結果
| 問題 |
No.907 Continuous Kadomatu
|
| コンテスト | |
| ユーザー |
 beet
|
| 提出日時 | 2019-10-11 23:07:17 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 16,127 bytes |
| コンパイル時間 | 5,373 ms |
| コンパイル使用メモリ | 265,712 KB |
| 最終ジャッジ日時 | 2025-01-07 21:49:48 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 5 |
| other | AC * 7 WA * 18 |
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<<7;
{
sum=Poly({});
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;
}