/*
Mayoeba Yabureru
*/
#include<bits/stdc++.h>
using namespace std;
long long dp[3003][6003][2][2];
int max_score(int n, int x, int y, long long k, vector<int> U, vector<int> V, vector<int> W) {
x ++, y ++;
vector dis(n + 1, vector<long long>(2));
vector<vector<pair<int, long long>>> gr(n + 1);
for (int i = 0; i < n - 1; i ++) {
int u = U[i] + 1, v = V[i] + 1, w = W[i];
gr[u].push_back({v, w});
gr[v].push_back({u, w});
}
function<void(int, int, int)> dfs = [&] (int v, int p, int wt) {
for (auto [u, w] : gr[v]) {
if (u == p) continue;
dis[u][wt] = dis[v][wt] + w;
dfs(u, v, wt);
}
};
dfs(x, 0, 0), dfs(y, 0, 1);
vector<int> vc, path, onpath(n + 1);
function<void(int, int)> go = [&] (int v, int p) {
vc.push_back(v);
if (v == y) path = vc;
for (auto [u, w] : gr[v]) {
if (u == p) continue;
go(u, v);
}
vc.pop_back();
};
go(x, 0);
long long minstart = 0, mn = 1e15;
for (int i = 1; i <= n; i ++) {
if (max(dis[i][0], dis[i][1]) < mn) {
minstart = i;
mn = max(dis[i][0], dis[i][1]);
}
}
long long sum = max(dis[minstart][0], dis[minstart][1]);
for (auto x : path) {
onpath[x] += 1;
if (x == minstart) break;
sum += dis[x][0];
}
for (int i = path.size() - 1; i >= 0; i --) {
int x = path[i];
onpath[x] += 2;
if (x == minstart) break;
sum += dis[x][1];
}
int ans = 0;
function f = [&] {
vector<int> did(n + 1);
multiset<pair<long long, int>> s;
for (int i = 1; i <= n; i ++) {
s.insert({dis[i][0], i});
s.insert({dis[i][1], i});
}
int cnt = 0;
vector<int> v;
while (s.size()) {
auto [x, y] = *s.begin();
s.erase(s.begin());
if (did[y]) continue;
if (x > k) break;
k -= x;
did[y] = 1;
cnt ++;
}
if (k >= 0) return cnt;
return -100000000;
};
long long kk = k;
ans = f();
if (sum > k) return ans;
k = kk;
for (int i = 1; i <= n; i ++) {
for (int j = 0; j <= 2 * n; j ++) {
dp[i][j][0][0] = dp[i][j][0][1] = dp[i][j][1][0] = dp[i][j][1][1] = 1e16;
}
}
vector dpp(2 * (n + 1), vector (2, vector<long long>(2, 1e16)));
vector<int> siz(n + 1);
function<void(int, int)> calcsiz = [&] (int x, int p) {
siz[x] = 1;
for (auto [u, w] : gr[x]) {
if (u == p) continue;
calcsiz(u, x);
siz[x] += siz[u];
}
};
calcsiz(minstart, 0);
map<vector<int>, int> did;
function<void(int, int, int, int)> calc = [&] (int x, int p, int rx, int ry) {
if (did[{x, rx, ry}]) return;
did[{x, rx, ry}] = 1;
if (rx == 0 && ry == 0) dp[x][0][rx][ry] = 0;
if (rx && ry == 0) dp[x][1][rx][ry] = min(dp[x][1][rx][ry], dis[x][0]);
if (ry && rx == 0) dp[x][1][rx][ry] = min(dp[x][1][rx][ry], dis[x][1]);
if (rx && ry) dp[x][2][rx][ry] = min(dp[x][2][rx][ry], max(dis[x][0], dis[x][1]));
int sumsiz = 1;
for (auto [u, w] : gr[x]) {
if (u == p) continue;
calc(u, x, rx, ry);
if (rx && ry) {
if (onpath[u] == 0) calc(u, x, 0, 0);
if (onpath[u] != 1) calc(u, x, 0, 1);
if (onpath[u] != 2) calc(u, x, 1, 0);
}
else if (rx && onpath[u] != 1) calc(u, x, 0, ry);
else if (ry && onpath[u] != 2) calc(u, x, rx, 0);
for (int i = 0; i <= rx; i ++) {
