#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #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 all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; constexpr long long INF = 1002003004005006007; vector dijkstra(const auto& to, int s = 0) { struct QueElem { int v; long long d; bool operator<(const QueElem& a) const { return d > a.d; } QueElem(int v, long long d) : v(v), d(d) {} }; priority_queue q; vector dist(to.size(), INF); dist[s] = 0; q.emplace(s, 0); while (!q.empty()) { auto [u, d] = q.top(); q.pop(); if (d > dist[u]) continue; for (auto [v, dv] : to[u]) { long long nd = d + dv; if (nd < dist[v]) { dist[v] = nd; q.emplace(v, nd); } } } return dist; } /** * @brief Dynamic-Li-Chao-Tree * */ template struct DynamicLiChaoTree { struct Line { T a, b; Line(T a, T b) : a(a), b(b) {} inline T get(T x) const { return a * x + b; } }; struct Node { Line x; Node *l, *r; Node(const Line &x) : x{x}, l{nullptr}, r{nullptr} {} }; Node *root; DynamicLiChaoTree() : root{nullptr} {} Node *add_line(Node *t, Line &x, const T &l, const T &r, const T &x_l, const T &x_r) { if (!t) return new Node(x); T t_l = t->x.get(l), t_r = t->x.get(r); if (t_l <= x_l && t_r <= x_r) { return t; } else if (t_l >= x_l && t_r >= x_r) { t->x = x; return t; } else { T m = (l + r) / 2; if (m == r) --m; T t_m = t->x.get(m), x_m = x.get(m); if (t_m > x_m) { swap(t->x, x); if (x_l >= t_l) t->l = add_line(t->l, x, l, m, t_l, t_m); else t->r = add_line(t->r, x, m + 1, r, t_m + x.a, t_r); } else { if (t_l >= x_l) t->l = add_line(t->l, x, l, m, x_l, x_m); else t->r = add_line(t->r, x, m + 1, r, x_m + x.a, x_r); } return t; } } void add_line(const T &a, const T &b) { Line x(a, b); root = add_line(root, x, x_low, x_high, x.get(x_low), x.get(x_high)); } Node *add_segment(Node *t, Line &x, const T &a, const T &b, const T &l, const T &r, const T &x_l, const T &x_r) { if (r < a || b < l) return t; if (a <= l && r <= b) { Line y{x}; return add_line(t, y, l, r, x_l, x_r); } if (t) { T t_l = t->x.get(l), t_r = t->x.get(r); if (t_l <= x_l && t_r <= x_r) return t; } else { t = new Node(Line(0, id)); } T m = (l + r) / 2; if (m == r) --m; T x_m = x.get(m); t->l = add_segment(t->l, x, a, b, l, m, x_l, x_m); t->r = add_segment(t->r, x, a, b, m + 1, r, x_m + x.a, x_r); return t; } void add_segment(const T &l, const T &r, const T &a, const T &b) { Line x(a, b); root = add_segment(root, x, l, r - 1, x_low, x_high, x.get(x_low), x.get(x_high)); } T query(const Node *t, const T &l, const T &r, const T &x) const { if (!t) return id; if (l == r) return t->x.get(x); T m = (l + r) / 2; if (m == r) --m; if (x <= m) return min(t->x.get(x), query(t->l, l, m, x)); else return min(t->x.get(x), query(t->r, m + 1, r, x)); } T query(const T &x) const { return query(root, x_low, x_high, x); } }; } int main() { ios::sync_with_stdio(false); cin.tie(0); int n, m; cin >> n >> m; VI w(n); rep(i, n) cin >> w[i]; vector>> to(n); rep(_, m) { int u, v; ll t; cin >> u >> v >> t; u--, v--; to[u].emplace_back(v, t); to[v].emplace_back(u, t); } auto dist1 = dijkstra(to); auto dist2 = dijkstra(to, n - 1); DynamicLiChaoTree cht; rep(i, n) cht.add_line(w[i], dist2[i]); ll ans = dist1[n - 1]; rep(i, n) chmin(ans, dist1[i] + cht.query(w[i])); cout << ans << '\n'; }