#include using ll = long long; using uint = unsigned int; using ull = unsigned long long; using ld = long double; template using max_heap = std::priority_queue; template using min_heap = std::priority_queue, std::greater>; constexpr int popcount(const ull v) { return v ? __builtin_popcountll(v) : 0; } constexpr int log2p1(const ull v) { return v ? 64 - __builtin_clzll(v) : 0; } constexpr int lsbp1(const ull v) { return __builtin_ffsll(v); } constexpr int clog(const ull v) { return v ? log2p1(v - 1) : 0; } constexpr ull ceil2(const ull v) { return 1ULL << clog(v); } constexpr ull floor2(const ull v) { return v ? (1ULL << (log2p1(v) - 1)) : 0ULL; } constexpr bool btest(const ull mask, const int ind) { return (mask >> ind) & 1ULL; } template void bset(T& mask, const int ind) { mask |= ((T)1 << ind); } template void breset(T& mask, const int ind) { mask &= ~((T)1 << ind); } template void bflip(T& mask, const int ind) { mask ^= ((T)1 << ind); } template void bset(T& mask, const int ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); } template class ds_table { using T = typename SemiGroup::T; public: ds_table(const std::vector& vs) : m_size{(int)vs.size()}, m_depth{(int)log2p1(m_size)}, m_vss(m_depth, vs), m_merge{} { for (int d = 0; d < m_depth; d++) { const int width = 1 << (m_depth - d - 1); for (int i = 1; i * width < m_size; i += 2) { int l = i * width - 1, r = i * width; for (int j = 1; j < width; j++) { m_vss[d][l - j] = m_merge(vs[l - j], m_vss[d][l - j + 1]); if (r + j < m_size) { m_vss[d][r + j] = m_merge(vs[r + j], m_vss[d][r + j - 1]); } } } } } T fold(const int l, int r) const { assert(0 <= l and l < r and r <= m_size); if (r - l == 1) { return m_vss.back()[l]; } r--; const int d = m_depth - log2p1(l ^ r); return m_merge(m_vss[d][l], m_vss[d][r]); } private: const int m_size, m_depth; std::vector> m_vss; const SemiGroup m_merge; }; template class static_rmq { using T = typename TotalOrd::T; public: static_rmq(const std::vector& vs) : m_comp{}, m_sz{(int)vs.size()}, m_bn{(int)wind(m_sz + bs - 1)}, m_vals{vs}, m_bucket_vals([&]() { std::vector ans(m_bn); for (int i = 0; i < m_sz; i++) { ans[wind(i)] = i % bs == 0 ? m_vals[i] : std::min(ans[wind(i)], m_vals[i], m_comp); } return ans; }()), m_masks(m_sz, 0), m_st(m_bucket_vals) { for (int i = 0; i < m_bn; i++) { std::vector g(bs, m_sz); std::stack stack; for (int j = 0; j < bs and (int) ind(i, j) < m_sz; j++) { for (; not stack.empty() and not m_comp(m_vals[stack.top()], m_vals[ind(i, j)]); stack.pop()) {} g[j] = stack.empty() ? m_sz : stack.top(), stack.push(ind(i, j)); } for (int j = 0; j < bs and (int) ind(i, j) < m_sz; j++) { m_masks[ind(i, j)] = g[j] == m_sz ? static_cast(0) : (m_masks[g[j]] | static_cast(1) << (g[j] - i * bs)); } } } T fold(const int l, const int r) const { assert(0 <= l and l < r and r <= m_sz); const int lb = (l + bs - 1) / bs, rb = r / bs; if (lb > rb) { return brmq(l, r); } else { return lb < rb ? (l < bs * lb ? (bs * rb < r ? std::min({m_st.fold(lb, rb), brmq(l, bs * lb), brmq(bs * rb, r)}, m_comp) : std::min(m_st.fold(lb, rb), brmq(l, bs * lb), m_comp)) : (bs * rb < r ? std::min(m_st.fold(lb, rb), brmq(bs * rb, r), m_comp) : m_st.fold(lb, rb))) : (l < bs * lb ? (bs * rb < r ? std::min(brmq(l, bs * lb), brmq(bs * rb, r), m_comp) : brmq(l, bs * lb)) : (bs * rb < r ? brmq(bs * rb, r) : T{})); } } private: static constexpr int bs = sizeof(B) * 8; static constexpr int bslog = log2p1(bs) - 1; static constexpr uint wind(const uint n) { return n >> (bslog); } static constexpr uint bind(const uint n) { return n ^ (wind(n) << bslog); } static constexpr uint ind(const uint w, const uint b) { return (w << bslog) | b; } T brmq(const int l, const int r) const { const B w = m_masks[r - 1] >> (l % bs); return w == 0 ? m_vals[r - 1] : m_vals[l + lsbp1(w) - 1]; } struct SemiGroup { using T = typename TotalOrd::T; T operator()(const T& x1, const T& x2) const { return std::min(x1, x2, TotalOrd{}); } }; const TotalOrd m_comp; int m_sz, m_bn; std::vector