#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]);
}
K = min(K , 74);
priority_queue<pair<LL , pair<int , int>> , vector<pair<LL , pair<int , int>>> , greater<pair<LL , pair<int , int>>>> pq;
dist[0][0] = 0;
LL ans = -1;
pq.push({0 , {0 , 0}});
while(!pq.empty()){
LL D = pq.top().first;
auto [u , x] = 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(arr[v] == 0){
nD = 0;
}
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;
}
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