#include "cyberland.h"
#include <bits/stdc++.h>
#define IOS ios_base::sync_with_stdio(false);cin.tie();cout.tie();
#define all(x) x.begin(), x.end()
//#define int long long
#define vi vector<int>
#define pi pair<int, int >
#define pq priority_queue
#define lb lower_bound
#define ub upper_bound
#define pb push_back
#define eb emplace_back
#define mset multiset
#define F first
#define S second
#define pid pair<int, double>
#define pdi pair<double, int>
using namespace std;
// START
vector<pid> adj[100001];
double mindis[100001];
bool reach[100001];
int h, n;
void dfs(int s) {
reach[s] = 1;
if (s == h) return;
for (auto i: adj[s]) if(!reach[i.F]) dfs(i.F);
}
void dij(vector<int> &arr) {
pq<pdi> q;
for (int i = 0; i < n; i++) {
if (reach[i] && mindis[i] < 1e18) q.push({mindis[i], i});
}
vector<bool> vis(n, 0);
while(!q.empty()) {
int s = q.top().S; q.pop();
if (vis[s]) continue;
vis[s] = 1;
if (s == h) continue;
for (auto i: adj[s]) {
if(reach[i.F] && !vis[i.F] && mindis[i.F] > mindis[s] + i.S) {
mindis[i.F] = mindis[s] + i.S;
q.push({mindis[i.F], i.F});
}
}
}
vector<pid> tmp;
for (int s = 0; s < n; s++) {
double mn = mindis[s];
if (reach[s] && arr[s] == 2)
for (auto i: adj[s])
if (reach[i.F] && i.F != h) mn = min(mn, (mindis[i.F] + i.S) / 2.0);
if (mn < mindis[s]) tmp.pb({s, mn});
}
for(auto i: tmp) mindis[i.F] = min(mindis[i.F], i.S);
}
double solve(int N, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr) {
h = H; n = N;
K = min(K, 70);
for (int i = 0; i < N; i++) {
adj[i].clear();
reach[i] = 0;
mindis[i] = 1e18;
}
for(int i = 0; i < M; i++) {
adj[x[i]].pb({y[i], (double)c[i]});
adj[y[i]].pb({x[i], (double)c[i]});
}
dfs(0);
if(!reach[H]) return -1;
mindis[0] = 0;
for (int i = 1; i < N; i++)
if (reach[i] && !arr[i])
mindis[i] = 0;
for (int i = 0; i <= K; i++) dij(arr);
return mindis[H];
}
//END