m_vals, m_bucket_vals; std::vector m_masks; ds_table m_st; }; template class graph { public: graph(const int size) : m_size{size}, m_eis(m_size) {} void add_edge(const int u, const int v, const T& c, const bool bi = false) { const int ei = (int)m_us.size(); m_eis[u].push_back(ei); if (bi) { m_eis[v].push_back(ei); } m_us.push_back(u), m_vs.push_back(v), m_cs.push_back(c); } void add_edge(const int u, const int v, const bool bi = false) { add_edge(u, v, 1, bi); } const std::vector& operator[](const int u) const { return m_eis[u]; } std::vector& operator[](const int u) { return m_eis[u]; } std::tuple edge(const int u, const int i) const { return std::make_tuple(u, m_us[i] ^ m_vs[i] ^ u, m_cs[i]); } int size() const { return m_size; } friend std::ostream& operator<<(std::ostream& os, const graph& g) { for (int u = 0; u < g.size(); u++) { for (const int ei : g[u]) { const auto& [from, to, cost] = g.edge(u, ei); os << "[" << ei << "]: " << from << "->" << to << "(" << cost << ")\n"; } } return os; } private: int m_size; std::vector> m_eis; std::vector m_us, m_vs; std::vector m_cs; }; template class hl_decomp { public: hl_decomp(graph& g, const int r = 0) : m_pars(g.size(), -1), m_tops{m_pars}, m_ins{m_pars}, m_ords{m_pars}, m_outs{m_pars} { const int N = g.size(); std::vector szs(N, 1); auto dfs1 = [&](auto self, const int u, const int p) -> int { m_pars[u] = p; for (int& ei : g[u]) { [[maybe_unused]] const auto& [from, to, cost] = g.edge(u, ei); if (p == to) { continue; } szs[u] += self(self, to, u); if (szs[std::get<1>(g.edge(u, g[u][0]))] < szs[to]) { std::swap(g[u][0], ei); } } return szs[u]; }; dfs1(dfs1, r, -1); m_tops[r] = r; auto dfs2 = [&](auto&& self, const int u, const int p, int& ind) -> void { m_ins[u] = ind++, m_ords[m_ins[u]] = u; for (const int ei : g[u]) { [[maybe_unused]] const auto& [from, to, cost] = g.edge(u, ei); if (to == p) { continue; } m_tops[to] = (ei == g[u][0] ? m_tops[u] : to); self(self, to, u, ind); } m_outs[u] = ind; }; int ind = 0; dfs2(dfs2, r, -1, ind); } int pos(const int v) const { return m_ins[v]; } int at(const int n) const { return m_ords[n]; } std::pair sub(const int v) const { return {m_ins[v], m_outs[v]}; } std::vector> path(int u, int v) const { using P = std::pair; std::vector

head, tail; for (int pu = m_tops[u], pv = m_tops[v]; pu != pv;) { if (m_ins[pu] < m_ins[pv]) { tail.push_back({m_ins[pv], m_ins[v]}); v = m_pars[pv], pv = m_tops[v]; } else { head.push_back({m_ins[u], m_ins[pu]}); u = m_pars[pu], pu = m_tops[u]; } } head.push_back({m_ins[u], m_ins[v]}); std::reverse(tail.begin(), tail.end()); for (const auto& p : tail) { head.push_back(p); } return head; } friend std::ostream& operator<<(std::ostream& os, const hl_decomp& hld) { os << "ord = {"; for (const int v : hld.m_ords) { os << v << ","; } os << "}\ntops = {"; for (const int v : hld.m_tops) { os << v << ","; } return os << "}"; } private: std::vector m_pars, m_tops, m_ins, m_ords, m_outs; }; template class lca_manager { public: lca_manager(const graph& g, const int r = 0) : m_ins(g.size(), 0), m_ds([&]() { std::vector> ans; std::vector used(g.size(), false); auto dfs = [&](auto self, const std::pair& s) -> void { const int pos = s.second; used[pos] = true, m_ins[pos] = ans.size(), ans.push_back(s); for (const int ei : g[pos]) { [[maybe_unused]] const auto& [from, to, cost] = g.edge(pos, ei); if (used[to]) { continue; } self(self, {s.first + 1, to}), ans.push_back(s); } }; dfs(dfs, {0, r}); return ans; }()), m_rmq(m_ds) {} int operator()(const int u, const int v) const { const int ul = m_ins[u], vl = m_ins[v]; return m_rmq.fold(std::min(ul, vl), std::max(ul, vl) + 1).second; } private: struct Ord { using T = std::pair; bool operator()(const T& p1, const T& p2) const { return p1 < p2; } }; std::vector m_ins; std::vector> m_ds; static_rmq m_rmq; }; template bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); } template bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); } template constexpr T inf_v = std::numeric_limits::max() / 