#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e16 + 7;
struct cmp {
  bool operator()(pair<long long, long long> a,
                  pair<long long, long long> b) const {
    return (a.first / 2 + a.first % 2) * a.second >
           (b.first / 2 + b.first % 2) * b.second;
  }
};
vector<vector<pair<long long, long long>>> gr;
multiset<pair<long long, long long>, cmp> edges;
long long bfs(long long v, long long p) {
  if (gr[v].size() == 1 && v) {
    edges.insert({gr[v][0].second, 1});
    return 1;
  }
  long long cnt = 0;
  for (auto t : gr[v]) {
    if (t.first == p) continue;
    cnt += bfs(t.first, v);
  }
  for (auto t : gr[v]) {
    if (t.first == p) {
      edges.insert({t.second, cnt});
      break;
    }
  }
  return cnt;
}
void solve() {
  gr.clear();
  edges.clear();
  long long n, s;
  cin >> n >> s;
  gr.resize(n);
  for (long long i = 0; i < n - 1; ++i) {
    long long v, u, w;
    cin >> v >> u >> w;
    gr[--v].push_back({--u, w});
    gr[u].push_back({v, w});
  }
  bfs(0, -1);
  long long sum = 0, ans = 0;
  for (auto x : edges) sum += x.first * x.second;
  while (sum > s) {
    auto t = *edges.begin();
    sum -= (t.first / 2 + t.first % 2) * t.second;
    edges.erase(edges.begin());
    if (t.first / 2) edges.insert({t.first / 2, t.second});
    ++ans;
  }
  cout << ans << '\n';
}
signed main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  long long t = 1;
  cin >> t;
  while (t--) solve();
  return 0;
}
