#include #include using namespace std; using namespace atcoder; istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); } istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); } istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } typedef long long ll; typedef pair pii; typedef pair pll; #define FOR(i,l,r) for (int i = l;i < (int)(r); i++) #define rep(i,n) for (int i = 0;i < (int)(n); i++) #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define my_sort(x) sort(x.begin(), x.end()) #define my_max(x) *max_element(all(x)) #define my_min(x) *min_element(all(x)) template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } const int INF = (1<<30) - 1; const ll LINF = (1LL<<62) - 1; const int MOD = 998244353; const int MOD2 = 1e9+7; const double PI = acos(-1); vector di = {1,0,-1,0}; vector dj = {0,1,0,-1}; #ifdef LOCAL # include # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using Edge = pair; using Graph = vector>; vector dijkstra(int st, Graph &g){ int N = g.size(); vector dist(N, LINF); dist[st] = 0ll; using P = pair; priority_queue, greater

> pq; pq.emplace(P{0ll, st}); while(!pq.empty()){ ll time = pq.top().first; int now = pq.top().second; pq.pop(); if (time > dist[now])continue; for(auto e : g[now]){ ll c = e.first; int nxt = e.second; if (c + time < dist[nxt]){ dist[nxt] = c + time; pq.push(P{c + time, nxt}); } } } return dist; } template class ConvexHullTrick { 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_line(node *cur, node *nw, T l, T r){ while(true){ if(nw->f(l) < cur->f(l)) swap(cur, nw); if(cur->f(r - 1) <= nw->f(r - 1)) break; const T mid = (l + r) / 2; if(cur->f(mid) <= nw->f(mid)){ if(!cur->right){ cur->right = new node(*nw); break; }else{ cur = cur->right, l = mid; } }else{ swap(cur, nw); if(!cur->left){ cur->left = new node(*nw); break; }else{ cur = cur->left, r = mid; } } } } T query(node *cur, const T k, T l, T r) const { T ans = numeric_limits::max(); while(cur){ ans = min(ans, cur->f(k)); const T mid = (l + r) / 2; if(k < mid){ cur = cur->left, r = mid; }else{ cur = cur->right, l = mid; } } return ans; } void clear(node *cur){ if(cur->left) clear(cur->left); if(cur->right) clear(cur->right); delete cur; } const T lpos, rpos; node *root; public: ConvexHullTrick(const T _lpos, const T _rpos) : lpos(_lpos), rpos(_rpos), root(new node()){ assert(lpos < rpos); } // ~ConvexHullTrick(){ clear(root); } // f(x) = a * x + b を挿入 void add_line(const T a, const T b){ node nw(a, b); return _add_line(root, &nw, lpos, rpos); } // x = k での最小値 T query(const T k) const { return query(root, k, lpos, rpos); } }; // 最大値は add_line(-a, -b) で -query(x) // https://ei1333.github.io/library/structure/convex-hull-trick/dynamic-li-chao-tree.hpp.html int main(){ cin.tie(0); ios_base::sync_with_stdio(false); int N, M; cin >> N >> M; vector W(N); rep(i,N) cin >> W[i]; Graph g(N); rep(i,M){ int u, v; cin >> u >> v; u--; v--; ll T; cin >> T; g[u].push_back({T, v}); g[v].push_back({T, u}); } auto dist1 = dijkstra(0, g); auto distN = dijkstra(N - 1, g); debug(dist1, distN); ConvexHullTrick cht(1, (ll)1e9); rep(j, N) cht.add_line(W[j], distN[j]); ll ans = dist1[N - 1]; rep(i, N) { chmin(ans, dist1[i] + cht.query(W[i])); debug(dist1[i], cht.query(W[i]), W[i]); } cout << ans << endl; }