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#define PROBLEM "https://yukicoder.me/problems/5436" #include "../template.hpp" #include "../Graph2/Rerooting.hpp" #include "../type/modint.hpp" using mint=ModInt<1000000007>; signed main(){ int n;cin>>n; Graph<mint> g(n); g.read(n-1,-1,true,false); using T=tuple<mint,mint,mint>; function<T(T,Edge<mint>)> f=[&](T dpch,Edge<mint> e){ auto [a2,a1,cnt]=dpch; return T(a1*2*e.w+a2+e.w*e.w*(cnt+1),a1+e.w*(cnt+1),cnt+1); }; function<T(T,T)> merge=[&](T l,T r){ return T(get<0>(l)+get<0>(r),get<1>(l)+get<1>(r),get<2>(l)+get<2>(r)); }; Rerooting<T,mint> R(g,f,merge,T(0,0,0)); R.build(); mint res=0; rep(i,n) res+=get<0>(R.ans[i]); cout<<res/2<<endl; return 0; }
#line 1 "test/yuki5436.test.cpp" #define PROBLEM "https://yukicoder.me/problems/5436" #line 1 "template.hpp" #include<bits/stdc++.h> using namespace std; #define ALL(x) begin(x),end(x) #define rep(i,n) for(int i=0;i<(n);i++) #define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl; #define mod 1000000007 using ll=long long; const int INF=1000000000; const ll LINF=1001002003004005006ll; int dx[]={1,0,-1,0},dy[]={0,1,0,-1}; // ll gcd(ll a,ll b){return b?gcd(b,a%b):a;} template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;} template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;} struct IOSetup{ IOSetup(){ cin.tie(0); ios::sync_with_stdio(0); cout<<fixed<<setprecision(12); } } iosetup; template<typename T> ostream &operator<<(ostream &os,const vector<T>&v){ for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" "); return os; } template<typename T> istream &operator>>(istream &is,vector<T>&v){ for(T &x:v)is>>x; return is; } #line 4 "test/yuki5436.test.cpp" #line 1 "Graph2/GraphTemplate.hpp" // graph template // ref : https://ei1333.github.io/library/graph/graph-template.hpp template<typename T=int> struct Edge{ int from,to; T w; int idx; Edge()=default; Edge(int from,int to,T w=1,int idx=-1):from(from),to(to),w(w),idx(idx){} operator int() const{return to;} }; template<typename T=int> struct Graph{ vector<vector<Edge<T>>> g; int V,E; Graph()=default; Graph(int n):g(n),V(n),E(0){} int size(){ return (int)g.size(); } void resize(int k){ g.resize(k); V=k; } inline const vector<Edge<T>> &operator[](int k)const{ return (g.at(k)); } inline vector<Edge<T>> &operator[](int k){ return (g.at(k)); } void add_directed_edge(int from,int to,T cost=1){ g[from].emplace_back(from,to,cost,E++); } void add_edge(int from,int to,T cost=1){ g[from].emplace_back(from,to,cost,E); g[to].emplace_back(to,from,cost,E++); } void read(int m,int pad=-1,bool weighted=false,bool directed=false){ for(int i=0;i<m;i++){ int u,v;cin>>u>>v; u+=pad,v+=pad; T w=T(1); if(weighted) cin>>w; if(directed) add_directed_edge(u,v,w); else add_edge(u,v,w); } } }; #line 2 "Graph2/Rerooting.hpp" template<typename T,typename GT=int> struct Rerooting{ using E=function<T(T,Edge<GT>)>;//集合,頂点番号 using M=function<T(T,T)>; using F=function<T(T,int)>; Graph<GT> g; // dp_v = fix(merge(f(dp_c1,edge(v,c1)),...,f(dp_ck,edge(v,ck))),v) E f; // f(T,Edge)->T 辺情報を考慮し,merge前の形 M merge;// TxT->T,子を集約する関数,モノイド T e; // mergeの単位元 F fix; // TxN->T 補正 vector<vector<T>> dp; vector<T> ans; Rerooting(Graph<GT> &g,E f,M merge,T e,F fix=[](T a,int b){return a;}): g(g),f(f),merge(merge),e(e),fix(fix),dp(g.size()),ans(g.size(),e){} T dfs1(int pre,int now){ T ret=e; for(int i=0;i<(int)g[now].size();i++)if(g[now][i]!