code:
#include <bits/stdc++.h>
using namespace std;
#define setIO(s) freopen(s".in","r",stdin)
const int N=200006;
const double eps=1e-6;
const double inf=-100000000;
struct node
{
int u,dep,val;
node(int u=0,int dep=0,int val=0):u(u),dep(dep),val(val){}
};
struct data
{
int len;
double dis;
data(int len=0,double dis=0.0):len(len),dis(dis){}
};
bool cmp(node a,node b) { return a.dep<b.dep; }
deque<data>q;
vector<node>G[N];
vector<int>tree[N];
int n,L,R,edges,root;
int hd[N],to[N<<1],nex[N<<1],val[N<<1];
int size[N],mx[N],vis[N],sn,max_dep,RT;
double maxv[N],tmp[N],mid;
inline void add(int u,int v,int c)
{
nex[++edges]=hd[u],hd[u]=edges,to[edges]=v,val[edges]=c;
}
void getroot(int u,int ff)
{
size[u]=1,mx[u]=0;
for(int i=hd[u];i;i=nex[i])
{
int v=to[i];
if(v==ff||vis[v]) continue;
getroot(v,u);
size[u]+=size[v];
mx[u]=max(mx[u],size[v]);
}
mx[u]=max(mx[u],sn-size[u]);
if(mx[u]<mx[root]) root=u;
}
void getdis(int u,int ff,int d)
{
max_dep=max(max_dep,d);
for(int i=hd[u];i;i=nex[i]) if(to[i]!=ff&&!vis[to[i]]) getdis(to[i],u,d+1);
}
void prepare(int u)
{
vis[u]=1;
for(int i=hd[u];i;i=nex[i])
{
int v=to[i];
if(vis[v]) continue;
max_dep=0;
getdis(v,u,1);
G[u].push_back(node(v,max_dep,val[i]));
}
sort(G[u].begin(),G[u].end(),cmp);
for(int i=hd[u];i;i=nex[i])
{
int v=to[i];
if(vis[v]) continue;
sn=size[v];
root=0;
getroot(v,u);
tree[u].push_back(root);
prepare(root);
}
}
void dfs(int u,int ff,int d,double dis)
{
maxv[d]=max(maxv[d],dis);
for(int i=hd[u];i;i=nex[i])
{
int v=to[i];
if(v==ff||vis[v]) continue;
dfs(v,u,d+1,dis+val[i]-mid);
}
}
int calculate(int u)
{
int flag=0;
for(int i=0;i<G[u].size();++i)
{
int v=G[u][i].u;
dfs(v,u,1,G[u][i].val-mid);
for(int j=1;j<=G[u][i].dep;++j) if(maxv[j]>=-eps&&j>=L&&j<=R) { flag=1; break; }
if(i)
{
int tl=min(R,G[u][i-1].dep);
for(int j=1;j<=min(R,G[u][i].dep);++j)
{
for(;tl>=L-j&&tl>0;--tl)
{
while(!q.empty()&&(tmp[tl]-eps)>=q.front().dis) q.pop_front();
q.push_front(data(tl,tmp[tl]));
}
while(!q.empty()&&q.back().len>R-j) q.pop_back();
if(!q.empty())
{
if(maxv[j]+q.back().dis>=-eps)
{
flag=1;
break;
}
}
}
}
while(!q.empty()) q.pop_front();
if(flag) break;
for(int j=1;j<=G[u][i].dep;++j) tmp[j]=max(tmp[j],maxv[j]);
for(int j=0;j<=G[u][i].dep;++j) maxv[j]=inf;
}
if(G[u].size())
{
for(int i=0;i<=G[u][G[u].size()-1].dep;++i) tmp[i]=maxv[i]=inf;
}
while(!q.empty()) q.pop_front();
return flag;
}
int solve(int u)
{
vis[u]=1;
if(calculate(u)) return 1;
for(int i=0;i<tree[u].size();++i) if(solve(tree[u][i])) return 1;
return 0;
}
int main()
{
// setIO("input");
int i,j;
scanf("%d%d%d",&n,&L,&R);
for(i=1;i<n;++i)
{
int x,y,z;
scanf("%d%d%d",&x,&y,&z);
add(x,y,z),add(y,x,z);
}
mx[0]=sn=n;
getroot(1,0);
RT=root;
prepare(root);
double l=0.0,r=1000000.0;
for(i=0;i<N;++i) maxv[i]=tmp[i]=inf;
for(int i=33;i>=1;--i)
{
mid=(l+r)/2;
memset(vis,0,sizeof(vis));
if(solve(RT))
{
l=mid;
}
else
{
r=mid;
}
}
printf("%.3f
",l);
return 0;
}