// #define _GLIBCXX_DEBUG // #pragma GCC optimize("O2,unroll-loops") #include using namespace std; #define rep(i, n) for (int i = 0; i < int(n); i++) #define per(i, n) for (int i = (n)-1; 0 <= i; i--) #define rep2(i, l, r) for (int i = (l); i < int(r); i++) #define per2(i, l, r) for (int i = (r)-1; int(l) <= i; i--) #define each(e, v) for (auto &e : v) #define MM << " " << #define pb push_back #define eb emplace_back #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define sz(x) (int)x.size() template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } using ll = long long; using pii = pair; using pll = pair; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template using minheap = std::priority_queue, std::greater>; template using maxheap = std::priority_queue; template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } // __int128_t gcd(__int128_t a, __int128_t b) { // if (a == 0) // return b; // if (b == 0) // return a; // __int128_t cnt = a % b; // while (cnt != 0) { // a = b; // b = cnt; // cnt = a % b; // } // return b; // } struct Union_Find_Tree { vector data; const int n; int cnt; Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {} int root(int x) { if (data[x] < 0) return x; return data[x] = root(data[x]); } int operator[](int i) { return root(i); } bool unite(int x, int y) { x = root(x), y = root(y); if (x == y) return false; // if (data[x] > data[y]) swap(x, y); data[x] += data[y], data[y] = x; cnt--; return true; } int size(int x) { return -data[root(x)]; } int count() { return cnt; }; bool same(int x, int y) { return root(x) == root(y); } void clear() { cnt = n; fill(begin(data), end(data), -1); } }; template struct Mod_Int { int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} static int get_mod() { return mod; } Mod_Int &operator+=(const Mod_Int &p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator-=(const Mod_Int &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator*=(const Mod_Int &p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int &operator/=(const Mod_Int &p) { *this *= p.inverse(); return *this; } Mod_Int &operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int &p) const { return x == p.x; } bool operator!=(const Mod_Int &p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Mod_Int &p) { long long a; is >> a; p = Mod_Int(a); return is; } }; ll mpow(ll x, ll n, ll mod) { ll ans = 1; x %= mod; while (n != 0) { if (n & 1) ans = ans * x % mod; x = x * x % mod; n = n >> 1; } ans %= mod; return ans; } template T modinv(T a, const T &m) { T b = m, u = 1, v = 0; while (b > 0) { T t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return u >= 0 ? u % m : (m - (-u) % m) % m; } ll divide_int(ll a, ll b) { if (b < 0) a = -a, b = -b; return (a >= 0 ? a / b : (a - b + 1) / b); } // const int MOD = 1000000007; const int MOD = 998244353; using mint = Mod_Int; // ----- library ------- template struct Li_Chao_Tree { struct Line { T a, b; Line(const T &a, const T &b) : a(a), b(b) {} T get(const T &x) const { return a * x + b; } }; struct Node { Node *lch, *rch; Line l; Node(const Line &l) : lch(NULL), rch(NULL), l(l) {} Node(const T &a, const T &b) : lch(NULL), rch(NULL), l(a, b) {} }; Node *root; const T INF_T = numeric_limits::max() / 2; Li_Chao_Tree() : root(NULL) {} ~Li_Chao_Tree() { rec_delete(root); } void rec_delete(Node *now) { if (!now) return; rec_delete(now->lch), rec_delete(now->rch); delete now; } Node *add_line(const Line &k, Node *now, const T &l, const T &r) { if (!now) return new Node(k); T l1 = now->l.get(l), l2 = k.get(l); T r1 = now->l.get(r), r2 = k.get(r); if (l1 <= l2 && r1 <= r2) return now; if (l1 >= l2 && r1 >= r2) { now->l = k; return now; } T m = (l + r - 1) / 2; T m1 = now->l.get(m), m2 = k.get(m); if (m1 > m2) { if (l1 <= l2) { now->lch = add_line(now->l, now->lch, l, m); } else { now->rch = add_line(now->l, now->rch, m + 1, r); } now->l = k; } else { if (l1 >= l2) { now->lch = add_line(k, now->lch, l, m); } else { now->rch = add_line(k, now->rch, m + 1, r); } } return now; } // 直線 y = ax+b を追加 void add_line(const T &a, const T &b) { Line k(is_min ? a : -a, is_min ? b : -b); root = add_line(k, root, min_x, max_x); } Node *add_segment(const T &s, const T &t, const Line &k, Node *now, const T &l, const T &r) { if (r < s || t < l) return now; if (s <= l && r <= t) return add_line(k, now, l, r); T m = (l + r - 1) / 2; if (!now) now = new Node(0, INF_T); now->lch = add_segment(s, t, k, now->lch, l, m); now->rch = add_segment(s, t, k, now->rch, m + 1, r); return now; } // [l,r) に直線 y = ax+b を追加 void add_segment(const T &l, const T &r, const T &a, const T &b) { Line k(is_min ? a : -a, is_min ? b : -b); root = add_segment(l, r - 1, k, root, min_x, max_x); } T query(const T &x, Node *now, const T &l, const T &r) const { if (!now) return INF_T; if (l == r) return now->l.get(x); T m = (l + r - 1) / 2; if (x <= m) return min(now->l.get(x), query(x, now->lch, l, m)); return min(now->l.get(x), query(x, now->rch, m + 1, r)); } T query(const T &x) const { T ret = query(x, root, min_x, max_x); return is_min ? ret : -ret; } }; // ----- library ------- int main() { ios::sync_with_stdio(false); std::cin.tie(nullptr); cout << fixed << setprecision(15); int n, m; cin >> n >> m; vector w(n); rep(i, n) cin >> w[i]; vector>> g(n); rep(i, m) { int u, v; ll t; cin >> u >> v >> t; u--, v--; g[u].eb(v, t); g[v].eb(u, t); } vector d1(n, 3e18), dn(n, 3e18); minheap> que; auto upd1 = [&](int i, ll d) { if (chmin(d1[i], d)) que.emplace(d, i); }; upd1(0, 0); while (sz(que)) { auto [nd, now] = que.top(); que.pop(); if (d1[now] != nd) continue; for (auto [to, cost] : g[now]) { upd1(to, nd + cost); } } auto updn = [&](int i, ll d) { if (chmin(dn[i], d)) que.emplace(d, i); }; updn(n - 1, 0); while (sz(que)) { auto [nd, now] = que.top(); que.pop(); if (dn[now] != nd) continue; for (auto [to, cost] : g[now]) { updn(to, nd + cost); } } Li_Chao_Tree lct; rep(i, n) lct.add_line(w[i], dn[i]); ll ans = dn[0]; rep(i, n) chmin(ans, lct.query(w[i]) + d1[i]); cout << ans << endl; }