#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<queue>
#include<stack>
#include<map>
#include<stack>
#include<set>
#include<bitset>
using namespace std;
#define PI acos(-1.0)
#define eps 1e-8
#define min(a,b) (a)<(b)?(a):(b)
#define max(a,b) (a)>(b)?(a):(b)
#define abs(a) (a)<0?-(a):(a)
typedef long long ll;
typedef pair<int,int > P;
const int N=2e5+100,M=2e6+100;
const int inf=0x3f3f3f3f;
const ll INF=1e18+7,mod=1e9+7;
struct edge
{
    int from,to;
    ll w;
    int next;
};
edge es[M];
int cnt,head[N];
ll dp[N];
void init()
{
    cnt=0;
    memset(head,-1,sizeof(head));
}
void addedge(int u,int v,ll w)
{
    cnt++;
    es[cnt].from=u,es[cnt].to=v;
    es[cnt].w=w;
    es[cnt].next=head[u];
    head[u]=cnt;
}
void dfs(int u,int fa,ll mid)
{
    dp[u]=0LL;
    int child=0;
    for(int i=head[u]; i!=-1; i=es[i].next)
    {
        edge e=es[i];
        if(e.to==fa) continue;
        child++;
        dfs(e.to,u,mid);
        if(e.w>mid) dp[u]+=dp[e.to];
        else dp[u]+=min(dp[e.to],e.w);
    }
    if(!child) dp[u]=inf;
}
int main()
{
    int n;
    ll m;
    while(~scanf("%d%lld",&n,&m))
    {
        if(n==0&&m==0) break;
        init();
        ll l=inf,r=-inf;
        for(int i=1; i<n; i++)
        {
            int u,v;
            ll w;
            scanf("%d%d%lld",&u,&v,&w);
            l=min(l,w),r=max(r,w);
            addedge(u,v,w);
            addedge(v,u,w);
        }
        ll ans=0;
        while(l<=r)
        {
            ll mid=(l+r)>>1;
            dfs(1,0,mid);
            if(dp[1]<=m) r=mid-1,ans=mid;
            else l=mid+1;
        }
        if(ans) printf("%d\n",ans);
        else printf("-1\n");
    }
    return 0;
}