#include<bits/stdc++.h>
#include "cyberland.h"
using namespace std;
#define ll long long
#define pb push_back
#define ff first
#define ss second
#define all(s) s.begin(),s.end()
#define rall(s) s.rbegin(),s.rend()
const double inf=1e18;
struct dsu{
vector<ll>p,sz;
void init(ll n){
p.resize(n);
iota(p.begin(),p.end(),0);
sz.resize(n);
fill(sz.begin(),sz.end(),1);
}
ll find(ll x){
if(p[x]==x){
return x;
}
return p[x]=find(p[x]);
}
bool same(ll x,ll y){
x=find(x);
y=find(y);
if(x==y){
return true;
}
else{
return false;
}
}
void merge(ll x,ll y){
x=find(x);
y=find(y);
if(x!=y){
if(sz[x]<sz[y]){
swap(x,y);
}
sz[x]+=sz[y];
p[y]=x;
}
}
}ds;
double solve(int N, int M, int K, int H, vector<int>x, vector<int>y, vector<int>c, vector<int>arr){
K=min(K,60);
vector<double>pw(K+1);
ds.init(N);
vector<pair<int,int>>adj[N];
for(int i=0;i<M;i++){
if(x[i]!=H&&y[i]!=H){
ds.merge(x[i],y[i]);
}
adj[x[i]].pb({c[i],y[i]});
adj[y[i]].pb({c[i],x[i]});
}
pw[0]=1;
for(int i=1;i<=K;i++){
pw[i]=pw[i-1]/2;
}
arr[0]=0;
vector<vector<double>>dist(K+1,vector<double>(N,inf));
using node=tuple<double,int,int>;
priority_queue<node,vector<node>,greater<node>>pq;
auto ck=[&](int k,int x,double d){
if(dist[k][x]>d){
dist[k][x]=d;
pq.push({d,k,x});
}
};
ck(K,H,0);
while(!pq.empty()){
auto [d,k,x]=pq.top();
pq.pop();
if(dist[k][x]<d){
continue;
}
if(arr[x]==0){
return d;
}
for(auto [c,y]:adj[x]){
if(!ds.same(y,0)){
continue;
}
ck(k,y,d+c*pw[K-k]);
if(arr[x]==2&&k>0){
ck(k-1,y,d+c*pw[K-k+1]);
}
}
}
return -1;
}
