結果
問題 | No.907 Continuous Kadomatu |
ユーザー | beet |
提出日時 | 2019-10-11 23:05:46 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 16,101 bytes |
コンパイル時間 | 4,292 ms |
コンパイル使用メモリ | 270,868 KB |
実行使用メモリ | 6,824 KB |
最終ジャッジ日時 | 2024-11-25 09:16:43 |
合計ジャッジ時間 | 6,057 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge4 |
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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 | 3 ms
6,816 KB |
testcase_01 | AC | 3 ms
6,820 KB |
testcase_02 | AC | 3 ms
6,820 KB |
testcase_03 | AC | 3 ms
6,816 KB |
testcase_04 | AC | 2 ms
6,816 KB |
testcase_05 | WA | - |
testcase_06 | WA | - |
testcase_07 | WA | - |
testcase_08 | WA | - |
testcase_09 | WA | - |
testcase_10 | WA | - |
testcase_11 | WA | - |
testcase_12 | WA | - |
testcase_13 | WA | - |
testcase_14 | WA | - |
testcase_15 | WA | - |
testcase_16 | WA | - |
testcase_17 | WA | - |
testcase_18 | WA | - |
testcase_19 | WA | - |
testcase_20 | WA | - |
testcase_21 | AC | 11 ms
6,816 KB |
testcase_22 | AC | 10 ms
6,820 KB |
testcase_23 | WA | - |
testcase_24 | WA | - |
testcase_25 | AC | 3 ms
6,816 KB |
testcase_26 | AC | 2 ms
6,820 KB |
testcase_27 | AC | 3 ms
6,816 KB |
testcase_28 | AC | 3 ms
6,816 KB |
testcase_29 | AC | 3 ms
6,820 KB |
ソースコード
#include<bits/stdc++.h> using namespace std; using Int = long long; template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;} struct FastIO{ FastIO(){ cin.tie(0); ios::sync_with_stdio(0); } }fastio_beet; template<typename T,T MOD = 1000000007> struct Mint{ static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;}; Mint operator-(Mint a) const{return Mint(v)-=a;}; Mint operator*(Mint a) const{return Mint(v)*=a;}; Mint operator/(Mint a) const{return Mint(v)/=a;}; Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} bool operator <(const Mint a)const{return v <a.v;} static Mint comb(long long n,int k){ Mint num(1),dom(1); for(int i=0;i<k;i++){ num*=Mint(n-i); dom*=Mint(i+1); } return num/dom; } }; template<typename T,T MOD> constexpr T Mint<T, MOD>::mod; template<typename T,T MOD> ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;} template<typename V> V compress(V v){ sort(v.begin(),v.end()); v.erase(unique(v.begin(),v.end()),v.end()); return v; } template<typename T> map<T, int> dict(const vector<T> &v){ map<T, int> res; for(int i=0;i<(int)v.size();i++) res[v[i]]=i; return res; } map<char, int> dict(const string &v){ return dict(vector<char>(v.begin(),v.end())); } template<typename T> struct FormalPowerSeries{ using Poly = vector<T>; using Conv = function<Poly(Poly, Poly)>; Conv conv; FormalPowerSeries(Conv conv):conv(conv){} Poly pre(const Poly &as,int deg){ return Poly(as.begin(),as.begin()+min((int)as.size(),deg)); } Poly add(Poly as,Poly bs){ int sz=max(as.size(),bs.size()); Poly cs(sz,T(0)); for(int i=0;i<(int)as.size();i++) cs[i]+=as[i]; for(int i=0;i<(int)bs.size();i++) cs[i]+=bs[i]; return cs; } Poly sub(Poly as,Poly bs){ int sz=max(as.size(),bs.size()); Poly cs(sz,T(0)); for(int i=0;i<(int)as.size();i++) cs[i]+=as[i]; for(int i=0;i<(int)bs.size();i++) cs[i]-=bs[i]; return cs; } Poly mul(Poly as,Poly bs){ return conv(as,bs); } Poly mul(Poly as,T k){ for(auto &a:as) a*=k; return as; } // F(0) must not be 0 Poly inv(Poly as,int deg){ assert(as[0]!