#include <bits/stdc++.h>
using namespace std;
template <class T>
ostream &operator<<(ostream &str, vector<T> &a) {
  for (auto &i : a) {
    str << i << " ";
  }
  return str;
}
template <class T>
istream &operator>>(istream &str, vector<T> &a) {
  for (auto &i : a) {
    str >> i;
  }
  return str;
}
template <class T>
ostream &operator<<(ostream &str, pair<T, T> &a) {
  str << a.first << " " << a.second;
  return str;
}
template <class T>
istream &operator>>(istream &str, pair<T, T> &a) {
  str >> a.first >> a.second;
  return str;
}
void solve();
signed main() {
  srand(time(0));
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cout.setf(ios::fixed);
  cout.precision(6);
  solve();
  return 0;
}
const long long MOD = 1e9 + 7, MAXN = 5e5 + 10, INF = 1e18 + 10, BASE = 37;
long long T = 1;
void dfs(long long v, long long p, vector<long long> &cnt,
         vector<vector<long long>> &g, vector<long long> &tin) {
  tin[v] = T++;
  if ((long long)((g[v]).size()) == 1 && v != 1) {
    cnt[v] = 1;
    return;
  }
  for (auto u : g[v]) {
    if (u != p) {
      dfs(u, v, cnt, g, tin);
      cnt[v] += cnt[u];
    }
  }
}
void query() {
  long long n, s;
  cin >> n >> s;
  vector<vector<long long>> g(n + 1);
  vector<long long> w(n + 1);
  map<pair<long long, long long>, long long> mp;
  for (long long i = 0; i < n - 1; ++i) {
    long long u, v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
    long long wt;
    cin >> wt;
    mp[{u, v}] = wt;
  }
  vector<long long> cnt(n + 1);
  T = 1;
  vector<long long> tin(n + 1);
  dfs(1, 0, cnt, g, tin);
  for (auto it : mp) {
    long long first = it.first.first, second = it.first.second;
    if (tin[first] > tin[second]) {
      w[first] = it.second;
    } else {
      w[second] = it.second;
    }
  }
  set<pair<long long, long long>> se;
  long long sum = 0;
  for (long long v = 2; v <= n; ++v) {
    se.insert({cnt[v] * w[v] - (w[v] / 2) * cnt[v], v});
    sum += cnt[v] * w[v];
  }
  long long ans = 0;
  while (sum > s) {
    auto it = *(--se.end());
    se.erase(it);
    long long v = it.second;
    sum -= cnt[v] * w[v];
    w[v] /= 2;
    sum += cnt[v] * w[v];
    se.insert({cnt[v] * w[v] - (w[v] / 2) * cnt[v], v});
    ans++;
  }
  cout << ans << '\n';
}
void solve() {
  long long t;
  cin >> t;
  for (long long i = 0; i < t; ++i) {
    query();
  }
}
