARGS__)) #define all ALL #define RALL1(v) (v).rbegin(), (v).rend() #define RALL2(v,E) (v).rbegin(), (v).rbegin()+((E)+1) #define RALL3(v,S,E) (v).rbegin()+(S), (v).rbegin()+((E)+1) #define RALL(...) EXPAND(overload3(__VA_ARGS__, RALL3, RALL2, RALL1)(__VA_ARGS__)) #define rall RALL template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; } template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; } template inline T MaxE(vector&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmax(m,v[i]); return m; } template inline T MinE(vector&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmin(m,v[i]); return m; } template inline T MaxE(vector &v) { return MaxE(v,0,(ll)v.size()-1); } template inline T MinE(vector &v) { return MinE(v,0,(ll)v.size()-1); } template inline auto maxe(T &&v,ll S,ll E){ return *max_element(ALL(v,S,E)); } template inline auto maxe(T &&v){ return *max_element(ALL(v)); } template inline auto mine(T &&v,ll S,ll E){ return *min_element(ALL(v,S,E)); } template inline auto mine(T &&v){ return *min_element(ALL(v)); } template inline T Sum(vector &v,ll S,ll E){ T s=T(); rep(i,S,E)s+=v[i]; return s; } template inline T Sum(vector &v) { return Sum(v,0,v.size()-1); } template::type::value_type> inline U sum(T &&v,ll S,ll E) {return accumulate(all(v,S,E),U());} template inline auto sum(T &&v) {return sum(v,0,v.end()-v.begin()-1);} template inline ll sz(T &&v){ return (ll)v.size(); } inline ll CEIL(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; } //負もOK inline ll FLOOR(ll a,ll b){ return -CEIL(-a,b); } //負もOK //pair用テンプレート template inline pair& operator+=(pair &a,const pair &b){ a.first+=b.first; a.second+=b.second; return a; } template inline pair& operator-=(pair &a,const pair &b){ a.first-=b.first; a.second-=b.second; return a; } template inline pair& operator*=(pair &a,const pair &b){ a.first*=b.first; a.second*=b.second; return a; } template inline pair& operator/=(pair &a,const pair &b){ a.first/=b.first; a.second/=b.second; return a; } template inline pair& operator%=(pair &a,const pair &b){ a.first%=b.first; a.second%=b.second; return a; } template inline pair& operator+=(pair &a,R b){ a.first+=b; a.second+=b; return a; } template inline pair& operator-=(pair &a,R b){ a.first-=b; a.second-=b; return a; } template inline pair& operator*=(pair &a,R b){ a.first*=b; a.second*=b; return a; } template inline pair& operator/=(pair &a,R b){ a.first/=b; a.second/=b; return a; } template inline pair& operator%=(pair &a,R b){ a.first%=b; a.second%=b; return a; } template inline pair operator+(const pair &a,R b){ pair c=a; return c+=b; } template inline pair operator-(const pair &a,R b){ pair c=a; return c-=b; } template inline pair operator*(const pair &a,R b){ pair c=a; return c*=b; } template inline pair operator/(const pair &a,R b){ pair c=a; return c/=b; } template inline pair operator%(const pair &a,R b){ pair c=a; return c%=b; } template inline pair operator-(R b,const pair &a){ pair c=-a; return c+=b; } template inline pair operator-(const pair &a,const pair &b){ pair c=a; return c-=b; } template inline pair operator-(const pair &a){ pair c=a; return c*=(-1); } template inline ostream &operator<<(ostream &os,const pair &a){ return os << a.first << ' ' << a.second; } //tuple用テンプレート 出力用のみ template inline ostream &operator<<(ostream &os,const tuple &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a); } template inline ostream &operator<<(ostream &os,const tuple &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a) << ' ' << get<3>(a); } //vector用テンプレート template inline ostream &operator<<(ostream &os,const vector &a){ for (ll i=0; i<(ll)a.size(); i++) os<<(i>0?" ":"")< inline array& operator+=(array &a,const array &b){ for (ll i=0; i<(ll)S; i++) a[i]+=b[i]; return a; } template inline array& operator-=(array &a,const array &b){ for (ll i=0; i<(ll)S; i++) a[i]-=b[i]; return a; } template inline array& operator*=(array &a,const array &b){ for (ll i=0; i<(ll)S; i++) a[i]*=b[i]; return a; } template inline array& operator/=(array &a,const array &b){ for (ll i=0; i<(ll)S; i++) a[i]/=b[i]; return a; } template inline array& operator%=(array &a,const array &b){ for (ll i=0; i<(ll)S; i++) a[i]%=b[i]; return a; } template inline array& operator+=(array &a,R b){ for (T &e: a) e+=b; return a; } template inline array& operator-=(array &a,R b){ for (T &e: a) e-=b; return a; } template inline array& operator*=(array &a,R b){ for (T &e: a) e*=b; return a; } template inline array& operator/=(array &a,R b){ for (T &e: a) e/=b; return a; } template inline array& operator%=(array &a,R b){ for (T &e: a) e%=b; return a; } template inline array operator+(const array &a,R b){ array c=a; return c+=b; } template inline array operator-(const array &a,R b){ array c=a; return c-=b; } template inline array operator*(const array &a,R b){ array c=a; return c*=b; } template inline array operator/(const array &a,R b){ array c=a; return c/=b; } template inline array operator%(const array &a,R b){ array c=a; return c%=b; } template inline array operator-(R b,const array &a){ array c=-a; return c+=b; } template inline array operator-(const array &a,const array &b){ array c=a; return c-=b; } template inline array operator-(const array &a){ array c=a; return c*=(-1); } template inline ostream &operator<<(ostream &os,const array &a){ for (ll i=0; i<(ll)S; i++) os<<(i>0?" ":"")< struct view1d; template struct view1dIter{ view1d *vw=nullptr; ll idx=INF; view1dIter(){} view1dIter(view1d *vw_,ll idx_):vw(vw_),idx(idx_){} view1dIter(const view1dIter &it):vw(it.vw),idx(it.idx){} R &operator*() { return (*vw)[idx]; } R &operator*() const{ return (*vw)[idx]; } R &operator[](ll i) { return (*vw)[idx+i]; } R &operator[](ll i)const{ return (*vw)[idx+i]; } auto &operator++(){ idx++; return *this; } auto &operator--(){ idx--; return *this; } auto operator++(int){ auto it=*this; idx++; return it; } auto operator--(int){ auto it=*this; idx--; return it; } auto &operator+=(ll n){ idx+=n; return *this; } auto &operator-=(ll n){ idx-=n; return *this; } auto operator+(ll n){ auto it=*this; return it+=n; } auto operator-(ll n){ auto it=*this; return it-=n; } ll operator- (const view1dIter &it)const{ return idx- it.idx; } bool operator< (const view1dIter &it)const{ return idx< it.idx; } bool operator> (const view1dIter &it)const{ return idx> it.idx; } bool operator<=(const view1dIter &it)const{ return idx<=it.idx; } bool operator>=(const view1dIter &it)const{ return idx>=it.idx; } bool operator!=(const view1dIter &it)const{ return idx!=it.idx; } bool operator==(const view1dIter &it)const{ return idx==it.idx; } using iterator_category = random_access_iterator_tag; using value_type = R; using difference_type = ll; using pointer = R*; using reference = R&; }; template struct view1d{ using Sll=array; T &data; //参照先データ Sll dsize; //参照先データ各軸のサイズ Sll s=Sll(); //view先頭 Sll d=Sll(); //view方向 ll len; //view長さ R &dummy; //範囲外の値参照 R dummyj=R(); //範囲外の値実体 /*---- コンストラクタ ----*/ view1d(T &v): data(v),dummy(dummyj){ SetDsize(v,dsize); d[S-1]=1; len=dsize[S-1]; } //このコンストラクタは、マイナス座標指定を末尾にしない(暫定) //代入時Array{...}等と書くため、使い勝手悪い。将来廃止するかも。 view1d(T &v,Sll s,Sll e,Sll d): data(v),s(s),d(d),len(Len(s,e,d)),dummy(dummyj){ SetDsize(v,dsize); } view1d(T &v,Sll s,Sll d,ll len,R &dmy_): data(v),s(s),d(d),len(len),dummy(dmy_){ SetDsize(v,dsize); } /*---- 演算 ----*/ template auto &operator =(const Q &b){ rep(i,0,len-1) (*this)[i] =b; return *this; } template auto &operator+=(const Q &b){ rep(i,0,len-1) (*this)[i]+=b; return *this; } template auto &operator-=(const Q &b){ rep(i,0,len-1) (*this)[i]-=b; return *this; } template auto &operator*=(const Q &b){ rep(i,0,len-1) (*this)[i]*=b; return *this; } template auto &operator/=(const Q &b){ rep(i,0,len-1) (*this)[i]/=b; return *this; } template auto &operator%=(const Q &b){ rep(i,0,len-1) (*this)[i]%=b; return *this; } auto &operator =(const string &b){ return CpSeq(b); } template auto &operator =(const char (&b)[Q]){ return *this=string(b); } template auto &operator =(const vector &b){ return CpSeq(b); } template auto &operator+=(const vector &b){ return PlSeq(b); } template auto &operator-=(const vector &b){ return MnSeq(b); } template auto &operator*=(const vector &b){ return PrSeq(b); } template auto &operator/=(const vector &b){ return DvSeq(b); } template auto &operator%=(const vector &b){ return RmSeq(b); } template auto &operator =(const view1d &b){ return CpSeq(b); } template auto &operator+=(const view1d &b){ return PlSeq(b); } template auto &operator-=(const view1d &b){ return MnSeq(b); } template auto &operator*=(const view1d &b){ return PrSeq(b); } template auto &operator/=(const view1d &b){ return DvSeq(b); } template auto &operator%=(const view1d &b){ return RmSeq(b); } template auto &CpSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i] =b[i]; return *this; } template auto &PlSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]+=b[i]; return *this; } template auto &MnSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]-=b[i]; return *this; } template auto &PrSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]*=b[i]; return *this; } template auto &DvSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]/=b[i]; return *this; } template auto &RmSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]%=b[i]; return *this; } //template static bool eq(const Q &a,const P &b){ // return equals(ALL(a),ALL(b)); //} template static bool eq(const Q &a,const P &b){ if ((ll)a.size()!=(ll)b.size()) return false; rep(i,0,(ll)a.size()-1){ if (a[i]!=b[i]) return false; } return true; } template static bool lt(const Q &a,const P &b){ ll n=min((ll)a.size(),(ll)b.size()); rep(i,0,n-1){ if (a[i]b[i])return false; } return (ll)a.size()<(ll)b.size(); } template bool operator==( const view1d &b){ return eq(*this,b); } template bool operator==( const Q &b){ return eq(*this,b); } template friend bool operator==(const Q &a,const view1d &b){ return eq( a,b); } template bool operator==( const char (&b)[Q]){ return eq(*this,string(b)); } template bool operator!=( const view1d &b){ return !(*this==b); } template bool operator!=( const Q &b){ return !(*this==b); } template friend bool operator!=(const Q &a,const view1d &b){ return !( a==b); } template bool operator< ( const view1d &b){ return lt(*this,b); } template bool operator< ( const Q &b){ return lt(*this,b); } template friend bool operator< (const Q &a,const view1d &b){ return lt( a,b); } template bool operator> ( const view1d &b){ return lt(b,*this); } template bool operator> ( const Q &b){ return lt(b,*this); } template friend bool operator> (const Q &a,const view1d &b){ return lt(b,a ); } template bool operator<=( const view1d &b){ return !