/* 
 * Problem: NOI Winter Camp 2010 Rebuild
 * Author: Guo Jiabao
 * Time: 2010.3.12 14:01
 * Label: Solved
 * Memo: Binary Search + Monoqueue + Devide & Conquer on tree
*/
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <iostream>
#include <sstream>
#include <vector>
#include <list>
#include <deque>
#include <string>
#include <queue>
using namespace std;
#define var(a,b) typeof(b) a(b)
#define foreach(a,b) for (var(a,b.begin());a!=b.end();++a)
 
const int MAXN = 100001,MAXM=MAXN*2,INF=~0U>>1;
const double LIM=1e6,FINF = 1e20;
 
struct Monoqueue
{
	struct element
	{
		int key;
		double value;
	}Q[MAXN];
	int head,rear;
	void reset()
	{
		rear = 0;
		head = 1;
	}
	void insert(int k,double v)
	{
		while (rear >= head && v > Q[rear].value)
			rear--;
		Q[++rear].value = v;
		Q[rear].key = k;
	}
	int getmax(int L)
	{
		while (Q[head].key < L)
			head++;
		return Q[head].key;
	}
}MQ;
 
struct edge
{
	edge *next;
	int t,c;
};
 
int N,L,U,EC,timestamp,Total;
int t_ctd,t_ctd_csm,md1,md2,*t_maxdpt;
int size[MAXN],depth[MAXN];
double length[MAXN],d1m[MAXN],d2m[MAXN],*t_dm;
edge *V[MAXN],ES[MAXM];
int ava[MAXN];
double Ans,t_delta;
 
inline void addedge(int a,int b,int c)
{
	edge *e=ES+ ++EC;
	e->next = V[a];
	e->t = b;
	e->c = c;
	V[a] = e;
}
 
void init()
{
    freopen("rebuild.in","r",stdin);
    freopen("rebuild.out","w",stdout);
    scanf("%d%d%d",&N,&L,&U);
    for (int i=1;i<N;i++)
    {
    	int a,b,c;
    	scanf("%d%d%d",&a,&b,&c);
    	addedge(a,b,c);
    	addedge(b,a,c);
		if (L == 1 && c > Ans)
			Ans = c;
    }
}
 
void get_depth(int i)
{
	for (edge *e=V[i];e;e=e->next)
	{
		int j = e->t;
		if (ava[j] != 0) continue;
		if (depth[j] == -1)
		{
			depth[j] = depth[i] + 1;
			get_depth(j);
		}
	}
}
 
int get_longest_line(int start)
{
	int i,maxdepth;
	memset(depth,-1,sizeof(depth));
	depth[start] = maxdepth = 0;
	get_depth(start);
	for (i=1;i<=N;i++)
		if (ava[i] == 0 && depth[i] > maxdepth)
		{
			maxdepth = depth[i];
			start = i;
		}
	memset(depth,-1,sizeof(depth));
	depth[start] = maxdepth = 0;
	get_depth(start);
	for (i=1;i<=N;i++)
		if (ava[i] == 0 && depth[i] > maxdepth)
			maxdepth = depth[i];
	return maxdepth;
}
 
void get_size(int i)
{
	int csm = 0;
	size[i] = 1;
	for (edge *e=V[i];e;e=e->next)
	{
		int j = e->t;
		if (ava[j] != 0) continue;
		if (size[j] == -1)
		{
			get_size(j);
			size[i] += size[j];
			if (size[j] > csm)
				csm = size[j];
		}
	}
	if (Total - size[i] > csm)
		csm = Total - size[i];
	if (csm < t_ctd_csm)
	{
		t_ctd_csm = csm;
		t_ctd = i;
	}
}
 
int get_centroid(int i)
{
	memset(size,-1,sizeof(size));
	t_ctd_csm = INF;
	get_size(i);
	memset(size,-1,sizeof(size));
	return t_ctd;
}
 
