#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef LOCAL # include "debug_print.hpp" # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using namespace std; #define rep1(a) for(int i = 0; i < a; i++) #define rep2(i, a) for(int i = 0; i < a; i++) #define rep3(i, a, b) for(int i = a; i < b; i++) #define rep4(i, a, b, c) for(int i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(a) for(int i = (a)-1; i >= 0; i--) #define rrep2(i, a) for(int i = (a)-1; i >= 0; i--) #define rrep3(i, a, b) for(int i = (b)-1; i >= a; i--) #define rrep4(i, a, b, c) for(int i = (b)-1; i >= a; i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ); #define pb push_back using ll = long long; using D = double; using LD = long double; using P = pair; using vi = vector; using vl = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) template using PQ = priority_queue>; template using minPQ = priority_queue, greater>; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } #line 1 "structure/convex-hull-trick/convex-hull-trick-add-monotone.hpp" template struct ConvexHullTrickAddMonotone { #define F first #define S second using P = pair; deque

H; ConvexHullTrickAddMonotone() = default; bool empty() const { return H.empty(); } void clear() { H.clear(); } static constexpr int sgn(T x) { return x == 0 ? 0 : (x < 0 ? -1 : 1); } static constexpr T floor_div(T n, T d) { return n / d - ((n ^ d) < 0 and n % d != 0); } static constexpr bool check(const P &a, const P &b, const P &c) { if (b.S == a.S || c.S == b.S) return sgn(b.F - a.F) * sgn(c.S - b.S) >= sgn(c.F - b.F) * sgn(b.S - a.S); // return (b.F-a.F)*(c.S-b.S) >= (b.S-a.S)*(c.F-b.F); if constexpr (is_integral::value) { return floor_div(b.S - a.S, a.F - b.F) >= floor_div(c.S - b.S, b.F - c.F); } else { return (b.F - a.F) * sgn(c.S - b.S) / abs(b.S - a.S) >= (c.F - b.F) * sgn(b.S - a.S) / abs(c.S - b.S); } } void add(T a, T b) { if (!isMin) a *= -1, b *= -1; P line(a, b); if (empty()) { H.emplace_front(line); return; } if (H.front().F <= a) { if (H.front().F == a) { if (H.front().S <= 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().F); if (H.back().F == a) { if (H.back().S <= b) return; H.pop_back(); } while (H.size() >= 2 && check(H[H.size() - 2], H.back(), line)) H.pop_back(); H.emplace_back(line); } } static constexpr T get_y(const P &a, const T &x) { return a.F * x + a.S; } T query(T x) const { assert(!empty()); int l = -1, r = H.size() - 1; while (l + 1 < r) { int m = (l + r) >> 1; if (get_y(H[m], x) >= get_y(H[m + 1], x)) l = m; else r = m; } if (isMin) return get_y(H[r], x); return -get_y(H[r], x); } T query_monotone_inc(T x) { assert(!empty()); while (H.size() >= 2 && get_y(H.front(), x) >= get_y(H[1], x)) H.pop_front(); if (isMin) return get_y(H.front(), x); return -get_y(H.front(), x); } T query_monotone_dec(T x) { assert(!empty()); while (H.size() >= 2 && get_y(H.back(), x) >= get_y(H[H.size() - 2], x)) H.pop_back(); if (isMin) return get_y(H.back(), x); return -get_y(H.back(), x); } #undef F #undef S }; int main(){ ios_base::sync_with_stdio(false); cin.tie(nullptr); int n,m; in(n,m); vector w(n); in(w); vector>> g(n); rep(i,m){ int u,v; ll t; in(u,v,t); u--; v--; g[u].pb({v,t}); g[v].pb({u,t}); } const ll INF = 2000000000000000000LL; vector d(n,INF),e(n,INF); d[0] = e[n-1] = 0; minPQ> pq; pq.emplace(0,0); while(!pq.empty()){ auto [cd,cv] = pq.top(); pq.pop(); if(d[cv] < cd) continue; for(auto&& [nv, w] : g[cv]){ if(chmin(d[nv], w+cd)){ pq.emplace(d[nv],nv); } } } pq.emplace(0,n-1); while(!pq.empty()){ auto [cd,cv] = pq.top(); pq.pop(); if(e[cv] < cd) continue; for(auto&& [nv, w] : g[cv]){ if(chmin(e[nv], w+cd)){ pq.emplace(e[nv],nv); } } } ConvexHullTrickAddMonotone t; vector idx(n); iota(ALL(idx),0); sort(ALL(idx), [&] (const int i, const int j){ return w[i] < w[j]; }); rep(i,n)if(e[idx[i]]!=INF) t.add(w[idx[i]],e[idx[i]]); ll ans = min(w[0]*w[n-1],d[n-1]); rep(i,n)if(d[idx[i]]!=INF and !t.empty()){ chmin(ans, t.query_monotone_inc(w[idx[i]])+d[idx[i]]); } out(ans); }