(*this>b); } template bool operator<=( const Q &b){ return !(*this>b); } template friend bool operator<=(const Q &a,const view1d &b){ return !( a>b); } template bool operator>=( const view1d &b){ return !(*this bool operator>=( const Q &b){ return !(*this friend bool operator>=(const Q &a,const view1d &b){ return !( a(OrgAt(s+d*i)); } const R &operator[](ll i) const { return OrgAt(s+d*i); } R &at(ll i){ if(i<0)i+=len; return (*this)[i]; } //vector tov(){ vector vvv(len); rep(i,0,len-1) vvv[i]=(*this)[i]; return vvv; } operator vector(){ vector v(len); rep(i,0,len-1) v[i]=(*this)[i]; return v; } bool contains(R a){ rep(i,0,len-1) if((*this)[i]==a)return true; return false; } auto begin(){ return view1dIter(this,0); } auto end(){ return view1dIter(this,len); } /*---- view設定 ----*/ view1d &dmy(R dmy_) { dummy=dmy_; return *this; }//ダミー値セット template view1d &st(Q... s_){//始点set 負は末尾からの位置 this->s=RevIfNeg(SllD(s_...)); this->len=AutoLen(this->s,this->d,this->dsize); return *this; } template view1d &en(Q... e_){//終了条件再設定 負は末尾から this->len=Len(s, RevIfNeg(SllD(e_...)), d); return *this; } template view1d &dir(Q... d_){//方向set、長さはdata端まで this->d=SllD(d_...); this->len=AutoLen(this->s,this->d,this->dsize); return *this; } template view1d &mv(Q... s_){ this->s+=SllD(s_...); return *this; }//平行移動 view1d &size(ll len_) { len=len_; return *this; }//長さset template view1d &size(Q &v){ len=(ll)v.size(); return *this; }//長さset view1d &rev() { s+=d*(len-1); d*=-1; return *this; }//反転 /*---- utility ----*/ template inline static ll sz(Q &v){ return (ll)v.size(); } Sll RevIfNeg(Sll pos){//!< 負なら末尾からの位置に変換 rep(i,0,S-1) if (pos[i]<0) pos[i]+=dsize[i]; return pos; } static ll AutoLen(Sll s_,Sll d_,Sll dsz){//位置s_から方向d_ではみ出すまでの長さ Sll e=dsz-1; rep(i,0,S-1) e[i] *= (d_[i]>=0);//方向が負の軸を0にする return Len(s_,e,d_); } /*---- 先頭位置s、方向d、終了条件eから長さlen計算 ----*/ //template static ll Len(array s,array e,array d){ // ll ret=INF; // rep(i,0,Q-1) chmin(ret, Len1(s[i],e[i],d[i])); // return ret; //} static ll Len(Sll s,Sll e,Sll d){ ll ret=INF; rep(i,0,S-1) chmin(ret, Len1(s[i],e[i],d[i])); return ret; } static ll Len1(ll s,ll e,ll d){ if (d==0) return INF; if (d<0){ s=-s; e=-e; d=-d; } if (s>e) return 0; return (e-s)/d+1; } /*---- 可変長引数をSllに変換 ----*/ template static Sll SllD(Q... args){ return SllRec(0,args...); } template static Sll SllRec(ll i,ll first,Q... rest) { Sll sll = (i==S-1) ? Sll() : SllRec(i+1,rest...); sll[i]=first; return sll; } static Sll SllRec(ll i){ return Sll(); } /*---- dataの位置posの値取得 ----*/ const R &OrgAt(Sll pos) const { rep(i,0,S-1){ if (pos[i]<0 || dsize[i]<=pos[i]) return dummy; } return OrgAt_(data,pos); } template using V = vector; template using VV = V>; template using VVV = V>>; using Vs = V; using VVs = VV; using ll1 = array; using ll2 = array; using ll3 = array; auto &OrgAt_(V &dat,ll1 pos)const{ auto [i] =pos; return dat[i]; } auto &OrgAt_(string &dat,ll1 pos)const{ auto [i] =pos; return dat[i]; } auto &OrgAt_(VV &dat,ll2 pos)const{ auto [i,j] =pos; return dat[i][j]; } auto &OrgAt_(Vs &dat,ll2 pos)const{ auto [i,j] =pos; return dat[i][j]; } auto &OrgAt_(VVV &dat,ll3 pos)const{ auto [i,j,k]=pos; return dat[i][j][k]; } auto &OrgAt_(VVs &dat,ll3 pos)const{ auto [i,j,k]=pos; return dat[i][j][k]; } /*---- dataの各軸size取得 ----*/ static void SetDsize(V &dat,ll1 &dsz){ dsz={sz(dat)}; } static void SetDsize(string &dat,ll1 &dsz){ dsz={sz(dat)}; } static void SetDsize(VV &dat,ll2 &dsz){ dsz={sz(dat),sz(dat[0])}; } static void SetDsize(Vs &dat,ll2 &dsz){ dsz={sz(dat),sz(dat[0])}; } static void SetDsize(VVV &dat,ll3 &dsz){ dsz={sz(dat),sz(dat[0]),sz(dat[0][0])}; } static void SetDsize(VVs &dat,ll3 &dsz){ dsz={sz(dat),sz(dat[0]),sz(dat[0][0])}; } typedef view1dIter iterator; using value_type = R; }; template using V = vector; template using VV = V>; template using VVV = V>>; template view1d( VVV ) -> view1d< VVV,3,T>; template view1d( VV ) -> view1d< VV,2,T>; template view1d( V ) -> view1d< V,1,T>; ; view1d(VV ) -> view1d,3,char>; ; view1d( V ) -> view1d< V,2,char>; ; view1d( string ) -> view1d< string ,1,char>; template view1d( VVV,S,S,S) -> view1d< VVV,3,T>; template view1d( VV,S,S,S) -> view1d< VV,2,T>; template view1d( V,S,S,S) -> view1d< V,1,T>; template view1d(VV,S,S,S) -> view1d,3,char>; template view1d( V,S,S,S) -> view1d< V,2,char>; template view1d( string ,S,S,S) -> view1d< string ,1,char>; template struct view2dIter{ VIEW2D *vw=nullptr; ll idx=INF; view2dIter(){} view2dIter(VIEW2D *vw_,ll idx_):vw(vw_),idx(idx_){} view2dIter(const view2dIter &it):vw(it.vw),idx(it.idx){} auto &operator*() { return (*vw)[x(idx)][y(idx)]; } auto &operator*() const{ return (*vw)[x(idx)][y(idx)]; } auto &operator[](ll i) { return (*vw)[x(idx+i)][y(idx+i)]; } auto &operator[](ll i)const{ return (*vw)[x(idx+i)][y(idx+i)]; } auto &operator++(){ idx++; return *this; } auto &operator--(){ idx--; return *this; } auto operator++(int){ auto it=*this; idx++; return it; } auto operator--(int){ auto it=*this; idx--; return it; } auto &operator+=(ll n){ idx+=n; return *this; } auto &operator-=(ll n){ idx-=n; return *this; } auto operator+(ll n){ auto it=*this; return it+=n; } auto operator-(ll n){ auto it=*this; return it-=n; } ll operator- (const view2dIter &it)const{ return idx- it.idx; } bool operator< (const view2dIter &it)const{ return idx< it.idx; } bool operator> (const view2dIter &it)const{ return idx> it.idx; } bool operator<=(const view2dIter &it)const{ return idx<=it.idx; } bool operator>=(const view2dIter &it)const{ return idx>=it.idx; } bool operator!