#include<bits/stdc++.h>
using namespace std;
 
#define fastio ios_base::sync_with_stdio(0); cin.tie(0)
#define LL long long 
#define mod 1000000007 
#define all(v) v.begin(),v.end()
#define FOR(i, j, k) for (auto i=j ; i<k ; i++)

const long long INF = 1e18;
const long long MAX = 2e5+10;
LL sum=0;
int dfs(int u, int p,vector<pair<LL,LL>>adj[],vector<int>&vis,priority_queue<pair<LL,LL>>&w,LL l){
    vis[u]=1; int cnt=0,le=0,tt;
    for(auto v : adj[u]) 
        if(!vis[v.first]){
            tt=dfs(v.first,u,adj,vis,w,l+v.second); 
            le+=tt; cnt++;
            w.push({v.second*tt,v.second});
        }
    if(cnt==0) {sum+=l; return 1; }
    return le;
}
int main(){
    fastio;
    int t=1; cin>>t;
    while(t--){
        LL n,s; cin>>n>>s;sum=0;
        vector<pair<LL,LL>>adj[n+1];  priority_queue<pair<LL,LL>>w; vector<int>vis(n+1,0);
        FOR(i,0,n-1){
            LL u,v,w; cin>>u>>v>>w;
            adj[u].push_back({v,w}); adj[v].push_back({u,w});
        }
        dfs(1,-1,adj,vis,w,0);
        int ans = 0; 
        while(sum>s && !w.empty()) {
            auto q = w.top(); w.pop();
            if(q.second) 
                sum-=q.first/2,w.push({q.first/2,q.second/2}),ans++;
        }
        cout<<ans<<"\n"; 
    }
}