// #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") // #define INTERACTIVE #include using namespace std; namespace templates { // type using ll = long long; using ull = unsigned long long; using Pii = pair; using Pil = pair; using Pli = pair; using Pll = pair; template using pq = priority_queue; template using qp = priority_queue, greater>; // clang-format off #define vec(T, A, ...) vector A(__VA_ARGS__); #define vvec(T, A, h, ...) vector> A(h, vector(__VA_ARGS__)); #define vvvec(T, A, h1, h2, ...) vector>> A(h1, vector>(h2, vector(__VA_ARGS__))); // clang-format on // for loop #define fori1(a) for (ll _ = 0; _ < (a); _++) #define fori2(i, a) for (ll i = 0; i < (a); i++) #define fori3(i, a, b) for (ll i = (a); i < (b); i++) #define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c)) #define overload4(a, b, c, d, e, ...) e #define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__) // declare and input // clang-format off #define INT(...) int __VA_ARGS__; inp(__VA_ARGS__); #define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__); #define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__); #define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__); #define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___); #define VEC(T, A, n) vector A(n); inp(A); #define VVEC(T, A, n, m) vector> A(n, vector(m)); inp(A); // clang-format on // const value const ll MOD1 = 1000000007; const ll MOD9 = 998244353; const double PI = acos(-1); // other macro #if !defined(RIN__LOCAL) && !defined(INTERACTIVE) #define endl "\n" #endif #define spa ' ' #define len(A) ll(A.size()) #define all(A) begin(A), end(A) // function vector stoc(string &S) { int n = S.size(); vector ret(n); for (int i = 0; i < n; i++) ret[i] = S[i]; return ret; } string ctos(vector &S) { int n = S.size(); string ret = ""; for (int i = 0; i < n; i++) ret += S[i]; return ret; } template auto min(const T &a) { return *min_element(all(a)); } template auto max(const T &a) { return *max_element(all(a)); } template auto clamp(T &a, const S &l, const S &r) { return (a > r ? r : a < l ? l : a); } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } template inline bool chclamp(T &a, const S &l, const S &r) { auto b = clamp(a, l, r); return (a != b ? a = b, 1 : 0); } template T sum(vector &A) { T tot = 0; for (auto a : A) tot += a; return tot; } template vector compression(vector X) { sort(all(X)); X.erase(unique(all(X)), X.end()); return X; } // input and output namespace io { // __int128_t std::ostream &operator<<(std::ostream &dest, __int128_t value) { std::ostream::sentry s(dest); if (s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if (dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } // vector template istream &operator>>(istream &is, vector &A) { for (auto &a : A) is >> a; return is; } template ostream &operator<<(ostream &os, vector &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << ' '; } return os; } // vector> template istream &operator>>(istream &is, vector> &A) { for (auto &a : A) is >> a; return is; } template ostream &operator<<(ostream &os, vector> &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << endl; } return os; } // pair template istream &operator>>(istream &is, pair &A) { is >> A.first >> A.second; return is; } template ostream &operator<<(ostream &os, pair &A) { os << A.first << ' ' << A.second; return os; } // vector> template istream &operator>>(istream &is, vector> &A) { for (size_t i = 0; i < A.size(); i++) { is >> A[i]; } return is; } template ostream &operator<<(ostream &os, vector> &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << endl; } return os; } // tuple template struct TuplePrint { static ostream &print(ostream &os, const T &t) { TuplePrint::print(os, t); os << ' ' << get(t); return os; } }; template struct TuplePrint { static ostream &print(ostream &os, const T &t) { os << get<0>(t); return os; } }; template ostream &operator<<(ostream &os, const tuple &t) { TuplePrint::print(os, t); return os; } // io functions void FLUSH() { cout << flush; } void print() { cout << endl; } template void print(Head &&head, Tail &&...tail) { cout << head; if (sizeof...(Tail)) cout << spa; print(std::forward(tail)...); } template void prisep(vector &A, S sep) { int n = A.size(); for (int i = 0; i < n; i++) { cout << A[i]; if (i != n - 1) cout << sep; } cout << endl; } template void priend(T A, S end) { cout << A << end; } template void prispa(T A) { priend(A, spa); } template bool printif(bool f, T A, S B) { if (f) print(A); else print(B); return f; } template void inp(T &...a) { (cin >> ... >> a); } } // namespace io using namespace io; // read graph vector> read_edges(int n, int m, bool direct = false, int indexed = 1) { vector> edges(n, vector()); for (int i = 0; i < m; i++) { INT(u, v); u -= indexed; v -= indexed; edges[u].push_back(v); if (!direct) edges[v].push_back(u); } return edges; } vector> read_tree(int n, int indexed = 1) { return read_edges(n, n - 1, false, indexed); } template vector>> read_wedges(int n, int m, bool direct = false, int indexed = 1) { vector>> edges(n, vector>()); for (int i = 0; i < m; i++) { INT(u, v); T w; inp(w); u -= indexed; v -= indexed; edges[u].push_back({v, w}); if (!direct) edges[v].push_back({u, w}); } return edges; } template vector>> read_wtree(int n, int indexed = 1) { return read_wedges(n, n - 1, false, indexed); } // yes / no namespace yesno { // yes inline bool yes(bool f = true) { cout << (f ? "yes" : "no") << endl; return f; } inline bool Yes(bool f = true) { cout << (f ? "Yes" : "No") << endl; return f; } inline bool YES(bool f = true) { cout << (f ? "YES" : "NO") << endl; return f; } // no inline bool no(bool f = true) { cout << (!f ? "yes" : "no") << endl; return f; } inline bool No(bool f = true) { cout << (!f ? "Yes" : "No") << endl; return f; } inline bool NO(bool f = true) { cout << (!f ? "YES" : "NO") << endl; return f; } // possible inline bool possible(bool f = true) { cout << (f ? "possible" : "impossible") << endl; return f; } inline bool Possible(bool f = true) { cout << (f ? "Possible" : "Impossible") << endl; return f; } inline bool POSSIBLE(bool f = true) { cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl; return f; } // impossible inline bool impossible(bool f = true) { cout << (!f ? "possible" : "impossible") << endl; return f; } inline bool Impossible(bool f = true) { cout << (!f ? "Possible" : "Impossible") << endl; return f; } inline bool IMPOSSIBLE(bool f = true) { cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl; return f; } // Alice Bob inline bool Alice(bool f = true) { cout << (f ? "Alice" : "Bob") << endl; return f; } inline bool Bob(bool f = true) { cout << (f ? "Bob" : "Alice") << endl; return f; } // Takahashi Aoki inline bool Takahashi(bool f = true) { cout << (f ? "Takahashi" : "Aoki") << endl; return f; } inline bool Aoki(bool f = true) { cout << (f ? "Aoki" : "Takahashi") << endl; return f; } } // namespace yesno using namespace yesno; } // namespace templates using namespace templates; 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 &xl, const T &xr) { if (!t) return new Node(x); T tl = t->x.get(l); T tr = t->x.get(r); if (tl <= xl && tr <= xr) return t; else if (tl >= xl && tr >= xr) { t->x = x; return t; } else { T m = (l + r) / 2; if (m == r) m--; T tm = t->x.get(m); T xm = x.get(m); if (tm > xm) { swap(t->x, x); if (xl >= tl) t->l = add_line(t->l, x, l, m, tl, tm); else t->r = add_line(t->r, x, m + 1, r, tm + x.a, tr); } else { if (tl >= xl) t->l = add_line(t->l, x, l, m, xl, xm); else t->r = add_line(t->r, x, m + 1, r, xm + x.a, xr); } return t; } } void add_line(const T &a, const T &b) { Line x(a, b); root = add_line(root, x, low, upp, x.get(low), x.get(upp)); } Node *add_segment(Node *t, Line &x, const T &a, const T &b, const T &l, const T &r, const T &xl, const T &xr) { if (r < a || b < l) return t; if (a <= l && r <= b) { Line y{x}; return add_line(t, y, l, r, xl, xr); } if (t) { T tl = t->x.get(l); T tr = t->x.get(r); if (tl <= xl && tr <= xr) return t; } else { t = new Node(Line(0, inf)); } T m = (l + r) / 2; if (m == r) m--; T xm = x.get(m); t->l = add_segment(t->l, x, a, b, l, m, xl, xm); t->r = add_segment(t->r, x, a, b, m + 1, r, xm + x.a, xr); 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, low, upp, x.get(low), x.get(upp)); } T query(const Node *t, const T &l, const T &r, const T &x) const { if (!t) return inf; 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, low, upp, x); } ~DynamicLiChaoTree() { delete root; } }; void solve() { LL(n, m); VEC(ll, W, n); auto edges = read_wedges(n, m); const ll inf = 1LL << 60; auto f = [&](int s) -> vector { vec(ll, dist, n, inf); dist[s] = 0; qp hq; hq.push({0, s}); while (!hq.empty()) { auto [d, pos] = hq.top(); hq.pop(); if (dist[pos] < d) continue; for (auto [to, w] : edges[pos]) { if (chmin(dist[to], d + w)) { hq.push({dist[to], to}); } } } return dist; }; auto ds = f(0); auto dt = f(n - 1); ll ans = ds[n - 1]; DynamicLiChaoTree lc; fori(j, n) { lc.add_line(W[j], dt[j]); } fori(i, n) { auto res = lc.query(W[i]); chmin(ans, res + ds[i]); } print(ans); } int main() { #ifndef INTERACTIVE cin.tie(0)->sync_with_stdio(0); #endif // cout << fixed << setprecision(12); int t; t = 1; // cin >> t; while (t--) solve(); return 0; } // // #pragma GCC target("avx2") // // #pragma GCC optimize("O3") // // #pragma GCC optimize("unroll-loops") // // #define INTERACTIVE // // #include "kyopro-cpp/template.hpp" // // #include "data_structure/DynamicLiChaoTree.hpp" // // void solve() { // LL(n, m); // VEC(ll, W, n); // auto edges = read_wedges(n, m); // // const ll inf = 1LL << 60; // auto f = [&](int s) -> vector { // vec(ll, dist, n, inf); // dist[s] = 0; // qp hq; // hq.push({0, s}); // while (!hq.empty()) { // auto [d, pos] = hq.top(); // hq.pop(); // if (dist[pos] < d) continue; // for (auto [to, w] : edges[pos]) { // if (chmin(dist[to], d + w)) { // hq.push({dist[to], to}); // } // } // } // return dist; // }; // // auto ds = f(0); // auto dt = f(n - 1); // ll ans = ds[n - 1]; // DynamicLiChaoTree lc; // fori(j, n) { // lc.add_line(W[j], dt[j]); // } // fori(i, n) { // auto res = lc.query(W[i]); // chmin(ans, res + ds[i]); // } // print(ans); // } // // int main() { // #ifndef INTERACTIVE // cin.tie(0)->sync_with_stdio(0); // #endif // // cout << fixed << setprecision(12); // int t; // t = 1; // // cin >> t; // while (t--) solve(); // return 0; // }