=(const view2dIter &it)const{ return idx!=it.idx; } bool operator==(const view2dIter &it)const{ return idx==it.idx; } ll x(ll i)const{ return i/vw->leny(); } ll y(ll i)const{ return i%vw->leny(); } using iterator_category = random_access_iterator_tag; using value_type = typename VIEW2D::value_type; using difference_type = ll; using pointer = value_type*; using reference = value_type&; }; template struct view2d{ using Sll=array; T &data; //参照先データ Sll dsize; //参照先データ各軸のサイズ Sll s=Sll(); //view始点 Sll dx=Sll(); //view x軸方向 Sll dy=Sll(); //view y軸方向 ll xl; //view x軸長さ ll yl; //view y軸長さ R dummy=R(); //範囲外の値 /*---- コンストラクタ ----*/ view2d(T &v): data(v){ view1d::SetDsize(v,dsize); dx[S-2]=1; dy[S-1]=1; xl=dsize[S-2]; yl=dsize[S-1]; } /*---- 演算 ----*/ //template auto &operator =(const Q &b){ rep(i,0,xl-1) (*this)[i] =b; return *this; } //template auto &operator+=(const view2d &b){ // rep(i,0,xl-1) (*this)[i] // return PlSeq(b); } /*---- getter ----*/ ll size() const { return xl; } array shape() const { return {xl,yl}; } ll lenx() const { return xl; } ll leny() const { return yl; } ///pll shape() const { return {xl,yl}; } view1d operator[](ll i){ return view1d(data,s+dx*i,dy,yl,dummy); } const view1d operator[](ll i) const { return view1d(data,s+dx*i,dy,yl,dummy); } R &at(ll i,ll j){ if(i<0)i+=xl; if(j<0)j+=yl; return (*this)[i][j]; } //vector> tovv(){ // vector> vvv(xl); // ///rep(i,0,xl-1) vvv[i]=(*this)[i].tov(); return vvv; // rep(i,0,xl-1) vvv[i]=(*this)[i]; return vvv; //} operator vector>(){ vector> v(xl); rep(i,0,xl-1) v[i]=(*this)[i]; return v; } auto begin(){ return view2dIter(this,0); } auto end(){ return view2dIter(this,xl*yl); } #if defined(_DEBUG) void dump(){ ::dump(tovv()); } #endif /*---- view設定 ----*/ view2d &dmy(R dmy_) { dummy=dmy_; return *this; }//ダミー値セット template view2d &st(Q... s_){//始点set 負は末尾からの位置 this->s=RevIfNeg(view1d::SllD(s_...)); this->xl=view1d::AutoLen(this->s,this->dx,this->dsize); this->yl=view1d::AutoLen(this->s,this->dy,this->dsize); return *this; } template view2d &dirx(Q... d_){//x軸set、長さはdata端まで this->dx=view1d::SllD(d_...); this->xl=view1d::AutoLen(this->s,this->dx,this->dsize); return *this; } template view2d &diry(Q... d_){//y軸set、長さはdata端まで this->dy=view1d::SllD(d_...); this->yl=view1d::AutoLen(this->s,this->dy,this->dsize); return *this; } template view2d &mv(Q... s_){//平行移動 this->s += view1d::SllD(s_...); return *this; } view2d &lenx(ll xl_) { xl=xl_; return *this; } view2d &leny(ll yl_) { yl=yl_; return *this; } view2d &shape(ll xl_,ll yl_) { xl=xl_; yl=yl_; return *this; } template view2d &shape(Q &v) { xl=v.lenx(); yl=v.leny(); return *this; } view2d &rot90 () { s+=dx*(xl-1); swap(xl,yl); swap(dx,dy); dy*=-1; return *this; } view2d &rot270() { s+=dy*(yl-1); swap(xl,yl); swap(dx,dy); dx*=-1; return *this; } view2d &rot180() { s+=dx*(xl-1)+dy*(yl-1); dx*=-1; dy*=-1; return *this; } view2d &revx() { s+=dx*(xl-1); dx*=-1; return *this; } view2d &revy() { s+=dy*(yl-1); dy*=-1; return *this; } view2d &swapxy() { swap(xl,yl); swap(dx,dy); return *this; }//xy軸入替 /*---- utility ----*/ Sll RevIfNeg(Sll pos){//!< 負なら末尾からの位置に変換 rep(i,0,S-1) if (pos[i]<0) pos[i]+=dsize[i]; return pos; } using value_type = R; }; template view2d( VVV) -> view2d< VVV,3,T>; template view2d( VV) -> view2d< VV,2,T>; ; view2d(VV) -> view2d,3,char>; ; view2d( V) -> view2d< V,2,char>; /* zipは参照のpairを返す。それをさらに参照するのはまずいので、コピーする。 */ template struct zipIter{ ZIP *z=nullptr; ll idx=INF; zipIter(){} zipIter(ZIP *z_,ll idx_):z(z_),idx(idx_){} zipIter(const zipIter &it):z(it.z),idx(it.idx){} auto operator*() { return (*z)[idx]; }//参照ではなく値戻し auto operator*() const{ return (*z)[idx]; }//同上 auto operator[](ll i) { return (*z)[idx+i]; }//同上 auto operator[](ll i)const{ return (*z)[idx+i]; }//同上 auto &operator++(){ idx++; return *this; } auto &operator--(){ idx--; return *this; } auto operator++(int){ auto it=*this; idx++; return it; } auto operator--(int){ auto it=*this; idx--; return it; } auto &operator+=(ll n){ idx+=n; return *this; } auto &operator-=(ll n){ idx-=n; return *this; } auto operator+(ll n){ auto it=*this; return it+=n; } auto operator-(ll n){ auto it=*this; return it-=n; } ll operator- (const zipIter &it)const{ return idx- it.idx; } bool operator< (const zipIter &it)const{ return idx< it.idx; } bool operator> (const zipIter &it)const{ return idx> it.idx; } bool operator<=(const zipIter &it)const{ return idx<=it.idx; } bool operator>=(const zipIter &it)const{ return idx>=it.idx; } bool operator!=(const zipIter &it)const{ return idx!