void count_size(int i)
{
	size[i] = 1;
	for (edge *e=V[i];e;e=e->next)
	{
		int j = e->t;
		if (ava[j] != 0) continue;
		if (size[j] == -1)
		{
			count_size(j);
			size[i] += size[j];
		}
	}
}
 
void count_depth_max_length(int i)
{
	//求最大深度
	if (depth[i] > *t_maxdpt)
		*t_maxdpt = depth[i];
	for (edge *e=V[i];e;e=e->next)
	{
		int j = e->t;
		if (ava[j] != 0) continue;
		//求該深度最大帶權長度
		if (length[i] > t_dm[depth[i]])
			t_dm[depth[i]] = length[i];
		if (depth[j] == -1)
		{
			length[j] = length[i] + e->c - t_delta;
			depth[j] = depth[i] + 1;
			count_depth_max_length(j);
		}
	}
}
 
bool check(double delta,int ctd,edge *f)
{
	edge *e;
	int i,j,k;
	for (i=0;i<=N;i++)
		d1m[i] = d2m[i] = -FINF;
	t_delta = delta;
	memset(depth,-1,sizeof(depth));
	memset(length,-1,sizeof(length));
	md1 = md2 = 0;
	length[ctd] = depth[ctd] = 0;
 
	//統計部份1
	t_dm = d1m;
	t_maxdpt = &md1;
	for (e=V[ctd];e != f;e=e->next)
	{
		int j=e->t;
		if (ava[j] !=0) continue;
		length[j] = e->c - t_delta;
		depth[j] = 1;
		count_depth_max_length(j);
	}
	//統計部份2
	t_dm = d2m;
	t_maxdpt = &md2;
	for (e=f;e;e=e->next)
	{
		int j=e->t;
		if (ava[j] !=0) continue;
		length[j] = e->c - t_delta;
		depth[j] = 1;
		count_depth_max_length(j);
	}
	//單調隊列維護最大值
	//確定左邊界
	i = U-1;
	if (i > md1)
		i = md1;
	//確定右邊界
	k = L-i;
	if (k < 1)
		k = 1;
	MQ.reset();
	for (j=k;j<U-i && j<=md2 ;j++)
		MQ.insert(j,d2m[j]);
	double curv,maxv=-INF;
	for (;i>0 && L-i<=md2;i--)
	{
		j = U-i;
		if (j<=md2)
			MQ.insert(j,d2m[j]);
		int k = MQ.getmax(L-i);
		curv = d1m[i] + d2m[k];
		if (curv > maxv)
			maxv = curv;
	}
	return maxv >= 0;
}
 
double binary(int ctd,edge *f)
{
	double a=0,b=LIM,m;
	while (b - a >= 0.0001)
	{
		m = (a+b)/2;
		if (check(m,ctd,f))
			a = m;
		else
			b = m;
	}
	return a;
}
 
void dct(int start)
{
	int nowt = ++timestamp;
	int line = get_longest_line(start);
	if (line<=L || line<=2)
		return;
	int ctd = get_centroid(start); //取得重心
	double cur;
	//分割兩部份
	count_size(ctd);
	int pls = 0,pls2 = 0;
	edge *e,*f;
	for (e=V[ctd];e;e=e->next)
	{
		int j=e->t;
		if (ava[j] !=0) continue;
		pls += size[j];
		if (pls + pls + 1 >= size[ctd] - 1)
		{
			f = e->next;
			pls2 = size[ctd] - pls;
			pls++;
			break;
		}
	}
	//合併兩部份
	cur = binary(ctd,f);
	if (cur > Ans)
		Ans = cur;
	//遞歸部份1
	int j;
	if (pls-1 >= L)
	{
		for (e=f;e;e=e->next)
			if (ava[j=e->t] ==0)
				ava[j] = nowt;
		Total = pls;
		dct(ctd);
		for (edge *e=f;e;e=e->next)
			if (ava[j=e->t] ==nowt)
				ava[j] = 0;
	}
	//遞歸部份2
	if (pls2-1 >= L)
	{
		for (e=V[ctd];e!=f;e=e->next)
			if (ava[j=e->t] ==0)
				ava[j] = nowt;
		Total = pls2;
		dct(ctd);
		for (e=V[ctd];e!=f;e=e->next)
			if (ava[j=e->t] ==nowt)
				ava[j] = 0;
	}
}
 
