#include #define ll long long #define INF 1000000005 #define MOD 1000000007 #define EPS 1e-10 #define rep(i,n) for(int i=0;i<(int)(n);++i) #define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i) #define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i) #define each(a,b) for(auto& (a): (b)) #define all(v) (v).begin(),(v).end() #define len(v) (int)(v).size() #define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end()) #define cmx(x,y) x=max(x,y) #define cmn(x,y) x=min(x,y) #define fi first #define se second #define pb push_back #define show(x) cout<<#x<<" = "<<(x)<auto&operator<<(ostream&o,pairp){return o<<"{"<auto&operator<<(ostream&o,sets){for(auto&e:s)o< auto&operator<<(ostream&o,priority_queueq){while(!q.empty())o<auto&operator<<(ostream&o,map&m){for(auto&e:m)o<auto&operator<<(ostream&o,vectorv){for(auto&e:v)o<void ashow(T t,A...a){cout< struct TRI{S fi;T se;U th;TRI(){}TRI(S f,T s,U t):fi(f),se(s),th(t){} bool operator<(const TRI&_)const{return(fi==_.fi)?((se==_.se)?(th<_.th):(se<_.se)):(fi<_.fi);}}; template auto&operator<<(ostream&o,TRI&t){return o<<"{"< P; typedef pair pll; typedef TRI tri; typedef vector vi; typedef vector vl; typedef vector vvi; typedef vector vvl; typedef vector

vp; typedef vector vd; typedef vector vs; const int MAX_N = 200005; template class BSTNode { public: int from, to, sz; _Tp value, al, lazy; BSTNode *left, *right, *par; BSTNode(const int _from, const int _to) noexcept : from(_from), to(_to), sz(0), value(id1), al(id2), lazy(id1), left(nullptr), right(nullptr), par(nullptr){} BSTNode(const int _from, const int _to, const _Tp& _value) noexcept : from(_from), to(_to), sz(1), value(_value), al(value), lazy(id1), left(nullptr), right(nullptr), par(nullptr){} static const _Tp id1 = (_Tp)0; static const _Tp id2 = (_Tp)0; static void opr1(_Tp& arg1, const _Tp arg2) noexcept { arg1 += arg2; } static _Tp opr2(const _Tp arg1, const _Tp arg2) noexcept { return arg1 + arg2; } inline bool IsRoot() const noexcept { return !par; } inline bool IsVertex() const noexcept { return from == to; } void push() noexcept { if(lazy != id1){ if(IsVertex()) opr1(value, lazy); al += lazy * sz; if(left) opr1(left->lazy, lazy); if(right) opr1(right->lazy, lazy); lazy = id1; } } void eval() noexcept { sz = IsVertex(), al = value; if(left) left->push(), sz += left->sz, al = opr2(left->al, al); if(right) right->push(), sz += right->sz, al = opr2(al, right->al); } void rotate(const bool right_) noexcept { BSTNode *p = par, *g = p->par; if(right_){ if((p->left = right)) right->par = p; right = p, p->par = this; }else{ if((p->right = left)) left->par = p; left = p, p->par = this; } p->eval(), eval(); if(!(par = g)) return; if(g->left == p) g->left = this; if(g->right == p) g->right = this; g->eval(); } }; template BSTNode<_Tp>* splay(BSTNode<_Tp> *u) noexcept { if(!u) return nullptr; while(!(u->IsRoot())){ BSTNode<_Tp> *p = u->par, *gp = p->par; if(p->IsRoot()){ // zig p->push(), u->push(); u->rotate((u == p->left)); }else{ gp->push(), p->push(), u->push(); bool flag = (u == p->left); if((u == p->left) == (p == gp->left)){ // zig-zig p->rotate(flag), u->rotate(flag); }else{ // zig-zag u->rotate(flag), u->rotate(!flag); } } } u->push(); return u; } template BSTNode<_Tp>* join(BSTNode<_Tp> *root1, BSTNode<_Tp> *root2) noexcept { if(!root1 || !root2) return root1 ? root1 : root2; BSTNode<_Tp> *cur = nullptr, *nx = root1; do{ cur = nx, cur->push(), nx = cur->right; }while(nx); BSTNode<_Tp> *ver = splay(cur); ver->right = root2, ver->eval(), root2->par = ver; return ver; } template pair*, BSTNode<_Tp>*> split_lower_bond(BSTNode<_Tp> *ver) noexcept { BSTNode<_Tp> *res = splay(ver)->left; ver->left = nullptr, ver->eval(); if(res) res->par = nullptr; return make_pair(res, ver); } template pair*, BSTNode<_Tp>*> split_upper_bond(BSTNode<_Tp> *ver) noexcept { BSTNode<_Tp> *res = splay(ver)->right; ver->right = nullptr, ver->eval(); if(res) res->par = nullptr; return make_pair(ver, res); } template class EulerTourTree { private: struct pair_hash { template size_t operator() (const pair& p) const { size_t lhs = hash()(p.first), rhs = hash()(p.second); return lhs^(rhs+0x9e3779b9+(lhs<<6)+(lhs>>2)); } }; BSTNode** vertex_set; unordered_map, pair*, BSTNode*>, pair_hash> edge_set; BSTNode *reroot(BSTNode *ver) noexcept { BSTNode *res = splay(ver)->left; if(!res) return ver; ver->left = nullptr, ver->eval(); while(ver->right) ver->push(), ver = ver->right; splay(ver), ver->right = res, ver->eval(), res->par = ver; return ver; } void link(BSTNode *ver1, BSTNode *ver2) noexcept { BSTNode* e1 = new BSTNode(ver1->from, ver2->from); BSTNode* e2 = new BSTNode(ver2->from, ver1->from); edge_set[{ver1->from, ver2->from}] = {e1, e2}; join(join(reroot(ver1), e1), join(reroot(ver2), e2)); } void cut(BSTNode *edge1, BSTNode *edge2) noexcept { splay(edge1), splay(edge2); BSTNode *p = edge1->par; bool _right = (edge1 == edge2->right); if(p != edge2){ _right = (p == edge2->right); p->par = nullptr, edge1->rotate((edge1 == p->left)); } if(edge1->left) edge1->left->par = nullptr; if(edge1->right) edge1->right->par = nullptr; if(_right){ if(edge2->left) edge2->left->par = nullptr; join(edge2->left, edge1->right); }else{ if(edge2->right) edge2->right->par = nullptr; join(edge1->left, edge2->right); } // delete edge1; delete edge2; } bool IsConnected(BSTNode *ver1, BSTNode *ver2) noexcept { splay(ver1), splay(ver2); return ver1->par; } T& get(BSTNode *ver) noexcept { return splay(ver)->value; } void range(BSTNode *edge1, BSTNode *edge2, const T& val) noexcept { auto res1 = split_lower_bond(edge1); auto res2 = split_upper_bond(edge2); BSTNode::opr1(res2.first->lazy, val); join(join(res1.first,res2.first), res2.second); } T query(BSTNode *edge1, BSTNode *edge2) noexcept { auto res1 = split_lower_bond(edge1); auto res2 = split_upper_bond(edge2); T res = res2.first->al; return join(join(res1.first,res2.first), res2.second), res; } void dfs(const int u, const int p, const BSTNode *cur, bool *visit, vector*>& nodes, const vector >& G) noexcept { visit[u] = true; nodes.push_back(vertex_set[u]); for(auto& v : G[u]){ if(v != p){ BSTNode* e1 = new BSTNode(u, v); nodes.push_back(e1); dfs(v, u, cur, visit, nodes, G); BSTNode* e2 = new BSTNode(v, u); if(u < v) edge_set[{u, v}] = {e1, e2}; else edge_set[{v, u}] = {e2, e1}; nodes.push_back(e2); } } } void bst_build(vector* >& nodes) noexcept { int i, n = (int)nodes.size(), st = 2, isolate = ((n % 4 == 1) ? (n-1) : -1); while(st <= n){ for(i = st-1; i < n; i += 2*st){ nodes[i]->left = nodes[i-st/2], nodes[i-st/2]->par = nodes[i]; if(i+st/2 < n) nodes[i]->right = nodes[i+st/2], nodes[i+st/2]->par = nodes[i]; else if(isolate >= 0) nodes[i]->right = nodes[isolate], nodes[isolate]->par = nodes[i]; nodes[i]->eval(); } isolate = ((n % (4*st) >= st && (n % (4*st) < 2*st)) ? (i-2*st): isolate); st <<= 1; } } void build_forest(const vector >& forest) noexcept { bool *visit = new bool[V](); for(int i = 0; i < V; i++){ if(!visit[i]){ vector* > nodes; BSTNode *cur = nullptr; dfs(i, -1, cur, visit, nodes, forest); bst_build(nodes); } } delete[] visit; } void build_tree(const int root, const vector >& tree) noexcept { bool *visit = new bool[V](); vector* > nodes; BSTNode *cur = nullptr; dfs(root, -1, cur, visit, nodes, tree); bst_build(nodes); delete[] visit; } public: const int V; EulerTourTree(const vector& ver_value) noexcept : V((int)ver_value.size()){ vertex_set = new BSTNode*[V]; for(int