=it.idx; } bool operator==(const zipIter &it)const{ return idx==it.idx; } using iterator_category = random_access_iterator_tag; using value_type = typename ZIP::value_type; using difference_type = ll; using pointer = value_type*; using reference = value_type&; }; template struct zip2{ T &t; S &s; zip2(T &t_,S &s_):t(t_),s(s_){} ll size() const { return t.end()-t.begin(); } auto operator[](ll i) { return make_pair(ref(t.begin()[i]),ref(s.begin()[i])); } auto operator[](ll i)const{ return make_pair(ref(t.begin()[i]),ref(s.begin()[i])); } auto begin(){ return zipIter(this,0); } auto end(){ return zipIter(this,size()); } using value_type = pair; }; template struct zip3{ T &t; S &s; R &r; zip3(T &t_,S &s_,R &r_):t(t_),s(s_),r(r_){} ll size() const { return t.end()-t.begin(); } auto operator[](ll i) { return make_tuple(ref(t.begin()[i]),ref(s.begin()[i]),ref(r.begin()[i])); } auto operator[](ll i)const{ return make_tuple(ref(t.begin()[i]),ref(s.begin()[i]),ref(r.begin()[i])); } auto begin(){ return zipIter(this,0); } auto end(){ return zipIter(this,size()); } using value_type = tuple; }; #endif//テンプレートend #if defined(_MSC_VER) && __has_include() #include using namespace atcoder; #endif struct{ system_clock::time_point st = system_clock::now(); ll operator()()const{return duration_cast(system_clock::now()-st).count()/1000;} } timeget; ////////////////////////////////////////// template struct mll_{ using Int = long long; using ll = long long; ll val_=0; /*---- utility ----*/ mll_ &norm(){ return normR().normS(); }//正規化 mll_ &normR(){ val_%=MOD; return *this; }//剰余正規化のみ mll_ &normS(){ if (val_<0) val_+=MOD; return *this; }//正負正規化のみ mll_ &normP(){ if (val_>=MOD) val_-=MOD; return *this; }//加算時正規化 mll_ &invsg(){ val_=-val_; return normS(); }//正負反転 ll modinv(int a){//a^-1 mod MOD int ypre=0,y=1,apre=MOD; while (a>1){ int t=apre/a; apre-=a*t,swap(a,apre); ypre-=y*t,swap(y,ypre); } return y<0 ? y+MOD: y; } /*---- I/F ----*/ mll_(){} mll_(ll v): val_(v){ norm(); } mll_(ll v,bool b): val_(v){} //正規化無のコンストラクタ Int val()const{ return (Int)val_; } bool isnone() const { return val_==-1; } //true:値なし mll_ &none() { val_=-1; return *this; } //値なしにする mll_ &inv(){ val_=modinv((int)val_); return *this; } mll_ &operator+=(mll_ b){ val_+=b.val_; return normP(); } mll_ &operator-=(mll_ b){ val_-=b.val_; return normS(); } mll_ &operator*=(mll_ b){ val_*=b.val_; return normR(); } mll_ &operator/=(mll_ b){ return *this*=b.inv(); } mll_ &operator+=(ll b){ return *this+=mll_(b); } mll_ &operator-=(ll b){ return *this-=mll_(b); } mll_ &operator*=(ll b){ return *this*=mll_(b); } mll_ &operator/=(ll b){ return *this/=mll_(b); } mll_ operator-()const{ return mll_(*this).invsg(); } mll_ operator+(mll_ b)const{ return mll_(*this)+=b; } mll_ operator-(mll_ b)const{ return mll_(*this)-=b; } mll_ operator*(mll_ b)const{ return mll_(*this)*=b; } mll_ operator/(mll_ b)const{ return mll_(*this)/=b; } mll_ operator+(ll b)const{ return mll_(*this)+=b; } mll_ operator-(ll b)const{ return mll_(*this)-=b; } mll_ operator*(ll b)const{ return mll_(*this)*=b; } mll_ operator/(ll b)const{ return mll_(*this)/=b; } friend mll_ operator+(ll a,mll_ b){ return b+a; } friend mll_ operator-(ll a,mll_ b){ return -b+a; } friend mll_ operator*(ll a,mll_ b){ return b*a; } friend mll_ operator/(ll a,mll_ b){ return mll_(a)/b; } bool operator==(mll_ b)const{ return val_==b.val_; } bool operator!=(mll_ b)const{ return val_!=b.val_; } bool operator==(ll b)const{ return *this==mll_(b); } bool operator!=(ll b)const{ return *this!=mll_(b); } friend bool operator==(ll a,mll_ b){ return mll_(a)==b; } friend bool operator!=(ll a,mll_ b){ return mll_(a)!=b; } friend ostream &operator<<(ostream &os,mll_ a){ return os << a.val_; } friend istream &operator>>(istream &is,mll_ &a){ return is >> a.val_; } mll_ pow(ll k)const{ mll_ ret(1,false),a(*this); for (; k>0; k>>=1,a*=a) if (k&1)ret*=a; return ret; } static constexpr int mod() { return MOD; } //enum{ modll=MOD }; }; #if 0 template struct mll_{ using ll = long long; ll val=0; /*---- utility ----*/ mll_ &norm(){ return normR().normS(); }//正規化 mll_ &normR(){ val%=MOD; return *this; }//剰余正規化のみ mll_ &normS(){ if (val<0) val+=MOD; return *this; }//正負正規化のみ mll_ &normP(){ if (val>=MOD) val-=MOD; return *this; }//加算時正規化 mll_ &invsg(){ val=-val; return normS(); }//正負反転 ll modinv(int a){//a^-1 mod MOD int ypre=0,y=1,apre=MOD; while (a>1){ int t=apre/a; apre-=a*t,swap(a,apre); ypre-=y*t,swap(y,ypre); } return y<0 ? y+MOD: y; } /*---- I/F ----*/ mll_(){} mll_(ll v): val(v){ norm(); } mll_(ll v,bool b): val(v){} //正規化無のコンストラクタ bool isnone() const { return val==-1; } //true:値なし mll_ &none() { val=-1; return *this; } //値なしにする mll_ &inv(){ val=modinv((int)val); return *this; } mll_ &operator+=(mll_ b){ val+=b.val; return normP(); } mll_ &operator-=(mll_ b){ val-=b.val; return normS(); } mll_ &operator*=(mll_ b){ val*=b.val; return normR(); } mll_ &operator/=(mll_ b){ return *this*=b.inv(); } mll_ &operator+=(ll b){ return *this+=mll_(b); } mll_ &operator-=(ll b){ return *this-=mll_(b); } mll_ &operator*=(ll b){ return *this*=mll_(b); } mll_ &operator/=(ll b){ return *this/=mll_(b); } mll_ operator-()const{ return mll_(*this).invsg(); } mll_ operator+(mll_ b)const{ return mll_(*this)+=b; } mll_ operator-(mll_ b)const{ return mll_(*this)-=b; } mll_ operator*(mll_ b)const{ return mll_(*this)*=b; } mll_ operator/(mll_ b)const{ return mll_(*this)/=b; } mll_ operator+(ll b)const{ return mll_(*this)+=b; } mll_ operator-(ll b)const{ return mll_(*this)-=b; } mll_ operator*(ll b)const{ return mll_(*this)*=b; } mll_ operator/(ll b)const{ return mll_(*this)/=b; } friend mll_ operator+(ll a,mll_ b){ return b+a; } friend mll_ operator-(ll a,mll_ b){ return -b+a; } friend mll_ operator*(ll a,mll_ b){ return b*a; } friend mll_ operator/(ll a,mll_ b){ return mll_(a)/b; } bool operator==(mll_ b)const{ return val==b.val; } bool operator!