#include "cyberland.h"
#include<iostream>
#include<stack>
#include<map>
#include<vector>
#include<string>
#include<unordered_map>
#include <queue>
#include<cstring>
#include<limits.h>
#include <cassert>
#include<cmath>
#include<set>
#include<algorithm>
#include <iomanip>
#include<numeric> //gcd(a,b)
#include<bitset>
#include <cstdlib>
#include <cstdint>
using namespace std;
#define ll long long
#define f first
//#define endl "\n"
#define s second
#define pii pair<int,int>
#define ppii pair<int,pii>
#define vi vector<int>
#define pb push_back
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define F(n) for(int i=0;i<n;i++)
#define lb lower_bound
#define ub upper_bound
#define fastio ios::sync_with_stdio(false);cin.tie(NULL);
#pragma GCC optimize ("03,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
using namespace std;
//#define int long long
//#define double long double
const ll inf=1e18,mxn=1e5;
double pre=1e-7;
struct info{
double cost;
int cur,use,bro;
bool operator<(info a)const{return (cost>a.cost);};
};
vector<pii>adj[mxn+10];
double what[mxn+10][70][2];
int vis[mxn+10][70][2];
priority_queue<info>pq;
double_t solve(int32_t n,int32_t m,int32_t k,int32_t H,vector<int32_t>x,vector<int32_t>y,vector<int32_t>c,vector<int32_t> arr){
k=min(k,69);
for(int i=0;i<n;i++)adj[i].clear();
for(int i=0;i<m;i++){
adj[x[i]].pb({y[i],c[i]});
adj[y[i]].pb({x[i],c[i]});
// p[find(x[i])]=find(y[i]);
}
adj[H].clear();
for(int i=0;i<n;i++)for(int j=0;j<=k;j++)for(int g=0;g<2;g++)what[i][j][g]=inf,vis[i][j][g]=0;
//for(int i=0;i<n;i++)if(arr[i]==0&&find(0)==find(i))pq.push({0,i,0,0});
what[0][0][0]=0;
pq.push({0,0,0,0});
double ans=inf;
while(!pq.empty()){
int cur=pq.top().cur,use=pq.top().use,bro=pq.top().bro;
double cost=pq.top().cost;
pq.pop();
if(vis[cur][use][bro])continue;
if(cur==H)return cost;
if(arr[cur]==2&&use<k&&bro==0){
if(what[cur][use+1][1]>(cost*1.0)/2){
what[cur][use+1][1]=(cost*1.0)/2;;
pq.push((info){what[cur][use+1][1],cur,use+1,1});
}
}
for(auto i:adj[cur]){
if(what[cur][use][bro]+i.s<what[i.f][use][0]){
what[i.f][use][0]=cost+i.s;
if(arr[i.f]==0)what[i.f][use][0]=0;
pq.push((info){what[i.f][use][0]*1.0,i.f,use,0});
}
}
}
return -1;
}
#undef int
/*
int32_t main(){
int t;cin>>t;
int n,m,k,h;cin>>n>>m>>k>>h;
vector<int>x(m),y(m),z(m),arr(n);
for(int i=0;i<n;i++)cin>>arr[i];
for(int i=0;i<m;i++)cin>>x[i]>>y[i]>>z[i];
cout<<solve(n,m,k,h,x,y,z,arr);
}*/
/*
1
4 4 30
3
1 1 2 1
0 1 5
0 2 4
1 3 2
2 3 4
*/
