#ifdef ONLINE_JUDGE #pragma GCC target("avx2,avx") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #endif #include using namespace std; using ll = long long; using ull = unsigned long long; using i128 = __int128_t; using pii = pair; using pll = pair; #define rep(i, n) for (int i = 0; i < (n); i++) #define rrep(i, n) for (int i = int(n) - 1; i >= 0; i--) #define all(x) (x).begin(), (x).end() constexpr char ln = '\n'; istream& operator>>(istream& is, __int128_t& x) { x = 0; string s; is >> s; int n = int(s.size()), it = 0; if (s[0] == '-') it++; for (; it < n; it++) x = (x * 10 + s[it] - '0'); if (s[0] == '-') x = -x; return is; } ostream& operator<<(ostream& os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; deque deq; while (x) deq.emplace_front(x % 10), x /= 10; for (int e : deq) os << e; return os; } template ostream& operator<<(ostream& os, const pair& p) { return os << "(" << p.first << ", " << p.second << ")"; } template ostream& operator<<(ostream& os, const vector& v) { os << "{"; for (int i = 0; i < int(v.size()); i++) { if (i) os << ", "; os << v[i]; } return os << "}"; } template inline int SZ(Container& v) { return int(v.size()); } template inline void UNIQUE(vector& v) { v.erase(unique(v.begin(), v.end()), v.end()); } template inline bool chmax(T1& a, T2 b) { if (a < b) {a = b; return true ;} return false ;} template inline bool chmin(T1& a, T2 b) { if (a > b) {a = b; return true ;} return false ;} inline int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); } inline int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); } inline int popcount(ull x) { return __builtin_popcountll(x); } inline int kthbit(ull x, int k) { return (x>>k) & 1; } inline constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x-1) * 10; } inline void print() { cout << "\n"; } template inline void print(const vector& v) { for (int i = 0; i < int(v.size()); i++) { if (i) cout << " "; cout << v[i]; } print(); } template inline void print(const T& x, const Args& ... args) { cout << x << " "; print(args...); } #ifdef MINATO_LOCAL inline void debug_out() { cerr << endl; } template inline void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); } #define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " : " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// template struct Dijkstra { struct Edge { int to; Int cost; Edge (int to, Int cost) : to(to), cost(cost) {} bool operator<(const Edge& o) const { return cost > o.cost; } }; int n; Int INF; vector> g; vector dist; vector from; Dijkstra() {} Dijkstra(int n, Int INF) : n(n), INF(INF), g(n), dist(n), from(n) {} void add_edge(int u, int v, Int cost) { assert(0 <= u and u < n); assert(0 <= v and v < n); g[u].emplace_back(v,cost); } void build(int s = 0) { fill(dist.begin(), dist.end(), INF); fill(from.begin(), from.end(), -1); dist[s] = 0; priority_queue pq; pq.emplace(s, dist[s]); while (!pq.empty()) { Edge t = pq.top(); pq.pop(); int v = t.to; Int d = t.cost; if (d > dist[v]) continue; for (Edge& e : g[v]) { if (dist[e.to] > d + e.cost) { dist[e.to] = d + e.cost; from[e.to] = v; pq.emplace(e.to, dist[e.to]); } } } } Int operator[](int k) { return dist[k]; } vector restore(int to) { vector ret; if (from[to] == -1) return ret; while (~to) { ret.emplace_back(to); to = from[to]; } reverse(ret.begin(), ret.end()); return ret; } }; constexpr ll INF = 1e18; int main() { ll N,Q,C; cin >> N >> Q >> C; Dijkstra D(N,INF); vector> G(N); rep(i,N-1) { int u,v,w; cin >> u >> v >> w; u--; v--; D.add_edge(u,v,w); D.add_edge(v,u,w); G[u].emplace_back(v); G[v].emplace_back(u); } vector x(Q); rep(i,Q) cin >> x[i], x[i]--; vector> dist(N, vector(N)); rep(i,N) { auto DD = D; DD.build(i); rep(j,N) dist[i][j] = DD[j]; } vector dp(N,INF); dp[x[0]] = 0; rep(k,Q-1) { vector arr(N); rep(i,N) { if (i==x[k]) arr[i] = pll(dp[i]+dist[i][x[k+1]],i); else arr[i] = pll(dp[i]+dist[i][x[k+1]]+C,i); } sort(all(arr)); vector seen(N); vector nex(N); rep(i,N) nex[i] = dp[i]+dist[x[k]][x[k+1]]; chmin(nex[x[k+1]],arr[0].first); seen[x[k+1]] = 1; auto getpath=[&](int s) { vector ret; auto dfs=[&](auto self, int v, int pv)->bool { if (seen[v]) return true; ret.emplace_back(v); for (int nv : G[v]) { if (nv==pv) continue; if (self(self,nv,v)) return true; } ret.pop_back(); return false; }; dfs(dfs,s,-1); return ret; }; rep(i,N) { auto[val,s] = arr[i]; auto path = getpath(s); for (auto e : path) { chmin(nex[e],val); seen[e] = 1; } } swap(dp,nex); } cout << *min_element(all(dp)) << ln; }