#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
using namespace std;
template <typename T>
void etch(T V) {
  for (auto x : V) cout << x << ' ';
  cout << '\n';
}
vector<string> vec_splitter(string s) {
  s += ',';
  vector<string> res;
  while (!s.empty()) {
    res.push_back(s.substr(0, s.find(',')));
    s = s.substr(s.find(',') + 1);
  }
  return res;
}
void debug_out(vector<string> __attribute__((unused)) args,
               __attribute__((unused)) long long int idx,
               __attribute__((unused)) long long int LINE_NUM) {
  cerr << endl;
}
template <typename Head, typename... Tail>
void debug_out(vector<string> args, long long int idx, long long int LINE_NUM,
               Head H, Tail... T) {
  if (idx > 0)
    cerr << ", ";
  else
    cerr << "Line(" << LINE_NUM << ") ";
  stringstream ss;
  ss << H;
  cerr << args[idx] << " = " << ss.str();
  debug_out(args, idx + 1, LINE_NUM, T...);
}
const long long int MOD = 1e9 + 7;
const long long int MOD1 = 998244353;
const long long int N = 2e5 + 5;
const long long int INF = 1000111000111000111LL;
const long double EPS = 1e-12;
const long double PI = 3.141592653589793116;
struct edge {
  long long int v, w, c;
};
vector<edge> g[N];
multiset<pair<long long int, pair<long long int, long long int>>> st1, st2;
long long int sum;
long long int dfs(long long int node, long long int par = -1,
                  long long int w = 0) {
  long long int below = 0;
  for (auto to : g[node]) {
    if (to.v != par) {
      long long int child = dfs(to.v, node);
      below += child;
      long long int change = child * (to.w - to.w / 2);
      if (to.c == 1) {
        st1.insert({change, {child, to.w}});
      } else {
        st2.insert({change, {child, to.w}});
      }
      sum += child * to.w;
    }
  }
  if (!below) below++;
  return below;
}
vector<long long int> seq(
    multiset<pair<long long int, pair<long long int, long long int>>> st) {
  long long int sum = 0;
  vector<long long int> moves;
  while ((long long int)((st).size())) {
    auto node = *st.rbegin();
    st.erase(st.find(node));
    sum += node.first;
    node.second.second /= 2;
    long long int change =
        node.second.first * (node.second.second - node.second.second / 2);
    if (change > 0) {
      st.insert({change, {node.second.first, node.second.second}});
    }
    moves.push_back(sum);
  }
  return moves;
}
void solve() {
  long long int n, s;
  cin >> n >> s;
  for (long long int i = 0; i < n; i++) g[i].clear();
  st1.clear();
  st2.clear();
  for (long long int i = 0; i < n - 1; i++) {
    long long int u, v, w, c;
    cin >> u >> v >> w >> c;
    --u, --v;
    edge tmp;
    tmp.v = v;
    tmp.w = w;
    tmp.c = c;
    g[u].push_back(tmp);
    tmp.v = u;
    g[v].push_back(tmp);
  }
  sum = 0;
  dfs(0);
  vector<long long int> one = seq(st1), two = seq(st2);
  long long int toChange = sum - s;
  long long int ans = INF;
  if (toChange <= 0) {
    ans = 0;
  }
  if ((long long int)((two).size()) && two.back() > toChange) {
    ans = min(ans, 2LL * (lower_bound((two).begin(), (two).end(), toChange) -
                          two.begin() + 1LL));
  }
  for (long long int i = 0; i < (long long int)((one).size()); i++) {
    long long int tar = toChange - one[i];
    long long int cost = i + 1;
    if (tar > 0) {
      cost += 2LL * (lower_bound((two).begin(), (two).end(), tar) -
                     two.begin() + 1LL);
      if ((long long int)((two).size())) {
        tar -= two.back();
      }
    }
    if (tar <= 0) {
      ans = min(ans, cost);
    }
  }
  cout << ans << '\n';
}
int32_t main() {
  std::ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int T;
  cin >> T;
  while (T--) {
    solve();
  }
  return 0;
}
