1 #define Troy 09/30/2017
  2
  3 #define inf 0x7fffffff
  4
  5 #include <bits/stdc++.h>
  6
  7 using namespace std;
  8
  9 typedef long long ll;
 10
 11 const int N=500100;
 12 const double eps=1e-4;
 13
 14 inline int read(){
 15     int s=0,k=1;char ch=getchar();
 16     while(ch<'0'|ch>'9')  ch=='-'?k=-1:0,ch=getchar();
 17     while(ch>47&ch<='9')  s=s*10+(ch^48),ch=getchar();
 18     return s*k;
 19 }
 20
 21 struct edges{
 22     int v;ll w;edges *last;
 23 }edge[N<<1],*head[N];int cnt;
 24
 25 inline void push(int u,int v,ll w){
 26     edge[++cnt]=(edges){v,w,head[u]};head[u]=edge+cnt;
 27 }
 28
 29 int n,up,low,tot,top,root,size[N],heavy[N],T[N],Tdis[N],part,from;
 30 ll t[N],dis[N];
 31 bool vis[N];
 32 double ans,maxr;
 33
 34 inline void dfs(int x,int fa,int deep){
 35     size[x]=1;
 36     heavy[x]=0;
 37     for(edges *i=head[x];i;i=i->last)if(i->v!=fa&&(!vis[i->v])){
 38         dfs(i->v,x,deep+1);
 39         size[x]+=size[i->v];
 40         heavy[x]=max(size[i->v],heavy[x]);
 41     }
 42     heavy[x]=max(heavy[x],tot-size[x]);
 43     if(heavy[x]<top)
 44         top=heavy[x],root=x;
 45 }
 46
 47 inline void calc(int x,int fa,ll d,int lens){
 48     if(lens>up)  return ;
 49     if(Tdis[lens]!=part){
 50         Tdis[lens]=part;
 51         dis[lens]=d;
 52     }else
 53         dis[lens]=max(dis[lens],d);
 54     for(edges *i=head[x];i;i=i->last)    if(i->v!=fa&&(!vis[i->v])){
 55         calc(i->v,x,d+i->w,lens+1);
 56     }
 57 }
 58
 59 inline void get_new(int x,int fa,ll d,int lens){
 60     if(lens>up)  return;
 61     if(T[lens]!=T[0])
 62         T[lens]=T[0],t[lens]=d;
 63     else
 64         t[lens]=max(t[lens],d);
 65     from=max(from,lens);
 66     for(edges *i=head[x];i;i=i->last)    if(i->v!=fa&&(!vis[i->v])){
 67         get_new(i->v,x,d+i->w,lens+1);
 68     }
 69 }
 70
 71 int q[N];
 72 double nq[N];
 73
 74 inline bool Judge(double x){
 75     int l=0,r=0;
 76     int pos=min(up-1,from);
 77     bool flag=1;
 78     while(pos>=low){
 79         if(T[pos]!=T[0]){
 80             pos--;continue;
 81         }
 82         while(r>l&&nq[r-1]<t[pos]-x*pos)
 83             r--;
 84         nq[r]=t[pos]-x*pos;
 85         q[r++]=pos;
 86         pos--;
 87     }
 88     for(int i=low-pos;i<=up;i++){
 89         if(Tdis[i]!=part)   break;
 90         if(pos>=0&&i+pos>=low&&T[pos]==T[0]){
 91             while(r>l&&nq[r-1]<t[pos]-x*pos)
 92                 r--;
 93             nq[r]=t[pos]-x*pos;
 94             q[r++]=pos;
 95         }
 96         while(l<r&&q[l]+i>up)
 97             l++;
 98         pos--;
 99         if(l<r&&nq[l]+dis[i]-i*x>=0)
100             return true;
101     }
102     return false;
103 }
104
105 struct node{
106     int v,w;
107     friend bool operator <(node x,node y){
108         return size[x.v]<size[y.v];
109     }
110 }sons[N];
111
112
113 inline void solve(int u){
114     tot=size[u];
115     top=inf;
116     dfs(u,u,0);
117     vis[root]=true;
118     T[0]++;
119     from=1;
120     int cc=0;
121     for(edges *i=head[root];i;i=i->last)if(!vis[i->v]){
122         cc++;
123         sons[cc].v=i->v;
124         sons[cc].w=i->w;
125     }
126     sort(sons+1,sons+1+cc);
127     for(int i=1;i<=cc;i++){
128         if(i>1){
129                 part++;
130                 calc(sons[i].v,0,sons[i].w,1);
131                 double l=ans,r=maxr,mid;
132                 while(l<r-eps){
133                     mid=(l+r)/2;
134                     if(Judge(mid))  l=mid;
135                     else    r=mid;
136                 }
137                 ans=l;
138             }
139             if(i<cc)
140                 get_new(sons[i].v,0,sons[i].w,1);
141     }
142     for(edges *i=head[root];i;i=i->last) if(!vis[i->v])
143         solve(i->v);
144 }
145
146 int main(){
147     n=read();
148     low=read(),up=read();
149     for(int i=1,u,v,w;i<n;i++){
150         u=read(),v=read(),w=read();
151         push(u,v,w),push(v,u,w);
152         maxr=max(maxr,w+0.0);
153     }
154     size[1]=n;
155     solve(1);
156     printf("%.3lf\n",ans);
157 }