#include "cyberland.h"
#include <bits/stdc++.h>
using namespace std;
const int MAXN=100000;
vector<vector<pair<int,double>>> adj;
bool alc[MAXN], vis[MAXN];
void dfs(int u, const int& ban){
    alc[u]=true;
    for(auto [v,t]:adj[u]){
        if(v==ban)continue;
        if(!alc[v]){
            dfs(v, ban);
        }
    }
}
double solve(int N, int M, int K, int H, std::vector<int> x, std::vector<int> y, std::vector<int> c, std::vector<int> arr) {
    memset(alc, 0, sizeof(alc));
    memset(vis, 0, sizeof(vis));
    adj.clear();
    adj.resize(N);
    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]});
    }
    dfs(0,H);
    set<pair<double,int>> q;
    q.insert({0,0});
    double op1=1e18, op2=1e18;
    while(!q.empty()){
        auto [d,u]=*q.begin();
        q.erase(q.begin());
        if(vis[u])continue;
        vis[u]=true;
        if(u==H){
            op1=d;
            break; 
        }
        for(auto [v,t]:adj[u]){
            if(!vis[v]){
                q.insert({d+t,v});
            }
        }
    }
    if(op1==1e18)return -1;
    set<tuple<double,int,int>> q2;
    q2.insert({0,0,0}); 
    vector<vector<double>> dist(N, vector<double>(K+1, 1e18));
    dist[0][0]=0;
    while(!q2.empty()){
        auto [d,k,u]=*q2.begin();
        q2.erase(q2.begin());
        for(auto [v,t]:adj[u]){
            if(alc[v]){
                if(arr[v]==2&&k+1<=K){
                    if(dist[v][k+1]>(dist[u][k]+t)/2){
                        dist[v][k+1]=(dist[u][k]+t)/2;
                        q2.insert({dist[v][k+1],k+1,v});
                    }
                }
                if(dist[v][k]>dist[u][k]+t){
                    if(arr[v]==0)dist[v][k]=0;
                    else dist[v][k]=dist[u][k]+t;
                    q2.insert({dist[v][k],k,v});
                }
            }
        }
    }
    return *min_element(dist[H].begin(), dist[H].end());
}
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