#include #ifdef LOCAL #include #else #define debug(...) void(0) #endif template std::istream& operator>>(std::istream& is, std::vector& v) { for (auto& e : v) { is >> e; } return is; } template std::ostream& operator<<(std::ostream& os, const std::vector& v) { for (std::string_view sep = ""; const auto& e : v) { os << std::exchange(sep, " ") << e; } return os; } template bool chmin(T& x, U&& y) { return y < x and (x = std::forward(y), true); } template bool chmax(T& x, U&& y) { return x < y and (x = std::forward(y), true); } template void mkuni(std::vector& v) { std::ranges::sort(v); auto result = std::ranges::unique(v); v.erase(result.begin(), result.end()); } template int lwb(const std::vector& v, const T& x) { return std::distance(v.begin(), std::ranges::lower_bound(v, x)); } struct Line { mutable long long k, m, p; bool operator<(const Line& o) const { return k < o.k; } bool operator<(long long x) const { return p < x; } }; template struct LineContainer : std::multiset> { // (for doubles, use inf = 1/.0, div(a,b) = a/b) const long long inf = LLONG_MAX / 2; long long div(long long a, long long b) { // floored division return a / b - ((a ^ b) < 0 && a % b); } bool isect(iterator x, iterator y) { if (y == end()) { x->p = inf; return false; } 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(long long k, long long m) { if (isMin) k = -k, m = -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)); } long long query(long long x) { assert(!empty()); auto l = *lower_bound(x); long long s = 1; if (isMin) s = -1; return s * (l.k * x + l.m); } }; using ll = long long; using namespace std; constexpr ll INF = 4e18; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); int N, M; cin >> N >> M; vector W(N); cin >> W; vector>> G(N); for (; M--;) { int U, V; ll T; cin >> U >> V >> T; U--, V--; G[U].emplace_back(V, T); G[V].emplace_back(U, T); } auto calc = [&](int s) { vector dp(N, INF); priority_queue> pq; dp[s] = 0; pq.emplace(-dp[s], s); while (not pq.empty()) { auto [val, v] = pq.top(); pq.pop(); val *= -1; if (dp[v] != val) continue; for (auto [u, cost] : G[v]) { if (chmin(dp[u], val + cost)) { pq.emplace(-dp[u], u); } } } return dp; }; auto f = calc(0), g = calc(N - 1); ll ans = f[N - 1]; LineContainer lc; for (int i = 0; i < N; i++) lc.add(W[i], g[i]); for (int i = 0; i < N; i++) chmin(ans, f[i] + lc.query(W[i])); cout << ans << '\n'; return 0; }