=T(0)); Poly rs({T(1)/as[0]}); for(int i=1;i<deg;i<<=1) rs=pre(sub(add(rs,rs),mul(mul(rs,rs),pre(as,i<<1))),i<<1); return rs; } // not zero Poly div(Poly as,Poly bs){ while(as.back()==T(0)) as.pop_back(); while(bs.back()==T(0)) bs.pop_back(); if(bs.size()>as.size()) return Poly(); reverse(as.begin(),as.end()); reverse(bs.begin(),bs.end()); int need=as.size()-bs.size()+1; Poly ds=pre(mul(as,inv(bs,need)),need); reverse(ds.begin(),ds.end()); return ds; } // F(0) must be 1 Poly sqrt(Poly as,int deg){ assert(as[0]==T(1)); T inv2=T(1)/T(2); Poly ss({T(1)}); for(int i=1;i<deg;i<<=1){ ss=pre(add(ss,mul(pre(as,i<<1),inv(ss,i<<1))),i<<1); for(T &x:ss) x*=inv2; } return ss; } Poly diff(Poly as){ int n=as.size(); Poly rs(n-1); for(int i=1;i<n;i++) rs[i-1]=as[i]*T(i); return rs; } Poly integral(Poly as){ int n=as.size(); Poly rs(n+1); rs[0]=T(0); for(int i=0;i<n;i++) rs[i+1]=as[i]/T(i+1); return rs; } // F(0) must be 1 Poly log(Poly as,int deg){ return pre(integral(mul(diff(as),inv(as,deg))),deg); } // F(0) must be 0 Poly exp(Poly as,int deg){ Poly f({T(1)}); as[0]+=T(1); for(int i=1;i<deg;i<<=1) f=pre(mul(f,sub(pre(as,i<<1),log(f,i<<1))),i<<1); return f; } Poly partition(int n){ Poly rs(n+1); rs[0]=T(1); for(int k=1;k<=n;k++){ if(1LL*k*(3*k+1)/2<=n) rs[k*(3*k+1)/2]+=T(k%2?-1LL:1LL); if(1LL*k*(3*k-1)/2<=n) rs[k*(3*k-1)/2]+=T(k%2?-1LL:1LL); } return inv(rs,n+1); } Poly bernoulli(int n){ Poly rs(n+1,1); for(int i=1;i<=n;i++) rs[i]=rs[i-1]/T(i+1); rs=inv(rs,n+1); T tmp(1); for(int i=1;i<=n;i++){ tmp*=T(i); rs[i]*=tmp; } return rs; } }; template<typename M> class Enumeration{ private: static vector<M> fact,finv,invs; public: static void init(int n){ n=min<decltype(M::mod)>(n,M::mod-1); int m=fact.size(); if(n<m) return; fact.resize(n+1,1); finv.resize(n+1,1); invs.resize(n+1,1); if(m==0) m=1; for(int i=m;i<=n;i++) fact[i]=fact[i-1]*M(i); finv[n]=M(1)/fact[n]; for(int i=n;i>=m;i--) finv[i-1]=finv[i]*M(i); for(int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1]; } static M Fact(int n){ init(n); return fact[n]; } static M Finv(int n){ init(n); return finv[n]; } static M Invs(int n){ init(n); return invs[n]; } static M C(int n,int k){ if(n<k||k<0) return M(0); init(n); return fact[n]*finv[n-k]*finv[k]; } static M P(int n,int k){ if(n<k||k<0) return M(0); init(n); return fact[n]*finv[n-k]; } static M H(int n,int k){ if(n<0||k<0) return M(0); if(!n&&!k) return M(1); init(n+k-1); return C(n+k-1,k); } static M S(int n,int k){ init(k); M res(0); for(int i=1;i<=k;i++){ M tmp=C(k,i)*M(i).pow(n); if((k-i)&1) res-=tmp; else res+=tmp; } return res*=finv[k]; } static vector< vector<M> > D(int n,int m){ vector< vector<M> > dp(n+1,vector<M>(m+1,0)); dp[0][0]=M(1); for(int i=0;i<=n;i++){ for(int j=1;j<=m;j++){ if(i-j>=0) dp[i][j]=dp[i][j-1]+dp[i-j][j]; else dp[i][j]=dp[i][j-1]; } } return dp; } static M B(int n,int k){ if(n==0) return M(1); k=min(k,n); init(k); vector<M> dp(k+1); dp[0]=M(1); for(int i=1;i<=k;i++) dp[i]=dp[i-1]+((i&1)?