4; template constexpr Real pi_v = Real{3.141592653589793238462643383279502884}; template constexpr T TEN(const int n) { return n == 0 ? T{1} : TEN(n - 1) * T{10}; } template struct fix : F { fix(F&& f) : F{std::forward(f)} {} template auto operator()(Args&&... args) const { return F::operator()(*this, std::forward(args)...); } }; template auto nd_array(int const (&szs)[n], const T x = T{}) { if constexpr (i == n) { return x; } else { return std::vector(szs[i], nd_array(szs, x)); } } class printer { public: printer(std::ostream& os_ = std::cout) : m_os{os_} { m_os << std::fixed << std::setprecision(15); } template int ln(const Args&... args) { return dump(args...), m_os << '\n', 0; } template int el(const Args&... args) { return dump(args...), m_os << std::endl, 0; } private: template void dump(const T& v) { m_os << v; } template void dump(const std::vector& vs) { for (int i = 0; i < (int)vs.size(); i++) { m_os << (i ? " " : ""), dump(vs[i]); } } template void dump(const std::vector>& vss) { for (int i = 0; i < (int)vss.size(); i++) { m_os << (0 <= i or i + 1 < (int)vss.size() ? "\n" : ""), dump(vss[i]); } } template int dump(const T& v, const Args&... args) { return dump(v), m_os << ' ', dump(args...), 0; } std::ostream& m_os; }; printer out; class scanner { public: scanner(std::istream& is_ = std::cin) : m_is{is_} { m_is.tie(nullptr), std::ios::sync_with_stdio(false); } void fastio(const bool on) { if (on) { m_is.tie(nullptr), std::ios::sync_with_stdio(false); } else { m_is.tie(&std::cout), std::ios::sync_with_stdio(true); } } template T val() { T v; return m_is >> v, v; } template T val(const T offset) { return val() - offset; } template std::vector vec(const int n) { return make_v(n, [this]() { return val(); }); } template std::vector vec(const int n, const T offset) { return make_v(n, [this, offset]() { return val(offset); }); } template std::vector> vvec(const int n0, const int n1) { return make_v>(n0, [this, n1]() { return vec(n1); }); } template std::vector> vvec(const int n0, const int n1, const T offset) { return make_v>(n0, [this, n1, offset]() { return vec(n1, offset); }); } template auto tup() { return std::tuple...>{val()...}; } template auto tup(const Args&... offsets) { return std::tuple...>{val(offsets)...}; } private: template std::vector make_v(const int n, F f) { std::vector ans; for (int i = 0; i < n; i++) { ans.push_back(f()); } return ans; } std::istream& m_is; }; scanner in; int main() { const auto [N, Q, C] = in.tup(); graph g(N); for (int i = 0; i < N - 1; i++) { const auto [u, v, c] = in.tup(1, 1, 0); g.add_edge(u, v, c, true); } auto xs = in.vec(Q, 1); xs.push_back(0); std::vector ps(N, -1); std::vector ds(N, 0); fix([&](auto self, const int s, const int p) -> void { for (const int ei : g[s]) { const auto [from, to, cost] = g.edge(s, ei); if (to == p) { continue; } ps[to] = from, ds[to] = ds[from] + cost; self(to, s); } })(0, -1); const auto lca = lca_manager(g); auto dist = [&](const int i, const int j) { return ds[i] + ds[j] - 2LL * ds[lca(i, j)]; }; struct Ord { using T = ll; bool operator()(const T x, const T y) const { return x < y; } }; std::vector dp(N, inf_v); dp[xs[0]] = 0; static_cast(0); for (int i = 1; i < Q; i++) { const ll pmin = *std::min_element(dp.begin(), dp.end()); std::vector ndp(N, inf_v); const int y = lca(xs[i - 1], xs[i]); for (int v = xs[i - 1];; v = ps[v]) { ndp[v] = dist(xs[i - 1], xs[i]) + pmin; if (v == y) { break; } } for (int v = xs[i];; v = ps[v]) { ndp[v] = dist(xs[i - 1], xs[i]) + pmin; if (v == y) { break; } } for (int j = 0; j < N; j++) { chmin(ndp[j], dp[j] + dist(xs[i], xs[i - 1])); } const auto hld = hl_decomp(g, xs[i]); std::vector dp_depth(N, inf_v); for (int j = 0; j < N; j++) { dp_depth[hld.pos(j)] = dp[j] + dist(xs[i], j); } const auto rmq = static_rmq(dp_depth); for (int j = 0; j < N; j++) { const auto [l, r] = hld.sub(j); chmin(ndp[j], rmq.fold(l, r) + C); } dp = ndp; static_cast(0); } out.ln(*std::min_element(dp.begin(), dp.end())); }