#include "bits/stdc++.h"
using namespace std;
#define ff first
#define ss second
#define all(v) v.begin(), v.end()
#define ll long long
#define pb push_back
#define pii pair<int, int>
#define pli pair<ll, int>
#define pll pair<ll, ll>
#define tr(i, c) for(auto i = c.begin(); i != c.end(); ++i)
#define wr puts("----------------")
template<class T>bool umin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<class T>bool umax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
double solve(int n, int m, int k, int h, vector<int> x, vector<int> y, vector<int> c, vector<int> a){
umin(k, 69);
vector<pii> adj[n];
for(int i = 0; i < m; ++i){
adj[x[i]].pb({y[i], c[i]});
adj[y[i]].pb({x[i], c[i]});
}
vector<bool> vis(n, 0);
queue<int> Q;
Q.push(0);
vis[0] = 1;
while(!Q.empty()){
int x = Q.front();
Q.pop();
if(x == h)
continue;
for(auto &[i, w] : adj[x])
if(!vis[i]){
vis[i] = 1;
Q.push(i);
}
}
if(!vis[h])
return -1;
using node = pair<double, int>;
priority_queue<node, vector<node>, greater<node>> q[k+2];
vector<vector<bool>> mrk(n, vector<bool> (k+1, 0));
q[0].push({0, 0});
for(int i = 1; i < n; ++i)
if(!a[i] and vis[i])
q[0].push({0, i});
int pk = 0;
double answer = 1e18;
while(pk <= k){
if(q[pk].empty()){
++pk;
continue;
}
auto [val, x] = q[pk].top();
q[pk].pop();
if(x == h){
umin(answer, val);
mrk[x][pk] = 1;
}
if(mrk[x][pk])
continue;
mrk[x][pk] = 1;
for(auto [i, w] : adj[x])
if(a[i]){
if(!mrk[i][pk])
q[pk].push({val+w, i});
if(a[i] == 2)
q[pk+1].push({(val+w)/2, i});
}
}
return answer;
}
// int main(){
// double kk = solve(3, 2, 30, 2,{1, 2},{2, 0},{12, 4},{1, 2, 1});
// double kk1 = solve(4, 4, 30, 3,{0, 0, 1, 2},{1, 2, 3, 3},{5, 4, 2, 4},{1, 0, 2, 1});
// if(kk == 4.0 and kk1 == 2.0)
// puts("Correct.");
// else
// puts("Wrong Answer.");
// return 0;
// }
