#include <bits/stdc++.h>
using namespace std;
const long double pi = 3.141592653589793238462643383279502884;
const long long xd[] = {-1, 0, 1, 0};
const long long yd[] = {0, -1, 0, 1};
long long XX[] = {-1, -1, -1, 0, 0, 1, 1, 1};
long long YY[] = {-1, 0, 1, -1, 1, -1, 0, 1};
long long expo(long long a, long long b, long long m);
long long mmi(long long a, long long m);
void ipgraph(long long m);
const long long N = 5 * (1e5) + 10;
vector<pair<long long, long long> > adj[N];
long long a[N];
map<pair<long long, long long>, long long> m1;
map<pair<long long, long long>, long long> m2;
long long dfs(long long s1, long long p) {
  long long c = 0;
  for (auto u : adj[s1]) {
    if (u.first == p) continue;
    long long val = dfs(u.first, s1);
    m1[{min(s1, u.first), max(u.first, s1)}] += val;
    c += val;
  }
  if (c == 0) return 1;
  return c;
}
struct cmp {
  bool operator()(pair<long long, long long> p1,
                  pair<long long, long long> p2) {
    long long x = floor(p1.first / 2.0);
    long long y = floor(p2.first / 2.0);
    long long a1 = p1.first * p1.second - x * p1.second;
    long long b1 = p2.first * p2.second - y * p2.second;
    return a1 < b1;
  }
};
priority_queue<pair<long long, long long>, vector<pair<long long, long long> >,
               cmp>
    pq;
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t;
  cin >> t;
  while (t--) {
    m1.clear();
    m2.clear();
    long long n, s;
    cin >> n >> s;
    for (long long i = 0; i < n; i++) adj[i].clear();
    ipgraph(n - 1);
    dfs(0, -1);
    while (!pq.empty()) pq.pop();
    long long ts = 0;
    long long ops = 0;
    for (auto it : m2) {
      pair<long long, long long> p1 = it.first;
      pq.push({it.second, m1[p1]});
      ts = ts + it.second * m1[p1];
    }
    while (ts > s) {
      pair<long long, long long> p1 = pq.top();
      pq.pop();
      ts -= p1.first * p1.second;
      p1.first = floor(p1.first / 2.0);
      ts += p1.first * p1.second;
      if (p1.first != 0) pq.push(p1);
      ops++;
    }
    cout << ops << "\n";
  }
  return 0;
}
void ipgraph(long long m) {
  long long i, u, v, w;
  while (m--) {
    cin >> u >> v >> w;
    u--, v--;
    adj[u].push_back({v, w});
    adj[v].push_back({u, w});
    m2[{min(u, v), max(u, v)}] = w;
  }
}
long long expo(long long a, long long b, long long m) {
  if (b == 0) return 1;
  if (b == 1) return a;
  long long val = (expo(a, b / 2, m) * expo(a, b / 2, m)) % m;
  if (b & 1)
    return (val * a) % m;
  else
    return val;
}
long long mmi(long long a, long long m) { return expo(a, m - 2, m); }