=pre){ dp[now][i]=dfs1(now,g[now][i]); ret=merge(ret,f(dp[now][i],g[now][i])); } return fix(ret,now); } void dfs2(int pre,int now,T frompar){ for(int i=0;i<(int)g[now].size();i++){ if(g[now][i]==pre){ dp[now][i]=frompar; break; } } vector<T> lsum(g[now].size()+1),rsum(g[now].size()+1);//親も混ぜて累積 lsum[0]=e;rsum[g[now].size()]=e; for(int i=0;i<(int)g[now].size();i++) lsum[i+1]=merge(lsum[i],f(dp[now][i],g[now][i])); for(int i=(int)g[now].size();i>0;i--) rsum[i-1]=merge(rsum[i],f(dp[now][i-1],g[now][i-1])); for(int i=0;i<(int)g[now].size();i++)if(g[now][i]!=pre){ T fromme=merge(lsum[i],rsum[i+1]); dfs2(now,g[now][i],fix(fromme,now)); } } void build(int root=0){ for(int i=0;i<(int)g.size();i++) dp[i].resize(g[i].size()); dfs1(-1,root); dfs2(-1,root,e); for(int i=0;i<(int)g.size();i++){ for(int j=0;j<(int)g[i].size();j++) ans[i]=merge(ans[i],f(dp[i][j],g[i][j])); ans[i]=fix(ans[i],i); } } }; #line 6 "test/yuki5436.test.cpp" #line 1 "type/modint.hpp" template<int Mod> struct ModInt{ int x; ModInt():x(0){} ModInt(int y): x (y >= 0 ? y % Mod : (Mod - (-y) % Mod) % Mod){} ModInt(long long y){ if (y >= 0) { x = (int)(y % (ll)(Mod)); } else { int tmp = (int)((-y) % (ll)Mod); x = (Mod - tmp) % Mod; } } ModInt &operator+=(const ModInt &p){ if((x += p.x) >= Mod) x -= Mod; return *this; } ModInt &operator-=(const ModInt &p){ if((x += Mod - p.x) >= Mod) x -= Mod; return *this; } ModInt &operator*=(const ModInt &p){ x = (int)(1ll * x * p.x % Mod); return *this; } ModInt &operator/=(const ModInt &p){ (*this) *= p.inverse(); return *this; } ModInt operator-()const{return ModInt(-x);} ModInt operator+(const ModInt &p)const{return ModInt(*this)+=p;} ModInt operator-(const ModInt &p)const{return ModInt(*this)-=p;} ModInt operator*(const ModInt &p)const{return ModInt(*this)*=p;} ModInt operator/(const ModInt &p)const{return ModInt(*this)/=p;} bool operator==(const ModInt &p)const{return x==p.x;} bool operator!=(const ModInt &p)const{return x!=p.x;} ModInt inverse()const{ int a = x, b = Mod ,u = 1, v = 0, t; while(b>0){ t=a/b; swap(a-=t*b,b);swap(u-=t*v,v); } return ModInt(u); } ModInt pow(long long n)const{ ModInt ret(1),mul(x); while(n>0){ if(n&1) ret*=mul; mul*=mul;n>>=1; } return ret; } friend ostream &operator<<(ostream &os,const ModInt &p){return os<<p.x;} friend istream &operator>>(istream &is,ModInt &a){long long t;is>>t;a=ModInt<Mod>(t);return (is);} static int get_mod(){return Mod;} }; #line 8 "test/yuki5436.test.cpp" using mint=ModInt<1000000007>; signed main(){ int n;cin>>n; Graph<mint> g(n); g.read(n-1,-1,true,false); using T=tuple<mint,mint,mint>; function<T(T,Edge<mint>)> f=[&](T dpch,Edge<mint> e){ auto [a2,a1,cnt]=dpch; return T(a1*2*e.w+a2+e.w*e.w*(cnt+1),a1+e.w*(cnt+1),cnt+1); }; function<T(T,T)> merge=[&](T l,T r){ return T(get<0>(l)+get<0>(r),get<1>(l)+get<1>(r),get<2>(l)+get<2>(r)); }; Rerooting<T,mint> R(g,f,merge,T(0,0,0)); R.build(); mint res=0; rep(i,n) res+=get<0>(R.ans[i]); cout<<res/2<<endl; return 0; }