#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <cmath>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <queue>
using namespace std;
#define Fio                           \
    ios_base::sync_with_stdio(false); \
    cin.tie(nullptr);                 \
    cout.tie(nullptr)
#define f(i, n) for (long long int i = 0; i < n; i++)
#define ll long long int
#define fo(i, a, b) for (long long int i = a; i <= b; i++)
#define w(t)  \
    int t;    \
    cin >> t; \
    while (t--)
#define vi vector<int>
#define vl vector<long long int>
#define vvi vector<vector<int>>
#define vvl vector<vector<long long int>>
#define mii map<int, int>
#define umii unordered_map<int, int>
#define newl cout<<"\n"
#define pb push_back
#define mp make_pair
#define fi first
#define se second
const ll inf = 1e9 + 7;
const ll modc = 998244353;
#define MAX 100002

ll sum = 0;

int dfs(ll node,ll prev,vector<vector<pair<ll,ll>>> &G, vi &vis,priority_queue<pair<ll,ll>> &Q){
    int ans = 0;
    for(auto x: G[node]){
        if(x.fi==prev)continue;
        int tmp = dfs(x.fi,node,G,vis,Q);
        Q.push(mp(tmp,x.se));
        sum += tmp*x.se;
        ans += tmp;
    }
    if(!ans)ans = 1;
    return ans;
}


void solve(){
    ll n,S;
    cin>>n>>S;
    vector<vector<pair<ll,ll>>> G(n+1);
    f(i,n-1){
        ll u,v,w;
        cin>>u>>v>>w;
        G[u].pb(mp(v,w));
        G[v].pb(mp(u,w));
    }
    vi vis(n+1,0);
    priority_queue<pair<ll,ll>>Q;
    dfs(1,0,G,vis,Q);
    int mov = 0;
    while(sum>S){
        mov++;
        pair<ll,ll> A = Q.top();
        Q.pop();
        sum -= A.fi*A.se;
        A.se=A.se/2;
        if(A.se){
            sum += A.se*A.fi;
            Q.push(mp(A.fi,A.se));
        }
    }
    cout<<mov;
    newl;
    sum = 0;
}

int main(){
    Fio;
    w(t){
        solve();
    }

    return 0;
}