#include "cyberland.h"
#include<bits/stdc++.h>
using namespace std;
using db=double;
using pii=pair<int,int>;
using ll=long long;
#define eb emplace_back
#define f first
#define s second
const db eps=1e-2;
using A=pair<int,db>;
using B=pair<A,int>;
struct cmp{
bool operator()(const B &l,const B &r)const{
if(l.f.f!=r.f.f) return l.f.f>r.f.f;
return l.f.s-r.f.s > eps;
}
};
vector<pii> adj[100005];
A d[100005];
priority_queue<B,vector<B>,cmp> pq;
double solve(int N, int M, int K, int H, std::vector<int> U, std::vector<int> V, std::vector<int> W, std::vector<int> arr) {
for(int i=0;i<M;++i) adj[U[i]].eb(V[i],W[i]), adj[V[i]].eb(U[i],W[i]);
function<void(ll)> dijk=[&](ll lim){
pq.emplace(A(0,0),0);
d[0]={0,0};
for(int i=1;i<N;++i){
if(arr[i]==0) pq.emplace(A(0,0),i), d[i]={0,0};
else d[i]={1e9,0};
}
while(!pq.empty()){
auto [w,u]=pq.top(); pq.pop();
for(auto &[v,vw]:adj[u]){
A w2={w.f,w.s+vw};
if(arr[v]==2 && w2.s-lim>eps) ++w2.f, w2.s/=2;
if(d[v].f>w2.f || d[v].f==w2.f&&d[v].s-w2.s>eps){
d[v]=w2;
pq.emplace(w2,v);
}
}
}
};
// ll l=0,r=1e14;
// while(l<r){
// ll mid=(l+r>>1);
// dijk(mid);
// if(d[H].f>K) l=mid+1;
// else r=mid;
// }
dijk(0), dijk(1);
return d[H].s;
}
