#include <bits/stdc++.h>
using namespace std;
int n, dad[200000 + 1], u[200000 + 1], v[200000 + 1];
long long w[200000], pop[200000], initsum, S;
std::vector<int> adjl[200000 + 1];
int cnode(int node, int ed) { return node ^ u[ed] ^ v[ed]; }
void dfs(int u) {
  int isleaf = 1;
  if (u != 1) pop[dad[u]] = 0;
  for (int ed : adjl[u])
    if (ed != dad[u]) {
      isleaf = 0;
      int v = cnode(u, ed);
      dad[v] = ed;
      dfs(v);
      initsum += w[ed] * pop[ed];
      if (u != 1) pop[dad[u]] += pop[ed];
    }
  if (isleaf) pop[dad[u]] = 1;
}
struct good_cmp {
  bool operator()(int l, int r) {
    return pop[l] * ((w[l] + 1) / 2) < pop[r] * ((w[r] + 1) / 2);
  }
};
void run() {
  cin >> n >> S;
  for (int i = 1; i <= n; ++i) adjl[i].clear();
  for (int i = 1; i < n; ++i) {
    cin >> u[i] >> v[i] >> w[i];
    adjl[u[i]].emplace_back(i);
    adjl[v[i]].emplace_back(i);
  }
  initsum = 0;
  memset(dad + 1, 0, n * sizeof(int));
  dad[1] = -1;
  dfs(1);
  std::priority_queue<int, std::vector<int>, good_cmp> pq;
  for (int i = 1; i < n; ++i) pq.push(i);
  long long ans = 0;
  while (initsum > S) {
    ++ans;
    int top = pq.top();
    pq.pop();
    initsum -= pop[top] * ((w[top] + 1) / 2);
    w[top] /= 2;
    pq.push(top);
  }
  cout << ans << '\n';
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(nullptr);
  int t;
  cin >> t;
  while (t--) run();
  return 0;
}