-finv[i]:finv[i]); M res(0); for(int i=1;i<=k;i++) res+=M(i).pow(n)*finv[i]*dp[k-i]; return res; } static M montmort(int n){ init(n); M res(0); for(int k=2;k<=n;k++){ if(k&1) res-=finv[k]; else res+=finv[k]; } return res*=fact[n]; } static M LagrangePolynomial(vector<M> &y,M t){ int n=y.size()-1; if(t.v<=n) return y[t.v]; init(n+1); vector<M> dp(n+1,1),pd(n+1,1); for(int i=0;i<n;i++) dp[i+1]=dp[i]*(t-M(i)); for(int i=n;i>0;i--) pd[i-1]=pd[i]*(t-M(i)); M res(0); for(int i=0;i<=n;i++){ M tmp=y[i]*dp[i]*pd[i]*finv[i]*finv[n-i]; if((n-i)&1) res-=tmp; else res+=tmp; } return res; } }; template<typename M> vector<M> Enumeration<M>::fact=vector<M>(); template<typename M> vector<M> Enumeration<M>::finv=vector<M>(); template<typename M> vector<M> Enumeration<M>::invs=vector<M>(); constexpr int bmds(int x){ const int v[] = {1012924417, 924844033, 998244353, 897581057, 645922817}; return v[x]; } constexpr int brts(int x){ const int v[] = {5, 5, 3, 3, 3}; return v[x]; } template<int X> struct NTT{ static constexpr int md = bmds(X); static constexpr int rt = brts(X); using M = Mint<int, md>; vector< vector<M> > rts,rrts; void ensure_base(int n){ if((int)rts.size()>=n) return; rts.resize(n);rrts.resize(n); for(int i=1;i<n;i<<=1){ if(!rts[i].empty()) continue; M w=M(rt).pow((md-1)/(i<<1)); M rw=w.inv(); rts[i].resize(i);rrts[i].resize(i); rts[i][0]=M(1);rrts[i][0]=M(1); for(int k=1;k<i;k++){ rts[i][k]=rts[i][k-1]*w; rrts[i][k]=rrts[i][k-1]*rw; } } } void ntt(vector<M> &as,bool f,int n=-1){ if(n==-1) n=as.size(); assert((n&(n-1))==0); ensure_base(n); for(int i=0,j=1;j+1<n;j++){ for(int k=n>>1;k>(i^=k);k>>=1); if(i>j) swap(as[i],as[j]); } for(int i=1;i<n;i<<=1){ for(int j=0;j<n;j+=i*2){ for(int k=0;k<i;k++){ M z=as[i+j+k]*(f?rrts[i][k]:rts[i][k]); as[i+j+k]=as[j+k]-z; as[j+k]+=z; } } } if(f){ M tmp=M(n).inv(); for(int i=0;i<n;i++) as[i]*=tmp; } } vector<M> multiply(vector<M> as,vector<M> bs){ int need=as.size()+bs.size()-1; int sz=1; while(sz<need) sz<<=1; as.resize(sz,M(0)); bs.resize(sz,M(0)); ntt(as,0);ntt(bs,0); for(int i=0;i<sz;i++) as[i]*=bs[i]; ntt(as,1); as.resize(need); return as; } vector<int> multiply(vector<int> as,vector<int> bs){ vector<M> am(as.size()),bm(bs.size()); for(int i=0;i<(int)am.size();i++) am[i]=M(as[i]); for(int i=0;i<(int)bm.size();i++) bm[i]=M(bs[i]); vector<M> cm=multiply(am,bm); vector<int> cs(cm.size()); for(int i=0;i<(int)cs.size();i++) cs[i]=cm[i].v; return cs; } }; template<int X> constexpr int NTT<X>::md; template<int X> constexpr int NTT<X>::rt; struct ArbitraryModConvolution{ using ll = long long; static NTT<0> ntt0; static NTT<1> ntt1; static NTT<2> ntt2; static