#include<bits/stdc++.h>
#define reg register int
#define il inline
#define fi first
#define se second
#define mk(a,b) make_pair(a,b)
#define numb (ch^'0')
using namespace std;
typedef long long ll;
template<class T>il void rd(T &x){char ch;x=0;bool fl=false;while(!isdigit(ch=getchar()))(ch=='-')&&(fl=true);for(x=numb;isdigit(ch=getchar());x=x*10+numb);(fl==true)&&(x=-x);
}
template<class T>il void output(T x){if(x/10)output(x/10);putchar(x%10+'0');}
template<class T>il void ot(T x){if(x<0) putchar('-'),x=-x;output(x);putchar(' ');}
template<class T>il void prt(T a[],int st,int nd){for(reg i=st;i<=nd;++i) ot(a[i]);putchar('\n');}namespace Miracle{
const int N=1e5+5;
const ll inf=0x3f3f3f3f3f3f3f3f;
int n;
struct node{int nxt,to;int val;
}e[2*N];
int hd[N],cnt;
void add(int x,int y,int z){e[++cnt].nxt=hd[x];e[cnt].to=y;e[cnt].val=z;hd[x]=cnt;
}
ll ans,len;
ll L,R;
int mem[N],fa[N],vf[N];
int on[N];
ll sum[N];
struct po{ll v;int id;po(){}po(ll vv,int dd){v=vv;id=dd;}
};
struct qs{po p[N];int sz;void push(ll v,int d){p[++sz]=po(v,d);}void clear(){sz=0;}il po &operator[](const int &x){return p[x];}il const po &operator[](const int &x) const {return p[x];}
}su,sd,up,dw;//member's number is numbool cmpu(po a,po b){//shengreturn a.v<b.v;
}
bool cmpd(po a,po b){//jiangreturn a.v>b.v;
}
int st,nd,num;
ll mx;
struct tr{ll f[N];void clear(){memset(f,-0x3f,sizeof f);}void ins(int x,ll v){for(;x<=n;x+=x&(-x)) f[x]=max(f[x],v);}ll query(int x){ll ret=-inf;for(;x;x-=x&(-x)) ret=max(ret,f[x]);return ret;}
}t[2];
//t[0]:dp-sum
//t[1]:dp+sum
void dfs1(int x,ll dis){if(dis>mx) {mx=dis;st=x;}for(reg i=hd[x];i;i=e[i].nxt){int y=e[i].to;if(y==fa[x]) continue;fa[y]=x;dfs1(y,dis+e[i].val);}
}
void dfs2(int x,ll dis){if(dis>mx){mx=dis;nd=x;}for(reg i=hd[x];i;i=e[i].nxt){int y=e[i].to;if(y==fa[x]) continue;fa[y]=x;vf[y]=e[i].val;dfs2(y,dis+e[i].val);}
}
ll dp[N];
void fin(int x){dp[x]=0;for(reg i=hd[x];i;i=e[i].nxt){int y=e[i].to;if(y==fa[x]||on[y]) continue;fa[y]=x;fin(y);L=max(L,dp[x]+dp[y]+e[i].val);dp[x]=max(dp[x],dp[y]+e[i].val);}
}
struct pointer{int ptr;ll lim;void clear(){ptr=0;lim=-inf;}void upda(ll v){lim=max(lim,v);}
}p[5];
pair<int,int>tp;
void con(int l,int r){tp.fi=max(tp.fi,l);tp.se=min(tp.se,r);
}
bool che(ll mid){///warning!!!! dp[mem[...[].id]]t[0].clear();t[1].clear();for(reg i=1;i<=4;++i) p[i].clear();int ptr=0;for(reg j=1;j<=num;++j){while(ptr<num&&dw[ptr+1].v+up[j].v>mid) {++ptr;t[0].ins(dw[ptr].id,dw[ptr].v);t[1].ins(dw[ptr].id,sum[dw[ptr].id]+dp[mem[dw[ptr].id]]);}if(ptr){ll djss=dp[mem[up[j].id]]-sum[up[j].id],djas=up[j].v;ll diss=t[0].query(up[j].id-1),dias=t[1].query(up[j].id-1);p[1].upda(len-mid+djss+dias);p[2].upda(len-mid+diss+djas);p[3].upda(len-mid+dias+djas);p[4].upda(len-mid+diss+djss);}}p[1].ptr=p[4].ptr=1;for(reg b=1;b<=num;++b){while(p[1].ptr<=num&&su[p[1].ptr].v-p[1].lim<su[b].v) ++p[1].ptr;while(p[2].ptr<num&&su[p[2].ptr+1].v+p[2].lim<=su[b].v) ++p[2].ptr;while(p[3].ptr<num&&-sd[p[3].ptr+1].v+p[3].lim<=su[b].v) ++p[3].ptr;while(p[4].ptr<=num&&-sd[p[4].ptr].v-p[4].lim<su[b].v) ++p[4].ptr;tp.fi=1;tp.se=num;con(p[1].ptr,num);con(1,p[2].ptr);con(num-p[3].ptr+1,num);con(1,num-p[4].ptr+1);if(tp.fi<=tp.se) return true;}return false;///warning!!!! dp[mem[...[].id]]
}
void clear(){ans=inf;num=0;st=nd=0;memset(sum,0,sizeof sum);memset(fa,0,sizeof fa);memset(vf,0,sizeof vf);memset(on,0,sizeof on);memset(hd,0,sizeof hd);su.clear();sd.clear();up.clear();dw.clear();cnt=0;L=0,R=0;
}
int main(){while(1){clear();rd(n);rd(len);if(n==0&&len==0) break;mx=-1;int x,y,z;for(reg i=1;i<n;++i){rd(x);rd(y);rd(z);add(x,y,z);add(y,x,z);}if(n==1){puts("0");continue;}dfs1(1,0);fa[st]=0;mx=-1;dfs2(st,0);
/*RRR*/ R=mx;num=0;x=nd;while(x){mem[++num]=x;on[x]=1;sum[num]=sum[num-1]+vf[mem[num-1]];x=fa[x];}memset(fa,0,sizeof fa);
/*LLL*/ for(reg i=1;i<=num;++i){fin(mem[i]);}for(reg i=1;i<=num;++i){su.push(sum[i],i);sd.push(sum[i],i);up.push(dp[mem[i]]+sum[i],i);dw.push(dp[mem[i]]-sum[i],i);}sort(su.p+1,su.p+num+1,cmpu);sort(sd.p+1,sd.p+num+1,cmpd);sort(up.p+1,up.p+num+1,cmpu);sort(dw.p+1,dw.p+num+1,cmpd);while(L<=R){ll mid=(L+R)/2;if(che(mid)){ans=mid;R=mid-1;}else L=mid+1;}printf("%lld\n",ans);}return 0;
}}
signed main(){Miracle::main();return 0;
}/*Author: *Miracle*
*/