#include <bits/stdc++.h>
#include "cyberland.h"
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#include <x86intrin.h>
using namespace std;
typedef long long ll;
const int N = 1e5 + 1;
vector<pair<int, double>> g[N];
double d[N][70];
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)
{
k = min(k,69);
for (int i = 0; i < n; i++)
{
for(int j = 0;j <= k;j++){
d[i][j] = 1e15;
}
g[i].clear();
}
for (int i = 0; i < m; i++)
{
g[x[i]].push_back({y[i], c[i]});
g[y[i]].push_back({x[i], c[i]});
}
queue<int> q;
vector<int> can(n,0);
can[0] = 1;
q.push(0);
while(!q.empty()){
int v = q.front();
q.pop();
for(auto [to,w]:g[v]){
if(to == h || can[to]) continue;
q.push(to);
can[to] = 1;
}
}
priority_queue<pair<double,pair<int,int>>> st;
st.push({0,{0,0}});
for (int j = 0; j < n; j++)
{
if ((!arr[j] && can[j]) || !j)
{
st.push({0,{0,j}});
d[j][0] = 0;
}
}
double res = 1e15;
while(!st.empty()){
auto [col,v] = (st.top()).second;
st.pop();
if(v == h){
res = min(res,d[v][col]);
continue;
}
for(auto [to,w]:g[v]){
if(col + 1 <= k && arr[to] == 2 && d[to][col + 1] > (d[v][col] + w) / 2){
d[to][col + 1] = (d[v][col] + w) / 2;
st.push({-d[to][col + 1],{col + 1,to}});
}
if(d[to][col] > d[v][col] + w){
d[to][col] = d[v][col] + w;
st.push({-d[to][col],{col,to}});
}
}
}
if(res == 1e15) res = -1;
return res;
}
// int main() {
// int T;
// assert(1 == scanf("%d", &T));
// while (T--){
// int N,M,K,H;
// assert(4 == scanf("%d %d %d\n%d", &N, &M, &K, &H));
// std::vector<int> x(M);
// std::vector<int> y(M);
// std::vector<int> c(M);
// std::vector<int> arr(N);
// for (int i=0;i<N;i++)
// assert(1 == scanf("%d", &arr[i]));
// for (int i=0;i<M;i++)
// assert(3 == scanf("%d %d %d", &x[i], &y[i], &c[i]));
// printf("%.12lf\n", solve(N, M, K, H, x, y, c, arr));
// }
// }
