#include "cyberland.h"
#include <bits/stdc++.h>
#define LL double
using namespace std;
const int N = 1E5 + 1 , KM = 75;
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) {
vector<vector<pair<int , int>>> g(N);
for(int i = 0;i < M;i ++){
g[x[i]].emplace_back(y[i] , c[i]);
g[y[i]].emplace_back(x[i] , c[i]);
}
vector<bool> vis(N);
vis[0] = true;
function<void(int)> dfs = [&](int u){
if(u == H){
return;
}
for(auto [v , w] : g[u]){
if(!vis[v]){
vis[v] = true;
dfs(v);
}
}
};
dfs(0);
K = min(K , 74);
vector<vector<LL>> dist(N , vector<LL>(K + 1 , -1));
priority_queue<tuple<LL , int , int> , vector<tuple<LL , int , int>> , greater<tuple<LL , int , int>>> pq;
LL ans = -1;
for(int i = 0;i < N;i ++){
if(vis[i] && (i == 0 || arr[i] == 0)){
pq.push({0 , i , 0});
dist[i][0] = 0;
}
}
while(!pq.empty()){
auto [D , u , x] = pq.top();
pq.pop();
if(dist[u][x] != D){
continue;
}
if(u == H){
if(ans == -1){
ans = D;
}else{
ans = min(ans , D);
}
continue;
}
for(auto [v , w] : g[u]){
LL nD = D + (LL)w;
if(dist[v][x] == -1 || dist[v][x] > nD){
dist[v][x] = nD;
pq.push({dist[v][x] , v , x});
}
nD /= 2.0;
if(arr[v] == 2 && x < K && (dist[v][x + 1] == -1 || dist[v][x + 1] > nD)){
dist[v][x + 1] = nD;
pq.push({dist[v][x + 1], v , x + 1});
}
}
}
return (double)ans;
}
