#include "cyberland.h"
#include <vector>
#include <bits/stdc++.h>
using namespace std;
#define ld double
#define pii pair<int,int>
#define fs first
#define sc second
const ld inf = 1e15;
const int mxn = 1e5+10;
const int lim = 60;
ld dist[mxn];
vector<pii> paths[mxn];
int N,M;
struct DSU{
int dsu[mxn],sz[mxn];
void init(int n){
for(int i = 0;i<n;i++)dsu[i] = i,sz[i] = 1;
}
int root(int k){
return k == dsu[k]?k:dsu[k] = root(dsu[k]);
}
void onion(int a,int b){
a = root(a),b = root(b);
if(a == b)return;
if(sz[a]<sz[b])swap(a,b);
dsu[b] = a;
sz[a] += sz[b];
return;
}
};
namespace DIJKSTRA{
bitset<mxn> done;
priority_queue<pair<ld,int>,vector<pair<ld,int>>,greater<pair<ld,int>>> pq;
void GO(){
for(int i = 0;i<N;i++){
done[i] = 0;
pq.push(make_pair(dist[i],i));
}
while(!pq.empty()){
auto now = pq.top().sc;
pq.pop();
if(done[now])continue;
done[now] = true;
for(auto &[nxt,w]:paths[now]){
if(done[nxt])continue;
if(dist[nxt]>dist[now]+w){
dist[nxt] = dist[now]+w;
pq.push(make_pair(dist[nxt],nxt));
}
}
}
return;
}
}
DSU dsu;
void init(){
for(int i = 0;i<N;i++)paths[i].clear();
}
double solve(int NN, int MM, int K, int H, std::vector<int> x, std::vector<int> y, std::vector<int> z, std::vector<int> arr) {
init();
N = NN,M = MM;
dsu.init(N);
for(int i = 0;i<M;i++){
int a = x[i],b = y[i],c = z[i];
dsu.onion(a,b);
paths[a].push_back(pii(b,c));
paths[b].push_back(pii(a,c));
}
if(dsu.root(0) != dsu.root(H)){
return -1;
}
for(int i = 0;i<N;i++){
if(dsu.root(i) == dsu.root(0)&&arr[i] == 0)dist[i] = 0;
else dist[i] = inf;
}
dist[0] = 0;
ld ans = inf;
for(int i = 0;i<=min(K,lim);i++){
DIJKSTRA::GO();
ans = min(ans,dist[H]);
dist[H] = inf;
for(int j = 0;j<N;j++){
if(arr[j]==2)dist[j]/=2;
assert(dsu.root(0) != dsu.root(j)||arr[j] != 0||dist[j]<0.001);
}
}
return ans;
}
