#include "cyberland.h"
#include <bits/stdc++.h>
#define LL double
using namespace std;
const int N = 1E5 + 1 , KM = 75;
LL dist[N][KM];
vector<pair<int , LL>> g[N];
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) {
for(int i = 0;i < N;i ++){
g[i].clear();
for(int j = 0;j < min(K + 1 , KM);j ++){
dist[i][j] = -1;
}
}
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){
for(auto [v , w] : g[u]){
if(!vis[v]){
vis[v] = true;
dfs(v);
}
}
};
dfs(0);
K = min(K , 74);
priority_queue<pair<int , pair<LL , int>> , vector<pair<int , pair<LL , int>>> , greater<pair<int , pair<LL , int>>>> pq;
LL ans = -1;
for(int i = 0;i < N;i ++){
if(vis[i] && (i == 0 || arr[i] == 0)){
pq.push({0 , {0 , i}});
dist[i][0] = 0;
}
}
while(!pq.empty()){
int x = pq.top().first;
x = -x;
auto [D , u] = pq.top().second;
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 + w;
if(dist[v][x] == -1 || dist[v][x] > nD){
dist[v][x] = nD;
pq.push({-x , {dist[v][x] , v}});
}
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({-x - 1, {dist[v][x + 1] , v}});
}
}
}
return (double)ans;
}
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