#include "cyberland.h"
#include <bits/stdc++.h>
#define LL __int128
using namespace std;
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 , LL>>> 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]);
}
K = min(K , 60);
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;
dist[0][0] = 0;
LL ans = -1 , p = 0;
pq.push(tuple<LL , int , int>{0 , 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 = dist[H][x];
p = x;
continue;
}
LL left = ans * (1LL << x);
LL right = dist[H][x] * (1LL << p);
if(right < left){
ans = dist[H][x];
p = x;
}
continue;
}
for(auto [v , w] : g[u]){
LL nD = D + w * (1LL << x);
if(arr[v] == 0){
nD = 0;
}
if(dist[v][x] == -1 || dist[v][x] > nD){
dist[v][x] = nD;
pq.push(tuple<LL , int , int>{dist[v][x] , v , x});
}
if(arr[v] == 2 && x < K && (dist[v][x + 1] == -1 || dist[v][x + 1] > nD)){
dist[v][x + 1] = nD;
pq.push(tuple<LL , int , int>{dist[v][x + 1] , v , x + 1});
}
}
}
if(ans == -1){
return ans;
}
long double S = 1;
for(int i = 0;i < p;i ++){
S /= 2.0;
}
S *= (long double)ans;
return (double)S;
}