void solve()
{
	memset(ava,0,sizeof(ava));
	Total = N;
	dct(1);
}
 
int main()
{
	init();
	solve();
	printf("%.3lf\n",Ans);
    return 0;
}

/* 
 * Problem: NOI Winter Camp 2010 efield
 * Author: Guo Jiabao
 * Time: 2010.3.15 12:21
 * Label: Solved
 * Memo: Computing Geometry + Convex Hull + Graham Scan
*/
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <iostream>
#include <sstream>
#include <vector>
#include <list>
#include <deque>
#include <string>
#include <queue>
 
#define var(a,b) typeof(b) a(b)
#define foreach(a,b) for (var(a,b.begin());a!=b.end();++a)
using std::sort;
 
const int MAXN = 50002;
 
struct point
{
	double x,y;
	int id;
};
 
int N,ipole;
point P[MAXN],pole,convex[MAXN],A[MAXN];
 
point operator -(const point &a,const point &b)
{
	point t={a.x-b.x,a.y-b.y,0};
	return t;
}
 
double operator *(const point &a,const point &b)
{
	return a.x*b.y - b.x*a.y;
}
 
void init()
{
	freopen("efield.in","r",stdin);
	freopen("efield.out","w",stdout);
	scanf("%d",&N);
	ipole=0;
	for (int i=1;i<=N;i++)
	{
		double m,c;
		scanf("%lf%lf",&m,&c);
		P[i].x = m*c;
		P[i].y = m;
		P[i].id = i;
		if (P[i].y > P[ipole].y)
			ipole = i;
	}
	pole = P[ipole];
	P[ipole] = P[N--];
}
 
bool cmp(const point &a,const point &b)
{
	point p = a - pole;
	point q = b - pole;
	double fc = p * q;
	if (fc > 0)
		return true;
	if (fc < 0)
		return false;
	return (p.x * p.x + p.y * p.y > q.x * q.x + q.y * q.y);
}
 
void graham()
{
	int top;
	sort(&P[1],&P[N+1],cmp);
	convex[1] = pole;
	convex[top=2] = P[1];
	for (int i=2;i<=N;i++)
	{
		point p = convex[top] - convex[top-1];
		point q = P[i] - convex[top];
		if (p*q < 0)
		{
			top--;
			i--;
		}
		else
			convex[++top] = P[i];
	}
	N = top;
	convex[N+1] = convex[1];
}
 
void getSumArea()
{
	int i;
	printf("%d\n",N);
	for (i=1;i<N;i++)
		printf("%d ",convex[i].id);
	printf("%d\n",convex[i].id);
/*	double SumArea = 0;
	for (i=1;i<=N;i++)
		SumArea += convex[i] * convex[i+1];
	SumArea *= 0.5;*/
}
 
bool cmp2(const point &a,const point &b)
{
	return a * b > 0;
}
 
void getPair()
{
	int M = 1,i,j,ai,aj;
	double PairArea = 0;
	for (i=1;i<=N;i++)
	{
		A[i] = convex[i];
		if (convex[i].x < convex[i-1].x)
			M = i;
	}
	sort(&A[1],&A[N+1],cmp2);
	for (i=1,j=1;i<=N;i++)
	{
		while (j<M && A[i]*(convex[j]-convex[j+1]) <= 0)
			j++;
		if (j == M)
			break;
		double cur = A[i] * convex[j];
		if (cur > PairArea)
		{
			PairArea = cur;
			ai = A[i].id;
			aj = convex[j].id;
		}
	}
	printf("%d %d\n",ai,aj);
}
 
void solve()
{
	graham();
	getPair();
	getSumArea();
}
 
int main()
{
	init();
	solve();
	return 0;
}