#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 lazyseg { static_assert(std::is_same_v); static_assert(std::is_same_v); using T = typename MergeMonoid::T; using F = typename OpMonoid::F; static constexpr T e() { return MergeMonoid::e(); } static constexpr F id() { return OpMonoid::id(); } public: lazyseg(const std::vector& vs) : m_size{(int)vs.size()}, m_depth{clog(m_size)}, m_half{1 << m_depth}, m_vals(m_half << 1, MergeMonoid::e()), m_ops(m_half << 1, OpMonoid::id()), m_merge{}, m_compose{}, m_apply{} { std::copy(vs.begin(), vs.end(), m_vals.begin() + m_half); for (int i = m_half - 1; i >= 1; i--) { up(i); } } T get(const int a) { return assert(a < m_size), fold(a, a + 1); } void set(int a, const T& v) { assert(0 <= a and a < m_size); top_down(a += m_half), top_down(a + 1), m_ops[a] = id(), m_vals[a] = v; while (a >>= 1) { up(a); } } T fold(int l, int r) { assert(0 <= l and l <= r and r <= m_size); if (l >= r) { return e(); } top_down(l += m_half), top_down(r += m_half); T accl = e(), accr = e(); for (; l < r; l >>= 1, r >>= 1) { if (l & 1) { accl = m_merge(accl, m_vals[l++]); } if (r & 1) { accr = m_merge(m_vals[--r], accr); } } return m_merge(accl, accr); } void act(int l, int r, const F& f) { assert(0 <= l and l <= r and r <= m_size); const int lin = l + m_half, rin = r + m_half; top_down(l += m_half), top_down(r += m_half); for (int ls = 1, rs = 1; l < r; l >>= 1, r >>= 1, ls <<= 1, rs <<= 1) { if (l & 1) { update(l++, f, ls); } if (r & 1) { update(--r, f, rs); } } bottom_up(lin), bottom_up(rin); } friend std::ostream& operator<<(std::ostream& os, const lazyseg& lseg) { auto lseg2 = lseg; os << "["; for (int i = 0; i < lseg.m_size; i++) { os << lseg2.get(i) << (i + 1 == lseg2.m_size ? "" : ","); } return (os << "]\n"); } private: void up(const int i) { m_vals[i] = m_merge(m_vals[i << 1], m_vals[i << 1 | 1]); } void update(const int a, const F& f, const int l) { m_ops[a] = m_compose(f, m_ops[a]), m_vals[a] = m_apply(f, m_vals[a], l); } void down(const int a, const int l) { update(a << 1, m_ops[a], l >> 1), update(a << 1 | 1, m_ops[a], l >> 1), m_ops[a] = id(); } void top_down(const int a) { const int b = (a / (a & -a)) >> 1; for (int i = 0, l = m_half; i < m_depth; i++, l >>= 1) { const int v = a >> (m_depth - i); if (v > b) { break; } down(v, l); } } void bottom_up(int a) { a = (a / (a & -a)) >> 1; for (; a >= 1; a >>= 1) { up(a); } } const int m_size, m_depth, m_half; std::vector m_vals; std::vector m_ops; const MergeMonoid m_merge; const OpMonoid m_compose; const Act m_apply; }; 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 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 dss = nd_array({N, N}, 0); std::vector> hlds; for (int i = 0; i < N; i++) { 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; } dss[i][to] = dss[i][from] + cost; self(to, s); } })(i, -1); hlds.push_back(hl_decomp(g, i)); } struct Min { using T = ll; T operator()(const T x1, const T x2) const { return std::min(x1, x2); } static constexpr T e() { return inf_v; } }; struct Assign { using F = ll; F operator()(const F f1, const F f2) const { return f1 == inf_v ? f2 : f1; } static constexpr F id() { return inf_v; } }; struct Act { using T = ll; using F = ll; T operator()(const F& f, const T x, const int) const { return f == inf_v ? x : f; } }; lazyseg dp(std::vector(N, inf_v)); std::vector> segs(N, std::vector(N, inf_v)); auto xs = in.vec(Q, 1); xs.push_back(xs.back() == 0 ? 1 : 0); dp.set(hlds[xs[1]].pos(xs[0]), 0); segs[xs[1]].set(hlds[xs[1]].pos(xs[0]), dss[xs[1]][xs[0]]); for (int i = 1; i < Q; i++) { lazyseg ndp(std::vector(N, inf_v)); const auto ps = hlds[xs[i + 1]].path(xs[i - 1], xs[i]); for (auto [l, r] : ps) { if (l > r) { std::swap(l, r); } r++; ndp.act(l, r, dp.fold(0, N) + dss[xs[i]][xs[i - 1]]); } for (int j = 0; j < N; j++) { const int pos = hlds[xs[i + 1]].pos(j); ll min = dp.get(j) + dss[xs[i - 1]][xs[i]]; const auto [l, r] = hlds[xs[i]].sub(j); chmin(min, segs[xs[i]].fold(l, r) + C); ndp.set(pos, std::min(min, ndp.get(pos))); } for (int i = 0; i < N; i++) { dp.set(i, ndp.get(i)); } for (int j = 0; j < N; j++) { const int pos = hlds[xs[i + 1]].pos(j); segs[xs[i + 1]].set(pos, dss[xs[i + 1]][j] + dp.get(pos)); } } out.ln(dp.fold(0, N)); }