#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<ll, int>;
const int maxn = 1e5 + 5;
const int mod = 1e9 + 7;
struct edge {
  int to, w, c;
  edge(int a, int b, int c) : to(a), w(b), c(c) {}
};
priority_queue<P> pq1, pq2;
vector<edge> G[maxn];
int n, weight[maxn], sz[maxn];
ll S, now;
void init() {
  pq1 = {};
  pq2 = {};
  now = 0;
  for (int i = 1; i <= n; ++i) G[i].clear();
}
void dfs(int u, int fa) {
  sz[u] = 0;
  for (auto [v, w, c] : G[u]) {
    if (v == fa) continue;
    dfs(v, u);
    now += 1LL * w * sz[v];
    if (c == 1)
      pq1.emplace(1LL * (w - w / 2) * sz[v], v);
    else
      pq2.emplace(1LL * (w - w / 2) * sz[v], v);
    weight[v] = w;
    sz[u] += sz[v];
  }
  if (sz[u] == 0) sz[u] = 1;
}
void solve() {
  int res = 0;
  cin >> n >> S;
  init();
  for (int i = 1; i < n; ++i) {
    int u, v, w, c;
    cin >> u >> v >> w >> c;
    G[u].emplace_back(v, w, c);
    G[v].emplace_back(u, w, c);
  }
  dfs(1, -1);
  if (pq1.empty() || pq2.empty()) {
    auto& pq = pq1.empty() ? pq2 : pq1;
    while (now > S) {
      auto [val, idx] = pq.top();
      pq.pop();
      now -= val;
      weight[idx] /= 2;
      pq.emplace(1LL * (weight[idx] - weight[idx] / 2) * sz[idx], idx);
      ++res;
    }
    if (pq1.empty()) res *= 2;
  } else {
    while (now > S) {
      auto [val1_1, idx1] = pq1.top();
      pq1.pop();
      if (now - val1_1 <= S) {
        ++res;
        break;
      }
      ll val1_2 = 1LL * (weight[idx1] / 2 - weight[idx1] / 4) * sz[idx1];
      if (!pq1.empty() && pq1.top().first > val1_2) val1_2 = pq1.top().first;
      auto [val2, idx2] = pq2.top();
      if (val1_1 + val1_2 > val2) {
        now -= val1_1;
        weight[idx1] /= 2;
        pq1.emplace(1LL * (weight[idx1] - weight[idx1] / 2) * sz[idx1], idx1);
        ++res;
      } else {
        pq1.emplace(val1_1, idx1);
        pq2.pop();
        now -= val2;
        weight[idx2] /= 2;
        pq2.emplace(1LL * (weight[idx2] - weight[idx2] / 2) * sz[idx2], idx2);
        res += 2;
      }
    }
  }
  cout << res << '\n';
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int T;
  cin >> T;
  for (int Cas = 1; Cas <= T; ++Cas) solve();
  return 0;
}
