#include "cyberland.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
int n;int m;int KK;int HH;
ll ar[200005];
ll xar[200005];ll yar[200005];ll car[200005];
vector<pair<int,ll>>e[200005];
void inp(){
// cin>>n>>m>>KK>>HH;
HH++;
for(int i=1;i<=n;i++){
// cin>>ar[i];
e[i].clear();
}
for(int i=1;i<=m;i++){
//cin>>xar[i]>>yar[i]>>car[i];
xar[i]++;yar[i]++;
e[xar[i]].push_back({yar[i],car[i]});
e[yar[i]].push_back({xar[i],car[i]});
}
}
int uf[200005];
int fin(int x){
if(uf[x]==x){return x;}
uf[x]=fin(uf[x]);
return uf[x];
}
void mrg(int a,int b){
int pa=fin(a);int pb=fin(b);
if(pa==pb){return;}
uf[pa]=pb;
}
double dis[110][100005];
int vis[110][100005];
double slv(){
for(int i=1;i<=n;i++){
uf[i]=i;
}
for(int i=1;i<=m;i++){
if(xar[i]==HH||yar[i]==HH){continue;}
mrg(xar[i],yar[i]);
}
/*
*/
priority_queue<pair<double,pair<int,int>>,vector<pair<double,pair<int,int>>>,greater<pair<double,pair<int,int>>>>pq;
KK=min(KK,70);
for(int k=0;k<=KK;k++){
for(int i=1;i<=n;i++){
dis[k][i]=1e16;
vis[k][i]=0;
}
}
dis[0][1]=0;
pq.push({0,{0,1}});
for(int i=2;i<=n;i++){
if(ar[i]==0&&fin(i)==fin(1)){
pq.push({0,{0,i}});
dis[0][i]=0;
}
}
for(int i=1;i<=m;i++){
mrg(xar[i],yar[i]);
}
if(fin(1)!=fin(HH)){
return -1;
}
while(pq.size()){
int nw=pq.top().second.second;
int nwk=pq.top().second.first;
pq.pop();
if(vis[nwk][nw]){continue;}
vis[nwk][nw]=1;
if(nw==HH){continue;}
for(int i=0;i<e[nw].size();i++){
int v=e[nw][i].first;
ll w=e[nw][i].second;
if(vis[nwk][v]){continue;}
if(dis[nwk][v]>dis[nwk][nw]+w){
dis[nwk][v]=dis[nwk][nw]+w;
pq.push({dis[nwk][v],{nwk,v}});
}
}
}
for(int k=1;k<=KK;k++){
for(int i=1;i<=n;i++){
if(vis[k-1][i]&&ar[i]==2){
double vl=1e16;
for(int j=0;j<e[i].size();j++){
int v=e[i][j].first;
double w=e[i][j].second;
if(v==HH){continue;}
vl=min(vl,dis[k-1][v]+w);
}
dis[k][i]=vl/2.;
pq.push({dis[k][i],{k,i}});
}
}
while(pq.size()){
int nw=pq.top().second.second;
int nwk=pq.top().second.first;
pq.pop();
if(vis[nwk][nw]){continue;}
vis[nwk][nw]=1;
if(nw==HH){continue;}
for(int i=0;i<e[nw].size();i++){
int v=e[nw][i].first;
double w=e[nw][i].second;
if(vis[nwk][v]){continue;}
if(dis[nwk][v]>dis[nwk][nw]+w){
dis[nwk][v]=dis[nwk][nw]+w;
pq.push({dis[nwk][v],{nwk,v}});
}
}
}
}
double ans=dis[0][HH];
for(int i=1;i<=KK;i++){
if(!vis[i][HH]){continue;}
ans=min(ans,dis[i][HH]);
}
/*
for(int i=0;i<=3;i++){
for(int j=1;j<=n;j++){
cout<<dis[i][j]<<" ";
}cout<<endl;
}
*/
return ans;
}
//#define int int
double solve(int N, int M, int K, int H, std::vector<int> x, std::vector<int> y, std::vector<int> c, std::vector<int> arr){
/* cin>>N>>M>>K>>H;
for(int i=1;i<=N;i++){
int v;
cin>>v;
arr.push_back(v);
}
// cout<<M<<" ";
for(int i=1;i<=M;i++){
int a;int b;int cc;
cin>>a>>b>>cc;
x.push_back(a);y.push_back(b);c.push_back(cc);
// cout<<i<<" "<<M<<endl;
}
*/
n=N;m=M;KK=K;HH=H;
for(int i=0;i<x.size();i++){
xar[i+1]=x[i];
yar[i+1]=y[i];
car[i+1]=c[i];
}
for(int i=0;i<arr.size();i++){
ar[i+1]=arr[i];
}
// cout<<"hehe";
inp();
return slv();
}
/*
signed main()
{
cout<<fixed<<setprecision(7)<<solve(0,0,0,0,{},{},{},{});
// inp();
// cout<<slv();
return 0;
}
*/