for (int j = 0; j <= ry; j ++) {
for (int z = 2 * siz[u]; z >= 0; z --) {
for (int k = 2 * sumsiz; k >= 0; k --) {
dpp[k + z][rx][ry] = min(dpp[k + z][rx][ry], dp[x][k][rx][ry] + dp[u][z][i][j]);
}
}
}
}
sumsiz += siz[u];
for (int z = 0; z <= 2 * sumsiz; z ++) {
dp[x][z][rx][ry] = dpp[z][rx][ry];
dpp[z][rx][ry] = 1e16;
}
}
};
calc(minstart, 0, 1, 1);
for (int i = 0; i <= 2 * n; i ++) {
if (k >= dp[minstart][i][1][1]) ans = max(ans, i);
}
return ans;
}
/*
2
7 0 2 10
0 1 2
0 3 3
1 2 4
2 4 2
2 5 5
5 6 3
4 0 3 20
0 1 18
1 2 1
2 3 19
*/
#define sz(x) int(x.size())
#define all(x) begin(x), end(x)
using ll = long long;
using ii = pair<int, int>;
const ll INF = 1e18;
const int MAX_N = 2e5 + 9;
vector<ii> adj[MAX_N];
pair<ll, ll> val[MAX_N];
int n;
void dfs(int u, vector<ll> &dist, int p = -1, ll d = 0) {
dist[u] = d;
for (auto [v, w] : adj[u]) {
if (v != p) dfs(v, dist, u, d + w);
}
}
int non_overlaping(ll K) {
vector<ll> v(n);
for (int i = 0; i < n; i++) {
v[i] = val[i].first;
}
sort(all(v));
int ans = 0;
for (int i = 0; i < n; i++) {
if (v[i] <= K) {
K -= v[i];
ans++;
}
}
return ans;
}
int max_score1(int N, int X, int Y, ll K, vector<int> U, vector<int> V, vector<int> W) {
n = N;
for (int i = 0; i < n; i++) adj[i].clear();
for (int i = 0; i < n - 1; i++) {
adj[U[i]].emplace_back(V[i], W[i]);
adj[V[i]].emplace_back(U[i], W[i]);
}
vector<ll> distToX(n), distToY(n);
dfs(X, distToX), dfs(Y, distToY);
bool flag = false;
for (int i = 0; i < n; i++) {
val[i] = minmax(distToX[i], distToY[i]);
if (val[i].second <= K) flag = true;
}
if (!flag) return non_overlaping(K);
vector<bool> path(n, false);
path[Y] = true;
int u = Y;
while (u != X) {
for (auto [v, w] : adj[u]) {
if (distToX[v] + w == distToX[u]) {
u = v;
break;
}
}
path[u] = true;
}
vector<ll> prevDP(2 * n + 1, INF);
prevDP[0] = 0;
for (int i = 0; i < n; i++) {
vector<ll> currDP(2 * n + 1, INF);
if (!path[i]) currDP = prevDP;
for (int j = 1; j <= 2 * n; j++) {
currDP[j] = min(currDP[j], prevDP[j - 1] + val[i].first);
}
for (int j = 2; j <= 2 * n; j++) {
currDP[j] = min(currDP[j], prevDP[j - 2] + val[i].second);
}
prevDP = currDP;
}
for (int i = 2 * n; i >= 0; i--) {
if (prevDP[i] <= K) return max(i, non_overlaping(K));
}
return non_overlaping(K);
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int T = 1;
cin >> T;
while (T --) {
int n, x, y;
long long k;
cin >> n >> x >> y >> k;
vector<int> U(n - 1), V(n - 1), W(n - 1);
for (int i = 0; i < n - 1; i ++) cin >> U[i] >> V[i] >> W[i];
cout << max_score(n, x, y, k, U, V, W) << endl;
cout << max_score1(n, x, y, k, U, V, W) << endl;
}
}
/*
1
12 3 8 500
0 1 2
1 2 34
2 3 23
3 4 22
4 5 12
5 6 2
6 7 6
7 8 9
8 9 21
9 10 123
10 11 23
*/
Compilation message
/usr/bin/ld: /tmp/cczHdHHg.o: in function `main':
grader.cpp:(.text.startup+0x0): multiple definition of `main'; /tmp/ccGxljaj.o:closing.cpp:(.text.startup+0x0): first defined here
collect2: error: ld returned 1 exit status