constexpr int pow(int a,int b,int md){ int res=1; a=a%md; while(b){ if(b&1) res=(ll)res*a%md; a=(ll)a*a%md; b>>=1; } return res; } static constexpr int inv(int x,int md){ return pow(x,md-2,md); } inline void garner(int &c0,int c1,int c2,int m01,int MOD){ static constexpr int r01=inv(ntt0.md,ntt1.md); static constexpr int r02=inv(ntt0.md,ntt2.md); static constexpr int r12=inv(ntt1.md,ntt2.md); c1=(ll)(c1-c0)*r01%ntt1.md; if(c1<0) c1+=ntt1.md; c2=(ll)(c2-c0)*r02%ntt2.md; c2=(ll)(c2-c1)*r12%ntt2.md; if(c2<0) c2+=ntt2.md; c0+=(ll)c1*ntt0.md%MOD; if(c0>=MOD) c0-=MOD; c0+=(ll)c2*m01%MOD; if(c0>=MOD) c0-=MOD; } inline void garner(vector< vector<int> > &cs,int MOD){ int m01 =(ll)ntt0.md*ntt1.md%MOD; int sz=cs[0].size(); for(int i=0;i<sz;i++) garner(cs[0][i],cs[1][i],cs[2][i],m01,MOD); } vector<int> multiply(vector<int> as,vector<int> bs,int MOD){ vector< vector<int> > cs(3); cs[0]=ntt0.multiply(as,bs); cs[1]=ntt1.multiply(as,bs); cs[2]=ntt2.multiply(as,bs); size_t sz=as.size()+bs.size()-1; for(auto& v:cs) v.resize(sz); garner(cs,MOD); return cs[0]; } template<typename T,T MOD> decltype(auto) multiply(vector< Mint<T, MOD> > am, vector< Mint<T, MOD> > bm){ using M = Mint<T, MOD>; vector<int> as(am.size()),bs(bm.size()); for(int i=0;i<(int)as.size();i++) as[i]=am[i].v; for(int i=0;i<(int)bs.size();i++) bs[i]=bm[i].v; vector<int> cs=multiply(as,bs,MOD); vector<M> cm(cs.size()); for(int i=0;i<(int)cm.size();i++) cm[i]=M(cs[i]); return cm; } }; NTT<0> ArbitraryModConvolution::ntt0; NTT<1> ArbitraryModConvolution::ntt1; NTT<2> ArbitraryModConvolution::ntt2; //INSERT ABOVE HERE const int MOD = 1e9+7; using M = Mint<int, MOD>; M dp[256][512]={}; M nx[256][512]={}; signed main(){ int n; cin>>n; vector<int> as(n),bs(n); for(int i=0;i<n;i++) cin>>as[i]>>bs[i]; vector<int> vs; for(int a:as) vs.emplace_back(a); for(int b:bs) vs.emplace_back(b); vs.emplace_back(0); vs.emplace_back(1e9+6); vs=compress(vs); auto dc=dict(vs); int sz=dc.size(); ArbitraryModConvolution arb; FormalPowerSeries<M> FPS([&](auto as,auto bs){return arb.multiply(as,bs);}); using Poly = FormalPowerSeries<M>::Poly; Poly sum({1,1,500000004,333333336,208333335,933333340,384722225,953769848,884027784,28425375,878389832,120295265,667416506,229082322,168690037,792301837,189791907,537322580,270492550,482909819,434964639,603347984,256069033,40542057,910866921,438756389,689225591,456092267,413439436,942741942,190664686,782031312,604476028,573671381,838163729,26381583,992375502,930241799,68659206,750162938,475025082,44106509,953003110,354749308,929548052,773716788,337410579,936852063,239751572,561034786,757300345,866130835,553348107,173690227,339768055,709994974,599133150,808467741,396950722,936881852,933909478,737746550,781678380,976953545,580850150,325446247,537865815,281759879,678254613,501070706,851777585,443897119,629314534,760221421,466210161,508261591,65379122,70860701,553561602,854155236,407075847,92305888,282144425,99940577,300342438,587223921,290