#include<bits/stdc++.h>
#ifndef HOME
#include "cyberland.h"
//including problem's library
#endif //HOME
using namespace std;
#define left __left
#define right __right
#define next __next
#define prev __prev
#define div __div
#define pb push_back
#define pf push_front
#define all(v) v.begin(), v.end()
#define sz(v) (int)v.size()
#define compact(v) v.erase(unique(all(v)), end(v))
#define dbg(v) "[" #v " = " << (v) << "]"
#define file(name) if(fopen(name".inp", "r")) {freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
template<typename T>
bool minimize(T& a, const T& b){
if(a > b) return a = b, true;
return false;
}
template<typename T>
bool maximize(T& a, const T& b){
if(a < b) return a = b, true;
return false;
}
template<int dimension, typename T>
struct vec : public vector<vec<dimension - 1, T>> {
static_assert(dimension > 0, "Dimension must be positive !\n");
template<typename... Args>
vec(int n = 0, Args... args) : vector<vec<dimension - 1, T>> (n, vec<dimension - 1, T>(args...)) {}
};
template<typename T>
struct vec<1, T> : public vector<T> {
vec(int n = 0, T val = T()) : vector<T>(n, val) {}
};
double solve(int N, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr){
vector<vector<pair<int, int>>> adj(N);
for(int i = 0; i < M; ++i){
int u = x[i], v = y[i], w = c[i];
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
K = min(K, 68);
using node = tuple<double, int, int>;
const double inf = 1e18;
priority_queue<node, vector<node>, greater<node>> pq;
vector<vector<double>> d(71, vector<double>(N, inf));
vector<bool> visited(N);
auto dfs = [&](auto &self, int u){
visited[u] = true;
if(u == H) return;
for(auto [v, w] : adj[u]) if(!visited[v]){
self(self, v);
}
};
dfs(dfs, 0);
if(!visited[H]) return -1;
for(int i = 0; i < N; ++i){
if(visited[i] && arr[i] == 0){
d[0][i] = 0;
pq.push({d[0][i], 0, i});
}
}
d[0][0] = 0;
pq.push({d[0][0], 0, 0});
while(!pq.empty()){
double tot; int k, u;
tie(tot, k, u) = pq.top();
pq.pop();
if(u == H) continue;
if(d[k][u] != tot) continue;
for(auto [v, w] : adj[u]) if(arr[v] != 0){
if(arr[v] == 2 && k < K && d[k + 1][v] > (tot + w) / 2.0){
d[k + 1][v] = (tot + w) / 2.0;
pq.push({d[k + 1][v], k + 1, v});
}
if(d[k][v] > d[k][u] + w){
d[k][v] = d[k][u] + w;
pq.push({d[k][v], k, v});
}
}
}
double ans = inf;
for(int i = 0; i <= K; ++i){
ans = min(ans, d[i][H]);
}
return ans;
}
#ifdef HOME
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout << solve(3, 2, 30, 2, {1, 2}, {2, 0}, {12, 4}, {1, 2, 1}) << '\n';
cout << solve(4, 4, 30, 3, {0, 0, 1, 2}, {1, 2, 3, 3}, {5, 4, 2, 4}, {1, 0, 2, 1}) << '\n';
return 0;
}
#endif // HOME
