#include "cyberland.h"
#include<bits/stdc++.h>
using namespace std;
typedef long double ld;
ld dist[65][111111];
ld pw[65];
struct node{
int v,k;
ld dist = 0;
node(int _v,int _k,ld _dist = 0){
v = _v;
k = _k;
dist = _dist;
}
};
struct comp
{
bool operator() (node const &a, node const &b) { return a.dist - b.dist > 1e-10; }
};
vector<pair<int,int>>adj[111111];
double solve(int n, int m,int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr){
priority_queue<node,vector<node>,comp>pq;
for(int j=0;j<n;j++){
adj[j].clear();
for(int i=0;i<=64;i++){
dist[i][j] = 1e15;
}
}
pw[0] = 1;
for(int i=1;i<=64;i++)pw[i] = pw[i-1]*2;
for(int i=0;i<m;i++){
adj[x[i]].push_back({y[i],c[i]});
adj[y[i]].push_back({x[i],c[i]});
}
K = min(K,64);
dist[0][H] = 0;
pq.push(node(H,0));
while(!pq.empty()){
node tmp = pq.top();
int v = tmp.v;
int k = tmp.k;
//cout<<v<<" "<<k<<" "<<tmp.dist<<" "<<dist[k][v]<<'\n';
pq.pop();
if(abs(tmp.dist - dist[k][v]) > 1e-10)continue;
if(arr[v] == 0)continue;
for(pair<int,int>x : adj[v]){
int u = x.first;
if(u == H)continue;
ld w = x.second/pw[k];
if(dist[k][u] - dist[k][v] - w > 1e-10){
dist[k][u] = dist[k][v] + w;
pq.push(node(u,k,dist[k][u]));
}
if(arr[u] == 2 && k+1 <= K){
if(dist[k+1][u] - dist[k][v] - w > 1e-10){
dist[k+1][u] = dist[k][v] + w;
pq.push(node(u,k+1,dist[k+1][u]));
}
}
}
}
ld ans = 1e18;
for(int i=0;i<=K;i++)ans = min(ans,dist[i][0]);
queue<int>q;
vector<int>vis(n,0);
q.push(0);
vis[0] = 1;
while(!q.empty()){
int v = q.front();
q.pop();
if(arr[v] == 0){
for(int i=0;i<=K;i++)ans = min(ans,dist[i][v]);
}
if(v==H)continue;
for(pair<int,int>x:adj[v]){
int u = x.first;
if(!vis[u]){
q.push(u);
vis[u] = 1;
}
}
}
if(!vis[H])return -1;
return ans;
}