386237,874023958,985911658,291238936,785218916,678035252,407108295,192101397,507631876,885193819,934834163,385372845,417450165,966951672,684237800,52565350,530411501,135801688,482549358,210734100,761667073,954034475,693540720,576600855,148510276,919026764,583465058,956106104,181054957,41348431,224860616,517912143,860599260,727279538,906355640,153963332,118864415,34582699,44891509,32565076,105784827,928923967,903694428,235385416,883778964,689231689,547905546,909455137,465865460,662952760,195582959,432129855,680896262,758700879,501176266,776382822,454182726,365978689,459511347,816227295,999967985,931726294,294000060,267169976,42254724,349482774,808670797,253898299,508920118,703775403,785503876,423332329,660157859,247972241,450442033,165002242,361442380,392196376,978825741,920083817,560637228,355209713,832930192,440150331,375967478,305763913,635609914,188334856,10887821,335431951,444798249,529525353,226380424,33966925,136881343,434803890,922586534,569205127,117755704,850230335,9409131,93257910,499343559,777515079,650212468,412857608,653792744,679126849,627912655,420312949,612153221,845955439,166961824,673224688,890626117,315980351,994489857,197421005,255024280,293965643,551312195,954953948,756212493,145912941,421627841,799494402,930555555,355649848,186846433,48886853,726884935,842271550,621329810,400463499,99728277,259919265,910183168,345461687,647722720,465173355,355332005,670027204,429411872,891988152,9169256,451160948,499408796,131168601,198918642,129056918,498922473,98755571,915188909,895498700,154447049,565728210,321328855,10010840,606569580,973703597,842226469,741226137,421029601,247331280,864146768,199266677,950280814,999665342,469919529,13609624}); //cout<<sum.size()<<endl; /* const int deg = 1<<8; { for(int l=0;l<deg;l++){ Poly res({M(1)}); Poly bs({M(1),M(1)}); bs=FPS.inv(bs,deg); Poly tmp({M(1)}); for(int i=1;i<=l;i++){ tmp=FPS.pre(FPS.mul(tmp,bs),deg); res=FPS.pre(FPS.mul(res,FPS.sub(Poly({M(1)}),tmp)),deg); } sum=FPS.add(sum,res); } using E = Enumeration<M>; E::init(deg); for(int i=0;i<deg;i++) cout<<sum[i]<<endl; for(int i=0;i<deg;i++) sum[i]*=E::Finv(i); for(int i=0;i<deg;i++) cout<<sum[i]<<","; } */ for(int j=0;j+1<sz;j++) if(as[0]<=vs[j]&&vs[j+1]<=bs[0]) dp[1][j]=M(vs[j+1]-vs[j])/M(bs[0]-as[0]); for(int i=1;i<n;i++){ M rev=M(bs[i]-as[i]).inv(); vector<M> cof(sz,0); for(int j=0;j+1<sz;j++) cof[j]=M(as[i]<=vs[j]&&vs[j+1]<=bs[i])*M(vs[j+1]-vs[j])*rev; if(i&1){ for(int l=1;l<n;l++){ M tmp{0}; for(int j=0;j+1<sz;j++){ nx[l+1][j]+=dp[l][j]*cof[j]; nx[1][j]+=tmp; tmp+=sum[l]*dp[l][j]; } } for(int k=0;k+1<sz;k++) nx[1][k]*=cof[k]; }else{ for(int l=1;l<n;l++){ M tmp{0}; for(int j=sz-2;j>=0;j--){ nx[l+1][j]+=dp[l][j]*cof[j]; nx[1][j]+=tmp; tmp+=sum[l]*dp[l][j]; } } for(int k=0;k+1<sz;k++) nx[1][k]*=cof[k]; } for(int j=0;j<256;j++) for(int k=0;k<512;k++) dp[j][k]=nx[j][k],nx[j][k]=M(0); } M ans{0}; for(int i=1;i<=n;i++) for(int j=0;j+1<sz;j++) ans+=dp[i][j]*sum[i]; cout<<ans<<endl; return 0; }