=(mll_ b)const{ return val!=b.val; } bool operator==(ll b)const{ return *this==mll_(b); } bool operator!=(ll b)const{ return *this!=mll_(b); } friend bool operator==(ll a,mll_ b){ return mll_(a)==b; } friend bool operator!=(ll a,mll_ b){ return mll_(a)!=b; } friend ostream &operator<<(ostream &os,mll_ a){ return os << a.val; } friend istream &operator>>(istream &is,mll_ &a){ return is >> a.val; } mll_ pow(ll k)const{ mll_ ret(1,false),a(*this); for (; k>0; k>>=1,a*=a) if (k&1)ret*=a; return ret; } enum{ modll=MOD }; }; #endif #if 0 #define MODLL (1000000007LL) #else #define MODLL (998244353LL) #endif using mll = mll_; using vmll = std::vector; using vvmll = std::vector; using vvvmll = std::vector; using vvvvmll = std::vector; template struct Vector: vector{ using Int = long long; using vT=vector; using cvT=const vector; using cT=const T; using vT::vT; //親クラスのコンストラクタの隠蔽を回避 using vT::begin,vT::end,vT::insert,vT::erase; auto it(Int i){ return begin()+i; } auto it(Int i)const{ return begin()+i; } Vector(cvT& b):vT(b){} Vector(vT&& b):vT(move(b)){} Int size()const{ return (Int)vT::size(); } Vector &push_back(cT& x){ vT::push_back(x); return *this; } Vector &pop_back(){ vT::pop_back(); return *this; } Vector &push_front(cT& x){ insert(begin(),x); return *this; } Vector &pop_front(){ erase(0); return *this; } Vector &insert(Int i,cT& x){ insert(it(i),x); return *this; } Vector &insert(Int i,cvT& b){ insert(it(i),b.begin(),b.end()); return *this; } Vector &erase(Int i){ erase(it(i)); return *this; } Vector &erase(Int l,Int r){ erase(it(l),it(r+1)); return *this; } Vector &concat(cvT &b){ insert(end(),b.begin(),b.end()); return *this; } Vector &concat(cvT &b,Int n){ for (int i=0;i Vector &sort(Pr pr){ std::sort(begin(),end(),pr); return *this; } Vector &uniq(){ erase(unique(begin(),end()),end()); return *this; } Vector &sortq(){ return sort().uniq(); } Vector &fill(Int l,Int r,cT& x){ std::fill(it(l),it(r+1),x); return *this; } template Vector &iota(Int n,T s=0,S d=1){ vT::resize(n); if (n==0) return *this; (*this)[0]=s; for (int i=1;i Int countif(Pr pr)const{ return count_if(begin(),end(),pr); } template Int countif(Int l,Int r,Pr pr)const{ return count_if(it(l),it(r+1),pr); } Int find(cT& x)const{ return std::find(begin(),end(),x)-begin(); } Int find(Int l,Int r,cT& x)const{ return std::find(it(l),it(r+1),x)-begin(); } template Int findif(Pr pr)const{ return find_if(begin(),end(),pr)-begin(); } template Int findif(Int l,Int r,Pr pr)const{ return find_if(it(l),it(r+1),pr)-begin(); } Vector findall(cT& x)const{ return findall(0,size()-1,x); } Vector findall(Int l,Int r,cT& x)const{ return findallif(l,r,[&](cT& y){return y==x;}); } template Vector findallif(Pr pr)const{ return findallif(0,size()-1,pr); } template Vector findallif(Int l,Int r,Pr pr)const{ Vector ret; for (Int i=l;i<=r;++i) if (pr((*this)[i])) ret.push_back(i); return ret; } Int flooridx(cT& x)const{ return upper_bound(begin(),end(),x)-begin()-1; } Int ceilidx(cT& x)const{ return lower_bound(begin(),end(),x)-begin(); } Int leftnmof(cT& x)const{ return flooridx(x)+1; } Int rightnmof(cT& x)const{ return size()-ceilidx(x); } bool contains(cT& x)const{ Int i=flooridx(x); return i>=0 && (*this)[i]==x; } template Int flooridx(cT& x,Pr pr)const{ return upper_bound(begin(),end(),x,pr)-begin()-1; } template Int ceilidx(cT& x,Pr pr)const{ return lower_bound(begin(),end(),x,pr)-begin(); } template Int leftnmof(cT& x,Pr pr)const{ return flooridx(x,pr)+1; } template Int rightnmof(cT& x,Pr pr)const{ return size()-ceilidx(x,pr); } }; using Vll=Vector< ll>; using Vdd=Vector< dd>; using VVll=Vector< Vll>; using VVdd=Vector< Vdd>; using VVVll=Vector; using VVVdd=Vector; using Vpll=Vector< pll>; using Vtll=Vector< tll>; using Vqll=Vector< qll>; using VVpll=Vector; using VVtll=Vector; using VVqll=Vector; /* Vll a={9,8,7},b={1,2,3}; Vpll p={{5,3},{7,8},{0,2},}; - -------- 操作系 -------- a.push_front(x); a.push_back(x); a.pop_front(); a.pop_back(); a.insert(i,x); //a[i]にx挿入 a.insert(i,b); //a[i]にVll b挿入 a.erase(i); //a[i]削除 a.erase(l,r); //区間[l,r]削除 a.concat(b); //aにbを結合 a.concat(b,n); //aにbをn回結合 a.repeat(n); //aをn回繰り返す a.reverse(); //反転 a.sort(); //ソート a.rsort(); //逆順ソート p.sort([&](pll x,pll y){return x.second0; }; //検索条件 ll m=a.count(x); //xの個数 ll m=a.count(l,r,x); //xの個数in[l,r] ll m=a.countif(pr); //条件満たす個数 ll m=a.countif(l,r,pr); //条件満たす個数in[l,r] ll i=a.find(x); //xの最左位置i ない時N(配列長) ll i=a.find(l,r,x); //xの最左位置i in[l,r] ない時r+1 ll i=a.findif(pr); //条件満たす最左位置i ない時N(配列長) ll i=a.findif(l,r,pr); //条件満たす最左位置i in[l,r] ない時r+1 Vll is=a.findall(x); //xの位置i列挙 Vll is=a.findall(l,r,x); //xの位置i列挙in[l,r] Vll is=a.findallif(pr); //条件満たす位置i列挙 Vll is=a.findallif(l,r,pr); //条件満たす位置i列挙in[l,r] - -------- 昇順sort済み配列用 -------- ll i=a.flooridx(x); //x以下の最近傍位置i ない時-1 ll i=a.ceilidx(x); //x以上の最近傍位置i ない時N(配列長) ll m=a.leftnmof(x); //x以下の個数 ll m=a.rightnmof(x); //x以上の個数 - -------- 比較関数prでsort済みの配列用 -------- auto pr=[&](auto &x,auto &y){ return x>y; }; //降順ソート時 ll i=a.flooridx(x,pr); //x以左の最近傍位置i ない時-1 ll i=a.ceilidx(x,pr); //x以右の最近傍位置i ない時N(配列長) ll m=a.leftnmof(x,pr); //x以左の個数 ll m=a.rightnmof(x,pr); //x以右の個数 a.concat(b,n).pop_back().rsort().uniq(); //連続適用できる */ using Vmll = Vector; using VVmll = Vector; using VVVmll = Vector; using VVVVmll = Vector; namespace fpsspace{ using Int = long long; using ll = long long; constexpr int inf=int(1e9); /********* utility関数 *********/ template T POW(T a,ll n){//a^n n負も可 if (n<0) a=T(1)/a, n=-n; T r=1; for (; n>0; n>>=1,a*=a) if(n&1)r*=a; return r; } ll LimitMul(ll a,ll b){//min(a*b,9e18) a,b≧0 return (b==0 || a<=ll(9e18)/b) ? a*b : ll(9e18); } /*---- 1/i列挙 i=1~d ----*/ template struct Wrap{};//オーバロード解決用にKindを型に変換 template> vector &Invs(int d, Wrap){//Kind=1 or 2(modint系)の時 static vector invs(2,T(1)); int MOD = T::mod(); for (int i=(int)invs.size();i<=d;++i) invs.push_back(-invs[MOD%i]*T(MOD/i)); return invs; } template vector &Invs(int d, Wrap<0>){//その他の時 static vector invs(1); for (int i=(int)invs.size();i<=d;++i) invs.push_back(T(1)/i); return invs; } /********* FPS疎表現クラス *********/ template struct sparseFps: vector>{ using vector>::vector; //親クラスのコンストラクタの隠蔽を回避 /*---- I/F ----*/ template void set(S co,R deg){ this->emplace_back(T(co),Int(deg)); } Int deg()const{ return this->empty() ? -1 : this->back().second; }//最高次数 T co(Int i)const{ return (*this)[i].first; }//(*this)[i]の係数 T &co(Int i) { return (*this)[i].first; } Int deg(Int i)const{ return (*this)[i].second; }//(*this)[i]の次数 Int °(Int i) { return (*this)[i].second; } Int lowdeg()const{ return this->empty() ? inf : this->front().second; } sparseFps &operator*=(T b){ for (auto&&[c,_]:*this) c*=b; return *this; } sparseFps operator*(T b)const{ return sparseFps(*this)*=b; } template FPS pow(ll k,Int dmx,const vector &invs_=vector())const{ assert(!(k<0 && lowdeg()>0));//k負なら定数項必須 if (k==0) return FPS({1},dmx); //-- 計算後最高次数d:k<0ならdmx、k>0ならmin(dmx,deg()*k)まで int d = (k<0 || LimitMul(deg(),k)>(ll)dmx) ? int(dmx) : int(deg()*k); //-- invs[i]=1/iをi=1~dまで計算(計算済み分は再利用、足りない分だけ計算) const vector &invs = invs_.size() ? invs_ : Invs(d,Wrap{}); //-- 最低次数関連処理 int s=(int)lowdeg();//計算前最低次数 if (k>0 && LimitMul(s,k)>(ll)dmx) return FPS(dmx);//計算後all0の時 //-- 漸化式で計算 T f0inv=T(1)/co(0); FPS g({POW(co(0),k)},dmx); for (int i=1;i<=d-s*k;++i){ //k負の時必ずs=0なのでOK for (int j=1;j<(int)this->size();++j){ auto [c,dg]=(*this)[j]; int b=int(dg)-s; if (i-b<0)break; g.at(i)+=c*g.at(i-b)*(T(k)*b-i+b); } g.at(i)*=f0inv*invs[i]; } return g.shift(Int(s*k)); } }; /********* FPSクラス *********/ template< class T, //係数の型 int Kind //係数の種類 0:その他、1:NTTfriendly mod、2:任意mod > struct Fps: vector{ static_assert(0<=Kind && Kind<=2); static constexpr int kind=Kind; int dMx=inf; //次数上限(x^dMxまで保持) using vT = vector; //using vector::vector; //親クラスのコンストラクタの隠蔽を回避 /*---- utility ----*/ int isize()const{ return (int)vector::size(); } int NormSize()const{//leading zeroを除いたサイズ const用 int sv=isize(); while (sv>0 && (*this)[sv-1]==T(0)) --sv; return sv; } int Deg()const{ return NormSize()-1; } //最高次数 const用 Fps &Cut(){ return cut(dMx); } int MinD(const Fps &g)const{ return min(dMx,g.dMx); } void MergeD(const Fps &g){ dMx=MinD(g); Cut(); } template Fps &Add(const Fps &g){ MergeD(g); for (int i=min(dMx,g.Deg());i>=0;--i) at(i)+=Sign*g[i]; return *this; } Fps ProdSparse(const sparseFps &g,int d)const{//f*疎g mod x^(d+1) Fps ret(d); for (auto&&[co,dg]:g) for (int i=0;i<(int)isize();++i){ if (dg+i>d) break; ret.at(dg+i)+=co*(*this)[i]; } return ret; } Fps InvSparse(const sparseFps &g,int d)const{//f/疎g mod x^(d+1) g0≠0 assert(!g.empty() && g.deg(0)==0 && g.co(0)!=0); //-- g定数項を1にする T c0inv=T(1)/g.co(0); Fps ret=((*this)*c0inv).setdmx(d); if (g.size()==1u) return ret; sparseFps gg=g*c0inv; //-- 配るDP計算 for (int i=0; i+(int)gg.deg(1)<=d; ++i){ for (int j=1; j<(int)gg.size(); ++j){ auto [co,dg]=gg[j]; int ii=i+(int)dg; if (d i,Int dmx=inf): vT(i.begin(),i.end()),dMx(int(dmx)){ Cut(); } template ::iterator_category> Fps(It l,It r,Int dmx=inf): vT(l,r),dMx(int(dmx)){ Cut(); } Fps(const sparseFps &sf,Int dmx=inf):dMx(int(dmx)){ //疎f → f for (auto&&[co,deg]:sf) if (deg<=dmx) at(deg)=co; } /*---- I/F ----*/ constexpr sparseFps tosparse()const{ //f → 疎f sparseFps ret; for (int i=0;i::size(); } Int deg(){ fit(); return size()-1; } Int lowdeg()const{ for (int i=0;iresize(i+1); return (*this)[i]; } Fps &fit(){ this->resize(NormSize()); return *this; } Fps &operator+=(const Fps &g){ return Add<1>(g); } Fps &operator-=(const Fps &g){ return Add<-1>(g); } Fps &operator*=(const Fps &g){ return *this=*this*g; } Fps &operator/=(const Fps &g){ return *this=*this/g; } Fps &operator*=(const sparseFps &g){ return *this=*this*g; } Fps &operator/=(const sparseFps &g){ return *this=*this/g; } Fps &operator+=(T c){ at(0)+=c; return *this; } Fps &operator-=(T c){ at(0)-=c; return *this; } Fps &operator*=(T c){ for (auto&& e: *this) e*=c; return *this; } Fps &operator/=(T c){ return (*this)*=T(1)/c; } Fps operator+(const Fps &g)const{ return Fps(*this)+=g; } Fps operator-(const Fps &g)const{ return Fps(*this)-=g; } Fps operator*(const Fps &g)const{ return Prod(*this,g,MinD(g)+1); } Fps operator/(const Fps &g)const{ return InvSparse(g.tosparse(),MinD(g)); } Fps operator*(const sparseFps &g)const{ return ProdSparse(g,dMx); } Fps operator/(const sparseFps &g)const{ return InvSparse(g,dMx); } Fps operator+(T c)const{ return Fps(*this)+=c; } Fps operator-(T c)const{ return Fps(*this)-=c; } Fps operator*(T c)const{ return Fps(*this)*=c; } Fps operator/(T