#include #include #include using namespace atcoder; using mint = modint998244353; using namespace std; #define rep(i,n) for (int i = 0; i < (n); ++i) #define Inf32 1000000001 #define Inf64 1000000000000000001 /** * Author: Simon Lindholm * Date: 2017-04-20 * License: CC0 * Source: own work * Description: Container where you can add lines of the form kx+m, and query maximum values at points x. * Useful for dynamic programming (``convex hull trick''). * Time: O(\log N) * Status: stress-tested */ using ll =long long; struct Line { mutable ll k, m, p; bool operator<(const Line& o) const { return k < o.k; } bool operator<(ll x) const { return p < x; } }; struct LineContainer : multiset> { // (for doubles, use inf = 1/.0, div(a,b) = a/b) static const ll inf = LLONG_MAX - 1000000000LL; ll div(ll a, ll b) { // floored division return a / b - ((a ^ b) < 0 && a % b); } bool isect(iterator x, iterator y) { if (y == end()) return x->p = inf, 0; if (x->k == y->k) x->p = x->m > y->m ? inf : -inf; else x->p = div(y->m - x->m, x->k - y->k); return x->p >= y->p; } void add(ll k, ll m) { auto z = insert({k, m, 0}), y = z++, x = y; while (isect(y, z)) z = erase(z); if (x != begin() && isect(--x, y)) isect(x, y = erase(y)); while ((y = x) != begin() && (--x)->p >= y->p) isect(x, erase(y)); } ll query(ll x) { assert(!empty()); auto l = *lower_bound(x); return l.k * x + l.m; } }; vector get_distance(vector>> &E,int s){ int N = E.size(); vector dist(N,Inf64); dist[s] = 0; priority_queue,vector>,greater>> pq; pq.push({0,s}); while(!pq.empty()){ auto [d,u] = pq.top(); pq.pop(); if(dist[u] !=d )continue; for(auto [v,w]:E[u]){ if(dist[v] > dist[u] + w){ dist[v] = dist[u] + w; pq.push({dist[v],v}); } } } return dist; } int main(){ int N,M; cin>>N>>M; vector w(N); rep(i,N)cin>>w[i]; vector>> E(N); rep(i,M){ int u,v; long long ww; cin>>u>>v>>ww; u--,v--; E[u].emplace_back(v,ww); E[v].emplace_back(u,ww); //E[v].push_back({u,ww}); } auto x = get_distance(E,0),y = get_distance(E,N-1); long long ans = x[N-1]; LineContainer cht; rep(i,N){ if(x[i]==Inf64)continue; cht.add(-w[i],-x[i]); } if(!cht.empty()){ rep(i,N){ if(y[i]==Inf64)continue; ans = min(ans,-cht.query(w[i]) + y[i]); } } cout<