#include using namespace std; #if __has_include() #include using namespace atcoder; templateistream &operator>>(istream &is,static_modint &a){long long b;is>>b;a=b;return is;} istream &operator>>(istream &is,modint &a){long long b;cin>>b;a=b;return is;} #endif #ifdef LOCAL #include "debug.h" #else #define debug(...) static_cast(0) #define debugg(...) static_cast(0) #define esper(...) static_cast(0) templateostream &operator<<(ostream &os,const pair&p){os<; templateusing minque=priority_queue,greater>; templatebool chmax(T &a,const T &b){return (abool chmin(T &a,const T &b){return (a>b?(a=b,true):false);} templateistream &operator>>(istream &is,pair&p){is>>p.first>>p.second;return is;} templateistream &operator>>(istream &is,vector &a){for(auto &i:a)is>>i;return is;} templatevoid operator++(pair&a,int n){a.first++,a.second++;} templatevoid operator--(pair&a,int n){a.first--,a.second--;} templatevoid operator++(vector&a,int n){for(auto &i:a)i++;} templatevoid operator--(vector&a,int n){for(auto &i:a)i--;} #define reps(i,a,n) for(int i=(a);i<(n);i++) #define rep(i,n) reps(i,0,n) #define all(x) x.begin(),x.end() #define pcnt(x) __builtin_popcountll(x) #define fin(x) return cout<(0) ll myceil(ll a,ll b){return (a+b-1)/b;} template auto vec(const int (&d)[n],const T &init=T()){ if constexpr (id(d,init)); else return init; } void SOLVE(); int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); cout<>testcase; for(int i=0;i struct convex_hull_trick{ private: struct node{ node *left,*right; static const T inf=numeric_limits::max(); T a,b; node():node(0,inf){} node(const T a,const T b):left(nullptr),right(nullptr),a(a),b(b){} T f(const T x)const{return a*x+b;} }; static void swap(node *x,node *y){ std::swap(x->a,y->a),std::swap(x->b,y->b); } void add(node *cu,node *nw,T l,T r){ while(true){ if(nw->f(l)f(l))swap(cu,nw); if(cu->f(r-1)<=nw->f(r-1))return; T mid=(l+r)/2; if(cu->f(mid)<=nw->f(mid)){ if(!cu->right){ cu->right=new node(*nw); return; } else{ cu=cu->right,l=mid; } } else{ swap(cu,nw); if(!cu->left){ cu->left=new node(*nw); return; } else{ cu=cu->left,r=mid; } } } } T query(node *cu,T k,T l,T r)const{ T ans=numeric_limits::max(); while(cu){ chmin(ans,cu->f(k)); T mid=(l+r)/2; if(kleft,r=mid; } else{ cu=cu->right,l=mid; } } return ans; } void clear(node *cu){ if(cu->left)clear(cu->left); if(cu->right)clear(cu->right); delete cu; } const T l,r; node *root; public: convex_hull_trick(const T l,const T r):l(l),r(r),root(new node()){ assert(l>n>>m; vectorw(n); cin>>w; vector>>to(n); rep(i,m){ int u,v,t; cin>>u>>v>>t; u--,v--; to[u].push_back({v,t}); to[v].push_back({u,t}); } auto dij=[&](int st)->vector { vectordst(n,1e18); dst[st]=0; minque>que; que.push({0,st}); while(!que.empty()){ auto [d,x]=que.top();que.pop(); if(dst[x]!=d)continue; for(auto i:to[x])if(chmin(dst[i.first],d+i.second))que.push({dst[i.first],i.first}); } return dst; }; vectorl=dij(0),r=dij(n-1); ll ans=l[n-1]; convex_hull_trickcht(-1e11,1e11); rep(i,n)cht.add(w[i],l[i]); rep(i,n)chmin(ans,cht.query(w[i])+r[i]); cout<