c)const{ return Fps(*this)/=c; } Fps operator-()const{ return Fps(*this)*=T(-1); } friend Fps operator+(T c,const Fps &f){ return f+c; } friend Fps operator-(T c,const Fps &f){ return -f+c; } friend Fps operator*(T c,const Fps &f){ return f*c; } T prod1(const Fps &g,Int k_)const{ //[x^k]f*g int df=Deg(),dg=g.Deg(),k=(int)k_; if (MinD(g)=0; ++i,--j) ret+=(*this)[i]*g[j]; return ret; } Fps &cut(Int d){ //x^dまでにする if (d+1=max(0,-k);--i) ret.at(i+k)=(*this)[i]; return ret; } T eval(T x)const{ //f(c) T ret=T(0); for (int i=isize()-1;i>=0;--i) ret*=x,ret+=(*this)[i]; return ret; } Fps diff()const{ //微分 Fps ret(dMx); for (int i=Deg();i>=1;--i) ret.at(i-1)=(*this)[i]*i; return ret; } Fps integ()const{ //積分 Fps ret(dMx); for (int i=min(Deg(),dMx-1); i>=0; --i) ret.at(i+1)=(*this)[i]/(i+1); return ret; } T integrange(T l,T r)const{ //定積分 ∫_l^r f dx Fps itg=integ(); return itg.eval(r)-itg.eval(l); } Fps inv()const{ assert(at(0)!=0);//定数項≠0 Fps g{T(1)/at(0)}; for (int i=1;iint(dMx/k)) return Fps(dMx);//f(x)=0か結果=0の時 int m=int(dMx+1-z*k); //最終は先頭にゼロがz*k個→計算はdMx+1-z*k項でok Fps g=shift(-z).setdmx(m-1)/at(z); //定数項1にする変換 Fps gk=(g.log()*k).exp(); //g^k Fps ret=(gk*POW(at(z),k)).setdmx(dMx).shift(Int(z*k)); //変換を戻す return ret; } Fps powdbl(ll k)const{ //f^k Fps ret({1},dMx),g=*this; for (; k>0; k>>=1,g*=g) if(k&1)ret*=g; return ret; } Fps powsparse(ll k,const vector &invs=vector())const{ //疎f^k return tosparse().template pow(k,dMx,invs); } pair div(const Fps &g)const{ //多項式f/g,f%g const Fps &f=*this; int na=f.NormSize(),nb=g.NormSize(); assert(nb>0); int n=na-nb+1;//商の項数 if (n<=0) return {Fps(dMx),f}; int nu=f.isize(),nv=g.isize(); Fps aR(f.rbegin()+nu-na,f.rbegin()+min(nu-na+n,nu),n-1); Fps bR(g.rbegin()+nv-nb,g.rbegin()+min(nv-nb+n,nv),n-1); Fps qR=bR.inv()*aR; qR.resize(n); reverse(qR.begin(),qR.end()); qR.fit().setdmx(dMx); Fps r=(f-Prod(qR,g,dMx+1)).fit(); return {move(qR),move(r)}; } }; /********* 積をNTTmod畳み込み、任意mod畳み込み、畳み込み不使用から選択 *********/ template //f*g mod x^n 畳み込み不使用 Fps Prod(const Fps &f,const Fps &g,int n){ Fps ret(n-1); int nf=f.NormSize(), ng=g.NormSize(), nn=min(n,nf+ng-1); if (nf==0 || ng==0 || nn==0) return ret; for (int i=nn-1;i>=0;--i){ int st=min(i,nf-1),en=max(int(0),i-ng+1); for (int k=st;k>=en;--k){ ret.at(i)+=f[k]*g[i-k]; } } return ret; } template //f*g mod x^n NTTmod畳み込み Fps Prod(const Fps &f,const Fps &g,int n){ int nf=min(n,f.NormSize()), ng=min(n,g.NormSize()); vector ff,gg; ff.reserve(nf), gg.reserve(ng); for (int i=0;i hh=convolution(ff,gg); if ((int)hh.size()>n) hh.resize(n); return Fps(hh.begin(),hh.end(),n-1); } template //f*g mod x^n 任意mod畳み込み Fps Prod(const Fps &f,const Fps &g,int n){ static constexpr int m0 = 167772161; //m0 ff,gg; ff.reserve(nf), gg.reserve(ng); for (int i=0;i h0=convolution(ff,gg); vector h1=convolution(ff,gg); vector h2=convolution(ff,gg); Fps ret(n-1); int nn=min(n,(int)h0.size()); ret.reserve(nn); for (int i=0;i; //畳み込み不使用 using fps = fpsspace::Fps; //NTTfriendly mod //using fps = fpsspace::Fps; //任意mod using spfps = fpsspace::sparseFps; /* 各種演算の結果の次数上限は、一部例外を除きf,gの小さい方となる。 - -------- コンストラクタ -------- fps f; //f(x)=0 fps f(d); // 〃 次数上限d fps f{2,3,4,}; //f(x)=2+3x+4x^2 fps f({2,3,4,},d); // 〃 次数上限d fps f(all(v)); //vll等のvをコピー fps f(all(v),d); // 〃 次数上限d - -------- コンストラクタ疎版 -------- vectorと同じ spfps sf={{4,2},{-1,5}}; //f(x)=4x^2-x^5 次数昇順、係数≠0とすること - -------- 演算子(fps同士) -------- f+=g f-=g f+g f-g -f f*=g f*g //NTTmod,任意mod,愚直がテンプレートで切り替わる f*=疎g f*疎g //愚直 f/=g f/=疎g f/g f/疎g //漸化式で愚直 - -------- 演算子(定数) -------- f+=c f-=c f*=c f/=c f+c f-c f*c f/c 疎f*=c 疎f*c - -------- アクセス・操作 -------- f[i]=val; //直接操作 f.at(i)=val; //自動サイズ調整有 ll n=f.size(); //項数(次数+1) leading zero含む ll d=f.deg(); //非0の最高次の次数 f(x)=0の時-1 ll d=f.lowdeg(); //非0の最低次の次数 f(x)=0の時1e9 f.setdmx(d); //次数上限をx^dにセット & mod x^(d+1) d≧0 f.fit(); //最高次≠0になるよう縮める fps f(sf); //疎f→f 変換 fps f(sf,d); //疎f→f 変換 次数上限d spfps sf=f.tosparse(); //f→疎f 変換 - -------- 演算 -------- mll c=f.prod1(g,k); //[x^k]f*g f.cut(d); //x^dまでにする f.mod(n); //mod x^n fps g=f.shift(k); //f*=x^k k負も可 mll val=f.eval(c); //f(c) fps g=f.diff(); //微分 fps g=f.integ(); //積分 mll val=f.integrange(l,r); //定積分 ∫_l^r f dx fps g=f.inv(); //1/f 定数項≠0 fps g=f.log(); //log f 定数項=1 fps g=f.exp(); //exp f 定数項=0 fps g=f.pow(k); //f^k fps g=f.powdbl(k); //f^k doubling版 fps g=sf.pow(k,d); //疎f^k 次数上限d k負も可(定数項≠0必須) fps g=f.powsparse(k); //疎f^k k負も可(定数項≠0必須) auto[h,r]=f.div(g); //多項式の除算・剰余 h=f/g,r=f%g 次数上限はfの方 */ void cin2solve() { ll N,K; cin >> N >> K; ll M=99; ll n=N/2, nn=N-n; fps fb{1,1,1,1,1,1,1,1,1,1}; fps f=fb.powsparse(n).fit(); fps ff=fb.powsparse(nn).fit(); ll df=f.deg(); ll dff=ff.deg(); fps c; rep(rr,0,M-1){ ll r=-1; rep(i,0,M-1){ if ((i+rr)%9==0 and abs(i-rr)%11==0){r=i;break;} } assert(r!=-1); fps C; rep(m,0,INF-1){ ll ddd=99*m+r; if (ddd>df)break; C.at(m)=f.at(ddd); } fps CC; rep(m,0,INF-1){ ll ddd=99*m+rr; if (ddd>dff)break; CC.at(m)=ff.at(ddd); } fps CCC=(C*CC).fit(); rep(p,0,CCC.deg()){ c.at(99*p+r+rr)+=CCC[p]; } } mll ans=0; rep(d,0,c.deg()){ mll ct=c[d]; if (ct==0)continue; ans+=mll(d).pow(K)*ct; } cout << ans << '\n'; return; } ////////////////////////////////////////// int main(){ #if 1 //labo(); cin2solve(); //generand(); #else ll t; cin >> t; rep(i,0,t-1){ cin2solve(); //generand(); } #endif cerr << timeget() <<"ms"<< '\n'; return 0; }