i = 0; i < V; i++) vertex_set[i] = new BSTNode(i, i, ver_value[i]); } EulerTourTree(const vector& ver_value, const vector >& forest) noexcept : EulerTourTree(ver_value){ build_forest(forest); } EulerTourTree(const vector& ver_value, const int root, const vector >& tree) noexcept : EulerTourTree(ver_value){ build_tree(root, tree); } // ~EulerTourTree(){ // for(auto it : edge_set){ // delete (it.second).first; // delete (it.second).second; // } // for(int i = 0; i < V; ++i) delete vertex_set[i]; // delete[] vertex_set; // } // 根を node_id にする void reroot(const int node_id) noexcept { reroot(vertex_set[node_id]); } // 辺(node1_id, node2_id) を追加 void link(int node1_id, int node2_id) noexcept { if(node1_id > node2_id) swap(node1_id, node2_id); link(vertex_set[node1_id], vertex_set[node2_id]); } // 辺(node1_id, node2_id) を削除(逆向きでも問題ない) void cut(int node1_id, int node2_id){ if(node1_id > node2_id) swap(node1_id, node2_id); auto it = edge_set.find({node1_id, node2_id}); assert(it != edge_set.end()); BSTNode *edge1 = (it->second).first, *edge2 = (it->second).second; edge_set.erase(it); cut(edge1, edge2); } // node1_id と node2_id が同じ木(連結成分)に属するか bool IsConnected(const int node1_id, const int node2_id) noexcept { if(node1_id == node2_id) return true; return IsConnected(vertex_set[node1_id], vertex_set[node2_id]); } // 頂点 ver_id の値を取得 T& get(int ver_id) noexcept { return get(vertex_set[ver_id]); } // 頂点 ver_id の存在する連結成分内の頂点全体に val を加える void component_range(const int ver_id, const T& val){ range(ver_id, -1, val); } // 親が par_id であるような頂点 ver_id の部分木内に存在する頂点全体に val を加える void range(const int ver_id, const int par_id, const T& val){ if(par_id < 0) return BSTNode::opr1(splay(vertex_set[ver_id])->lazy, val); if(ver_id < par_id){ auto it = edge_set.find({ver_id, par_id}); assert(it != edge_set.end()); range((it->second).second, (it->second).first, val); }else{ auto it = edge_set.find({par_id, ver_id}); assert(it != edge_set.end()); range((it->second).first, (it->second).second, val); } } // 頂点 ver_id の存在する連結成分内の頂点全体の総和を取得 T component_query(const int ver_id){ return query(ver_id, -1); } // 親が par_id であるような頂点 ver_id の部分木内に存在する頂点全体の総和を取得 T query(const int ver_id, const int par_id){ if(par_id < 0) return splay(vertex_set[ver_id])->al; if(ver_id < par_id){ auto it = edge_set.find({ver_id, par_id}); assert(it != edge_set.end()); return query((it->second).second, (it->second).first); }else{ auto it = edge_set.find({par_id, ver_id}); assert(it != edge_set.end()); return query((it->second).first, (it->second).second); } } private: void check_dfs(const BSTNode* cur) const noexcept { cur->push(); if(cur->left) check_dfs(cur->left); if(cur->IsVertex()) cout <<"{" << (cur->from) << "," << (cur->value) << "} "; if(cur->right) check_dfs(cur->right); } }; #define getchar getchar_unlocked #define putchar putchar_unlocked inline int in() { int n = 0; short c; while ((c = getchar()) >= '0') n = n * 10 + c - '0'; return n; } inline void out(int n) { short res[10], i = 0; do { res[i++] = n % 10, n /= 10; } while (n); while (i) putchar(res[--i] + '0'); putchar('\n'); } int r[MAX_N]; struct SW { chrono::high_resolution_clock::time_point st,ed; void start() { st = chrono::high_resolution_clock::now(); } void end() { ed = chrono::high_resolution_clock::now(); cout << chrono::duration_cast(ed - st).count() << " msec" << endl; } }; int main() { int n = in(); rep(i,n) r[i] = in(); vector > G(n); rep(i,n-1){ int u = in(), v = in(); G[u-1].push_back(v-1), G[v-1].push_back(u-1); } EulerTourTree et(vi(n, 0), 0, G); rrep(i,n){ et.component_range(i, 1); for(auto& to : G[i]){ if(to < i) et.cut(to, i); } } int ans = 1; rep(i,n){ ans = (ll)ans * (et.get(i) + r[i]) % MOD; } out(ans); return 0; }