#include "cyberland.h"
#include <bits/stdc++.h>
using namespace std;
void dfs(int st, vector<array<int,2>>g[], bool vis[], int tar){
vis[st]=1;
if(st==tar)
return;
for(array<int,2>e:g[st]){
if(vis[e[0]])
continue;
dfs(e[0],g,vis,tar);
}
}
const int mxk = 65;
const double inf = 1e18;
double solve(int N, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr) {
vector<array<int,2>>g[N];
for(int i = 0;i<M;i++){
g[x[i]].push_back({y[i],c[i]});
g[y[i]].push_back({x[i],c[i]});
}
bool vis[N];
fill(vis,vis+N,0);
dfs(0,g,vis,H);
if(!vis[H])
return -1;
double dist[N][mxk];
for(int i = 0;i<N;i++){
fill(dist[i],dist[i]+mxk,inf);
}
priority_queue<tuple<double,int>,vector<tuple<double,int>>,greater<tuple<double,int>>>pq;
pq.push({0,0});
dist[0][0]=0;
for(int i = 0;i<N;i++){
if(vis[i]&&arr[i]==0){
pq.push({0,i});
dist[i][0]=0;
}
}
while(!pq.empty()){
auto [time,u] = pq.top();
pq.pop();
if(dist[u][0]<time){
continue;
}
for(array<int,2>e:g[u]){
if(dist[e[0]][0]>time+e[1]){
dist[e[0]][0]=time+e[1];
pq.push({time+e[0],e[0]});
}
}
}
for(int curk = 1;curk<mxk;curk++){
for(int i = 0;i<N;i++){
if(arr[i]==2&&vis[i]&&dist[i][curk-1]!=inf){
for(array<int,2>e:g[i]){
if(dist[e[0]][curk]>(dist[i][curk-1]+e[1])/2){
dist[e[0]][curk]=(dist[i][curk-1]+e[1])/2;
pq.push({dist[e[0]][curk],e[0]});
}
}
}
}
while(!pq.empty()){
auto [time,u] = pq.top();
pq.pop();
if(dist[u][curk]<time){
continue;
}
for(array<int,2>e:g[u]){
if(dist[e[0]][curk]>time+e[1]){
dist[e[0]][curk]=time+e[1];
pq.push({dist[e[0]][curk],e[0]});
}
}
}
}
double ans = inf;
for(int i = 0;i<=min(mxk-1,K);i++){
ans=min(ans,dist[H][i]);
}
return ans;
}
