#include using namespace std; using ll = long long; template struct ConvexHullTrick { private: deque> H; inline int sgn(T x) { return x == 0 ? 0 : (x < 0 ? -1 : 1); } inline bool check(const pair &a, const pair &b, const pair &c) { if(b.second == a.second || c.second == b.second) { return sgn(b.first - a.first) * sgn(c.second - b.second) >= sgn(c.first - b.first) * sgn(b.second - a.second); } if(is_integral::value) { return (b.second - a.second) / (a.first - b.first) >= (c.second - b.second) / (b.first - c.first); } else { return (b.first - a.first) * sgn(c.second - b.second) / abs(b.second - a.second) >= (c.first - b.first) * sgn(b.second - a.second) / abs(c.second - b.second); } } inline T get_y(const pair &a, const T &x) { return a.first * x + a.second; } public: ConvexHullTrick() = default; bool empty() const { return H.empty(); } void clear() { H.clear(); } void add(T a, T b) { // O(n) in total if(!isMin) { a *= -1, b *= -1; } pair line(a, b); if(empty()) { H.emplace_front(line); return; } if(H.front().first <= a) { if(H.front().first == a) { if(H.front().second <= b) { return; } H.pop_front(); } while(H.size() >= 2 && check(line, H.front(), H[1])) { H.pop_front(); } H.emplace_front(line); } else { assert(a <= H.back().first); if(H.back().first == a) { if(H.back().second <= b) { return; } H.pop_back(); } while(H.size() >= 2 && check(H[H.size() - 2], H.back(), line)) { H.pop_back(); } H.emplace_back(line); } } T query(T x) { // O(log n) assert(!empty()); int l = -1, r = H.size() - 1; while(l + 1 < r) { int m = (l + r) >> 1; get_y(H[m], x) >= get_y(H[m + 1], x) ? l = m : r = m; } return isMin ? get_y(H[r], x) : -get_y(H[r], x); } T query_inc(T x) { // query の x が広義単調増加の場合,全体で O(n+q) assert(!empty()); while(H.size() >= 2 && get_y(H.front(), x) >= get_y(H[1], x)) { H.pop_front(); } return isMin ? get_y(H.front(), x) : -get_y(H.front(), x); } T query_dec(T x) { // query の x が広義単調減少の場合,全体で O(n+q) assert(!empty()); while(H.size() >= 2 && get_y(H.back(), x) >= get_y(H[H.size() - 2], x)) { H.pop_back(); } return isMin ? get_y(H.back(), x) : -get_y(H.back(), x); } }; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); ll N, M; cin >> N >> M; vector W(N); for(auto &i : W) { cin >> i; } vector>> g(N); for(ll i = 0, u, v, t; i < M; i++) { cin >> u >> v >> t; u--, v--; g[u].emplace_back(v, t); g[v].emplace_back(u, t); } auto Dijkstra = [&](ll s) { auto chmin = [&](auto &a, const auto &b) { return a > b ? (a = b, true) : false; }; vector d(N, 1e18); d[s] = 0; priority_queue, vector>, greater>> q; q.emplace(0, s); while(!q.empty()) { auto [tmp, v] = q.top(); q.pop(); if(tmp > d[v]) { continue; } for(auto &[nv, c] : g[v]) { if(chmin(d[nv], d[v] + c)) { q.emplace(d[nv], nv); } } } return d; }; auto s = Dijkstra(0), t = Dijkstra(N - 1); vector idx(N); iota(idx.begin(), idx.end(), 0); ranges::sort(idx, [&](auto i, auto j) { return W[i] < W[j]; }); ConvexHullTrick C; for(ll i = 0; i < N; i++) { C.add(W[idx[i]], t[idx[i]]); } ll ans = s[N - 1]; for(ll i = 0; i < N; i++) { ans = min(ans, s[idx[i]] + C.query_inc(W[idx[i]])); } cout << ans << "\n"; }