#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>
using namespace std;
const long long INF = 1e18;
int N, K;
vector<long long> P;
vector<vector<int>> adj;
// --- K=1 Solution: Longest Path from Root ---
long long max_profit_k1 = -1;
vector<int> path_k1;
void dfs_k1(int u, int p, long long current_profit, vector<int>& current_path) {
current_path.push_back(u);
current_profit += P[u];
if (current_profit > max_profit_k1) {
max_profit_k1 = current_profit;
path_k1 = current_path;
}
for (int v : adj[u]) {
if (v != p) {
dfs_k1(v, u, current_profit, current_path);
}
}
current_path.pop_back();
}
void solve_k1() {
vector<int> current_path;
dfs_k1(1, 0, 0, current_path);
cout << max_profit_k1 << "\n";
cout << path_k1.size() << "\n";
for (int i = 0; i < path_k1.size(); i++) cout << path_k1[i] << (i == path_k1.size()-1 ? "" : " ");
cout << "\n";
}
// --- K=3 Solution: Visit All ---
void print_k3(int u, int p, bool reverse_mode) {
if (!reverse_mode) {
cout << u << " ";
for (int v : adj[u]) {
if (v != p) {
print_k3(v, u, true);
}
}
} else {
vector<int> children;
for (int v : adj[u]) if (v != p) children.push_back(v);
for (int i = children.size() - 1; i >= 0; i--) {
print_k3(children[i], u, false);
}
cout << u << " ";
}
}
void solve_k3() {
long long total = 0;
for (int i = 1; i <= N; i++) total += P[i];
cout << total << "\n";
cout << N << "\n";
print_k3(1, 0, false);
cout << "\n";
}
// --- K=2 Solution: Tree DP ---
struct DPState {
long long val;
int choice_a, choice_b, choice_c;
// a: D2 child (loop start), b: D2 child (loop end), c: D1 child (tail)
// special flag for dp1 jump: choice_a = -2 implies "Jump to dp3[choice_c]"
};
DPState dp[200005][3];
struct Cand {
long long gain;
int id;
};
// Optimization: Find top 3 candidates in O(Deg) instead of O(Deg log Deg)
void update_top3(vector<Cand>& top3, const Cand& c) {
top3.push_back(c);
int i = top3.size() - 1;
while(i > 0) {
if(top3[i].gain > top3[i-1].gain) {
swap(top3[i], top3[i-1]);
i--;
} else break;
}
if(top3.size() > 3) top3.pop_back();
}
void dfs_k2(int u, int p) {
vector<int> children;
long long sum_p = 0;
// Collect children and base sum
for (int v : adj[u]) {
if (v != p) {
dfs_k2(v, u);
children.push_back(v);
sum_p += P[v];
}
}
long long base = sum_p + P[u];
// Collect candidates for transitions
vector<Cand> cands_d1, cands_d2;
long long max_dp3_jump = -INF;
int dp3_jump_id = -1;
for (int v : children) {
// Gain if we replace single P[v] with a chain
update_top3(cands_d1, {dp[v][0].val - P[v], v});
update_top3(cands_d2, {dp[v][1].val - P[v], v});
// Track best pure jump (u -> dp3[v])
// This is exclusive: P[u] + dp3[v]
if (P[u] + dp[v][2].val > max_dp3_jump) {
max_dp3_jump = P[u] + dp[v][2].val;
dp3_jump_id = v;
}
}
// --- DP1: Start u, stay in subtree ---
dp[u][0] = {base, -1, -1, -1};
// Standard Mix: base + D2[a] (optional) + D1[b] (optional)
// Try all pairs from top 3
// Case 1: No specials (base) - set initially
// Case 2: Just D1[b]
for(auto& b : cands_d1) {
if(base + b.gain > dp[u][0].val) dp[u][0] = {base + b.gain, -1, -1, b.id};
}
// Case 3: Just D2[a]
for(auto& a : cands_d2) {
if(base + a.gain > dp[u][0].val) dp[u][0] = {base + a.gain, a.id, -1, -1};
}
// Case 4: Both D2[a] and D1[b]
for(auto& a : cands_d2) {
for(auto& b : cands_d1) {
if(a.id != b.id) {
if(base + a.gain + b.gain > dp[u][0].val) {
dp[u][0] = {base + a.gain + b.gain, a.id, -1, b.id};
