#ifndef call_from_test #include using namespace std; #endif #define call_from_test #ifndef call_from_test #include using namespace std; #endif //BEGIN CUT HERE template 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 constexpr T Mint::mod; template ostream& operator<<(ostream &os,Mint m){os<>h>>w>>k; using M = Mint; M ans{0}; for(int d=1;d using namespace std; #define call_from_test #include "../mod/mint.cpp" #undef call_from_test #endif //BEGIN CUT HERE 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 struct NTT{ static constexpr int md = bmds(X); static constexpr int rt = brts(X); using M = Mint; vector< vector > rts,rrts; void ensure_base(int n){ if((int)rts.size()>=n) return; rts.resize(n);rrts.resize(n); for(int i=1;i &as,bool f){ int n=as.size(); assert((n&(n-1))==0); ensure_base(n); for(int i=0,j=1;j+1>1;k>(i^=k);k>>=1); if(i>j) swap(as[i],as[j]); } for(int i=1;i multiply(vector as,vector bs){ int need=as.size()+bs.size()-1; int sz=1; while(sz multiply(vector as,vector bs){ vector 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 cm=multiply(am,bm); vector cs(cm.size()); for(int i=0;i<(int)cs.size();i++) cs[i]=cm[i].v; return cs; } }; template constexpr int NTT::md; template constexpr int NTT::rt; //END CUT HERE #ifndef call_from_test signed ATC001_C(){ cin.tie(0); ios::sync_with_stdio(0); int n; cin>>n; vector as(n+1,0),bs(n+1,0); for(int i=1;i<=n;i++) cin>>as[i]>>bs[i]; NTT<0> ntt; auto cs=ntt.multiply(as,bs); for(int i=1;i<=n*2;i++) cout< using namespace std; #define call_from_test #include "../mod/mint.cpp" #include "numbertheoretictransform.cpp" #undef call_from_test #endif //BEGIN CUT HERE 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 > &cs,int MOD){ int m01 =(ll)ntt0.md*ntt1.md%MOD; int sz=cs[0].size(); for(int i=0;i multiply(vector as,vector bs,int MOD){ vector< vector > 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 decltype(auto) multiply(vector< Mint > am, vector< Mint > bm){ using M = Mint; vector 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 cs=multiply(as,bs,MOD); vector 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; //END CUT HERE #ifndef call_from_test #define call_from_test #include "../tools/fastio.cpp" #include "../mod/enumeration.cpp" #undef call_from_test //INSERT ABOVE HERE signed YUKI_829(){ using ll = long long; int n,b; cin>>n>>b; vector s(n); for(int i=0;i>s[i]; using M = Mint; using E = Enumeration; E::init(3e5); vector cnt(n,0); for(int i=0;i > ; priority_queue

pq; pq.emplace(-1,vector(1,1)); int sum=0; for(int i=n-1;i>=0;i--){ if(cnt[i]==0) continue; M x=E::H(sum,cnt[i]); M y=E::H(sum+1,cnt[i])-x; x*=E::Fact(cnt[i]); y*=E::Fact(cnt[i]); pq.emplace(-2,vector({x.v,y.v})); sum+=cnt[i]; } const int MOD = 1e9+7; ArbitraryModConvolution arb; while(pq.size()>1u){ auto as=pq.top().second;pq.pop(); auto bs=pq.top().second;pq.pop(); auto cs=arb.multiply(as,bs,MOD); pq.emplace(-(int)cs.size(),cs); } auto dp=pq.top().second; M ans(0),res(1); for(int j=0;j<(int)dp.size();j++){ ans+=M((ll)j*(ll)dp[j])*res; res*=M(b); } cout<=MOD) return 0; ArbitraryModConvolution arb; auto inv=[&](int a){return ArbitraryModConvolution::inv(a,MOD);}; using ll = long long; auto add=[&](int a,int b){return a+b>=MOD?a+b-MOD:a+b;}; auto sub=[&](int a,int b){return a-b<0?a-b+MOD:a-b;}; auto mul=[&](int a,int b){return (ll)a*b%MOD;}; auto div=[&](int a,int b){return mul(a,inv(b));}; int d=1<<15; vector fact(d*2+1,1),finv(d*2+1,1); for(int i=1;i<=d*2;i++) fact[i]=mul(fact[i-1],i); finv[d*2]=inv(fact[d*2]); for(int i=d*2-1;i>=0;i--) finv[i]=mul(finv[i+1],i+1); vector seq({1,d+1}); seq.reserve(d+1); int sz=1; while(sz aux(sz,1); vector f(sz*4,0),g(sz*4,0); for(int i=0;i<=sz;i++){ f[i]=mul(mul(finv[i],finv[sz-i]),seq[i]); if(((sz+i)&1)&&(f[i]!=0)) f[i]=MOD-f[i]; } vector pf(f); vector as; as.emplace_back(sz+1); as.emplace_back(div(sz,d)); as.emplace_back(add(div(sz,d),sz+1)); for(int idx=0;idx<3;idx++){ for(int i=0;i>n; cout<