#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include "cyberland.h"
#define vi vector<int>
#define ve vector
#define ll long long
#define vl vector<ll>
#define vll vector<pair<ll,ll>>
#define onbit __builtin_popcount
#define ii pair<int,int>
#define vvi vector<vi>
#define vii vector<ii>
#define gii greater<ii>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define INF 1e18
#define eps 1e-7
#define eps1 1e-2
#define optimise ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define MAX_A 1e5+5
using namespace std;
using namespace __gnu_pbds;
template <class T>
using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const ll MOD = 1e9+7;
const int nax = 1e5+5;
const int MAX_VAL = 1e6;
double PI=3.14159265359;
int arx[8]={1,1,0,-1,-1,-1, 0, 1};
int ary[8]={0,1,1, 1, 0,-1,-1,-1};
void setIO(string s) {
freopen((s + ".in").c_str(), "r", stdin);
freopen((s + ".out").c_str(), "w", stdout);
}
vector<pair<int,double>> adj[nax];
int lst,cnt;
vector<bool> vis(nax,0);
double dis[nax][50];
void dfs(int x){
vis[x]=true;
if (x==lst) return;
for(auto u:adj[x]){
if (vis[u.fi]==true) continue;
dfs(u.fi);
}
return;
}
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) {
lst=H;
cnt=K;
for (int i = 0; i < N; ++i)
{
adj[i].clear();
for (int j = 0; j <= cnt; ++j)
{
dis[i][j]=1e18;
}
vis[i]=false;
}
for (int i = 0; i < M; ++i)
{
adj[x[i]].pb({y[i],c[i]});
adj[y[i]].pb({x[i],c[i]});
}
dfs(0);
priority_queue<pair<double,pair<int,int>>,vector<pair<double,pair<int,int>>>,greater<>> pq;
pq.push({0,{0,cnt}});
for (int i = 0; i < N; ++i)
{
if (arr[i]==0&&vis[i]==true) {
pq.push({0,{i,cnt}});
for (int j = 0; j <= cnt; ++j)
{
dis[i][j]=0;
}
}
}
while(!pq.empty()){
int node=pq.top().se.fi;
int lvl=pq.top().se.se;
double distance=pq.top().fi;
pq.pop();
if (node==lst){
return distance;
}
for(auto u:adj[node]){
double d=u.se+distance;
if (arr[u.fi]<=1){
if (dis[u.fi][lvl]<=d) continue;
dis[u.fi][lvl]=d;
pq.push({d,{u.fi,lvl}});
}else{
if (dis[u.fi][lvl]>d){
dis[u.fi][lvl]=d;
pq.push({d,{u.fi,lvl}});
}
if (lvl==0) continue;
if (dis[u.fi][lvl-1]>(d/2)){
dis[u.fi][lvl-1]=d/2;
pq.push({d/2,{u.fi,lvl-1}});
}
}
}
}
return -1;
}
/*int main(){
optimise;
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
int T;
assert(1 == scanf("%d", &T));
while (T--){
int N,M,K,H;
assert(4 == scanf("%d %d %d\n%d", &N, &M, &K, &H));
std::vector<int> x(M);
std::vector<int> y(M);
std::vector<int> c(M);
std::vector<int> arr(N);
for (int i=0;i<N;i++)
assert(1 == scanf("%d", &arr[i]));
for (int i=0;i<M;i++)
assert(3 == scanf("%d %d %d", &x[i], &y[i], &c[i]));
printf("%.12lf\n", solve(N, M, K, H, x, y, c, arr));
}
}*/