}
}
}
}
// Case 5: Jump to Grandchild (P[u] + dp3[v]) [Cite: 150]
if (max_dp3_jump > dp[u][0].val) {
// We use special marker -2 to indicate this jump
dp[u][0] = {max_dp3_jump, -2, -1, dp3_jump_id};
}
// --- DP2: Start u, End shallow (at child or u) ---
// Max: base + D2[a] (optional)
dp[u][1] = {base, -1, -1, -1};
for(auto& a : cands_d2) {
if(base + a.gain > dp[u][1].val) dp[u][1] = {base + a.gain, a.id, -1, -1};
}
// --- DP3: Start at child of u, stay in subtree ---
// Structure: D2[a] (start) -> u -> D2[b] (rev) -> singles -> D1[c] (end)
// a is mandatory (must start at child)
dp[u][2] = {-INF, -1, -1, -1};
for(auto& a : cands_d2) {
long long current = base + a.gain;
// Just a
if(current > dp[u][2].val) dp[u][2] = {current, a.id, -1, -1};
// a + b
for(auto& b : cands_d2) {
if(a.id != b.id) {
if(current + b.gain > dp[u][2].val) dp[u][2] = {current + b.gain, a.id, b.id, -1};
}
}
// a + c
for(auto& c : cands_d1) {
if(a.id != c.id) {
if(current + c.gain > dp[u][2].val) dp[u][2] = {current + c.gain, a.id, -1, c.id};
}
}
// a + b + c
for(auto& b : cands_d2) {
if(a.id == b.id) continue;
for(auto& c : cands_d1) {
if(a.id != c.id && b.id != c.id) {
if(current + b.gain + c.gain > dp[u][2].val) {
dp[u][2] = {current + b.gain + c.gain, a.id, b.id, c.id};
}
}
}
}
}
}
// Reconstruction Logic
void build_k2(int u, int p, int type, vector<int>& path);
// Helper: Add path of a child recursively
void add_child_path(int v, int u, int type, vector<int>& path, bool reverse_output) {
vector<int> sub;
build_k2(v, u, type, sub);
if(reverse_output) {
path.insert(path.end(), sub.rbegin(), sub.rend());
} else {
path.insert(path.end(), sub.begin(), sub.end());
}
}
void build_k2(int u, int p, int type, vector<int>& path) {
DPState& s = dp[u][type];
// Check for special Jump transition
if (type == 0 && s.choice_a == -2) {
// Path: u -> dp3[child]
path.push_back(u);
add_child_path(s.choice_c, u, 2, path, false);
return;
}
int va = s.choice_a;
int vb = s.choice_b;
int vc = s.choice_c;
auto add_singles = [&]() {
for (int v : adj[u]) {
if (v != p && v != va && v != vb && v != vc) {
path.push_back(v);
}
}
};
if (type == 0) { // DP1: u -> Rev(va) -> singles -> vc
path.push_back(u);
if (va != -1) add_child_path(va, u, 1, path, true); // Rev(D2)
add_singles();
if (vc != -1) add_child_path(vc, u, 0, path, false); // D1
}
else if (type == 1) { // DP2: u -> Rev(va) -> singles
path.push_back(u);
if (va != -1) add_child_path(va, u, 1, path, true); // Rev(D2)
add_singles();
}
else if (type == 2) { // DP3: va -> u -> Rev(vb) -> singles -> vc
if (va != -1) add_child_path(va, u, 1, path, false); // D2 (Forward)
path.push_back(u);
if (vb != -1) add_child_path(vb, u, 1, path, true); // Rev(D2)
add_singles();
if (vc != -1) add_child_path(vc, u, 0, path, false); // D1
}
}
void solve_k2() {
dfs_k2(1, 0);
cout << dp[1][0].val << "\n";
vector<int> path;
build_k2(1, 0, 0, path);
cout << path.size() << "\n";
for(size_t i=0; i<path.size(); ++i) cout << path[i] << (i==path.size()-1?"":" ");
cout << "\n";
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
if (!(cin >> N >> K)) return 0;
P.resize(N + 1);
adj.resize(N + 1);
for (int i = 0; i < N - 1; i++) {
int u, v;
cin >> u >> v;
adj[u].push_back(v);
adj[v].push_back(u);
}
for (int i = 1; i <= N; i++) cin >> P[i];
if (K == 1) solve_k1();
else if (K == 2) solve_k2();
else solve_k3();
return 0;
}
