#include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL #define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl #else #define dbg(x) {} #endif // lowest common ancestor (LCA) class for undirected weighted tree // 無向重み付きグラフの最小共通祖先 // struct UndirectedWeightedTree { using T = long long; // Arbitrary data structure (operator+, operator- must be defined) int INVALID = -1; int V, lgV; int E; int root; std::vector>> adj; // (nxt_vertex, edge_id) // vector edge; // edges[edge_id] = (vertex_id, vertex_id) std::vector weight; // w[edge_id] std::vector par; // parent_vertex_id[vertex_id] std::vector depth; // depth_from_root[vertex_id] std::vector acc_weight; // w_sum_from_root[vertex_id] void _fix_root_dfs(int now, int prv, int prv_edge_id) { par[now] = prv; if (prv_edge_id != INVALID) acc_weight[now] = acc_weight[prv] + weight[prv_edge_id]; for (auto nxt : adj[now]) if (nxt.first != prv) { depth[nxt.first] = depth[now] + 1; _fix_root_dfs(nxt.first, now, nxt.second); } } UndirectedWeightedTree() = default; UndirectedWeightedTree(int N) : V(N), E(0), adj(N) { lgV = 1; while (1 << lgV < V) lgV++; } void add_edge(int u, int v, T w) { adj[u].emplace_back(v, E); adj[v].emplace_back(u, E); // edge.emplace_back(u, v); weight.emplace_back(w); E++; } void fix_root(int r) { root = r; par.resize(V); depth.resize(V); depth[r] = 0; acc_weight.resize(V); acc_weight[r] = 0; _fix_root_dfs(root, INVALID, INVALID); } std::vector> doubling; void doubling_precalc() { doubling.assign(lgV, std::vector(V)); doubling[0] = par; for (int d = 0; d < lgV - 1; d++) for (int i = 0; i < V; i++) { if (doubling[d][i] == INVALID) doubling[d + 1][i] = INVALID; else doubling[d + 1][i] = doubling[d][doubling[d][i]]; } } int kth_parent(int x, int k) { if (depth[x] < k) return INVALID; for (int d = 0; d < lgV; d++) { if (x == INVALID) return INVALID; if (k & (1 << d)) x = doubling[d][x]; } return x; } int lowest_common_ancestor(int u, int v) { if (depth[u] > depth[v]) std::swap(u, v); v = kth_parent(v, depth[v] - depth[u]); if (u == v) return u; for (int d = lgV - 1; d >= 0; d--) { if (doubling[d][u] != doubling[d][v]) u = doubling[d][u], v = doubling[d][v]; } return par[u]; } T path_length(int u, int v) { // Not distance, but the sum of weights int r = lowest_common_ancestor(u, v); return (acc_weight[u] - acc_weight[r]) + (acc_weight[v] - acc_weight[r]); } }; template struct ShortestPath { int V, E; int INVALID = -1; std::vector>> to; ShortestPath() = default; ShortestPath(int V) : V(V), E(0), to(V) {} void add_edge(int s, int t, T len) { assert(0 <= s and s < V); assert(0 <= t and t < V); to[s].emplace_back(t, len); E++; } std::vector dist; std::vector prev; // Dijkstra algorithm // Complexity: O(E log E) void Dijkstra(int s) { assert(0 <= s and s < V); dist.assign(V, std::numeric_limits::max()); dist[s] = 0; prev.assign(V, INVALID); using P = std::pair; std::priority_queue, std::greater

> pq; pq.emplace(0, s); while (!pq.empty()) { T d; int v; std::tie(d, v) = pq.top(); pq.pop(); if (dist[v] < d) continue; for (auto nx : to[v]) { T dnx = d + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; pq.emplace(dnx, nx.first); } } } } }; int main() { int N, Q, C; cin >> N >> Q >> C; UndirectedWeightedTree tree(N); ShortestPath sp_(N); REP(i, N - 1) { int u, v, w; cin >> u >> v >> w; u--, v--; tree.add_edge(u, v, w); sp_.add_edge(u, v, w), sp_.add_edge(v, u, w); } vector D(N, vector(N)); REP(i, N) { tree.fix_root(i); D[i] = tree.acc_weight; } vector X(Q); for (auto &x : X) { cin >> x; x--; } vector dnow(N, 1e18); dnow[X[0]] = 0; FOR(t, 1, Q) { auto sp = sp_; const int now = X[t - 1]; const int nxt = X[t]; REP(i, N) sp.add_edge(now, i, dnow[i] - dnow[now] + C); sp.Dijkstra(now); REP(i, N) sp.dist[i] += dnow[now]; REP(i, N) dnow[i] = min(D[nxt][i] + sp.dist[i], dnow[i] + D[now][nxt]); } cout << *min_element(ALL(dnow)) << '\n'; }