#include <bits/stdc++.h>
using namespace std;
void fast(){ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);}
const int N=1e5;
const double INF=1e16;
vector<pair<int,int>> v[N+1];
priority_queue<tuple<double,int,int>, vector<tuple<double,int,int>>, greater<tuple<double,int,int>>> pq;
double solve(int n, int m, int k, int h, vector<int> x, vector<int> y, vector<int> c, vector<int> a){
for(int i=0; i<n; i++) v[i].clear();
for(int i=0; i<m; i++){
v[x[i]].push_back({y[i], c[i]});
v[y[i]].push_back({x[i], c[i]});
}
k=min(k, 70);
set<int> t;
vector<bool> vis(n);
queue<int> q;
q.push(0);
vis[0]=true;
while(!q.empty()){
int u=q.front(); q.pop();
if(u==h) continue;
for(auto [p, q1]:v[u]){
if(vis[p]) continue;
if(a[p]==0) t.insert(p);
q.push(p);
vis[p]=true;
}
}
double pw[k+1];
pw[0]=1.0;
for(int i=1; i<=k; i++) pw[i]=pw[i-1]*2;
vector<vector<double>> dp(n, vector<double>(k+1, INF));
for(int i=0; i<=k; i++) dp[h][i]=0;
pq.push({0, h, 0});
double ans=INF;
while(!pq.empty()){
auto[d, u, dis]=pq.top(); pq.pop();
if(d>dp[u][dis]) continue;
if(t.count(u)){
ans=min(ans, d);
continue;
}
for(auto [to, dist]:v[u]){
if(d+dist/pw[dis]<dp[to][dis]){
dp[to][dis]=d+dist/pw[dis];
pq.push({dp[to][dis], to, (dis+(dis<k && a[to]==2))});
}
}
}
for(int i=0; i<=k; i++) ans=min(ans, dp[0][i]);
if(ans==INF) return -1;
return ans;
}
/*
int main(){
fast();
int n, m, k, h; cin>>n>>m>>k>>h;
vector<int> x(N+1), y(N+1), c(N+1), a(N+1);
for(int i=0; i<m; i++){
cin>>x[i]>>y[i]>>c[i];
}
for(int i=0; i<n; i++) cin>>a[i];
cout<<solve(n, m, k, h, x, y, c, a);
}
*/
/*
const int N=1e5;
const double INF=1e16;
int n, m, k, h;
vector<pair<int,int>> v[N+1], ad; //adventure graph
vector<int> a;
bool f=false; //find cyberland
void dfs(int node, int p){
if(f) return;
for(auto [i, d]:v[node]){
if(i==p) continue;
int di=0;
if(a[i]!=0) di=d;
ad.push_back({di, a[i]});
if(i==h) f=true;
dfs(i, node);
}
if(f) return;
ad.pop_back();
}
priority_queue<tuple<double,int,int>, vector<tuple<double,int,int>>, greater<tuple<double,int,int>>> pq;
double solve(int nn, int mm, int kk, int hh, vector<int> x, vector<int> y, vector<int> c, vector<int> aa){
for(int i=0; i<n; i++) v[i].clear();
n=nn, m=mm, k=kk, h=hh, a=aa;
for(int i=0; i<m; i++){
v[x[i]].push_back({y[i], c[i]});
v[y[i]].push_back({x[i], c[i]});
}
// if(m==n-1){
// ad.clear();
// dfs(0, -1);
// priority_queue<int> pqq;
// double ans=0;
// for(auto [p, q]:ad){
// if(q==2) pqq.push(p);
// else ans+=p;
// }
// while(!pqq.empty()){
// int u=pqq.top(); pqq.pop();
// if(k) ans+=double(u)/2;
// else ans+=u;
// k--;
// }
// return ans;
// }
vector<vector<double>> dp(n+1, vector<double>(k+1, INF));
dp[0][0]=0;
pq.push({0, 0, 0}); //dist, node now, disc
while(!pq.empty()){
auto[d, u, dis]=pq.top(); pq.pop();
if(d>dp[u][dis]) continue;
for(auto [to, dist]:v[u]){
if(a[to]==0){
if(0<dp[to][dis]){
dp[to][dis]=0;
pq.push({0, to, dis});
}
}
else if(a[to]==1){
if(d+dist<dp[to][dis]){
dp[to][dis]=d+dist;
pq.push({dp[to][dis], to, dis});
}
}
else{
if(d+dist<dp[to][dis]){
dp[to][dis]=d+dist;
pq.push({dp[to][dis], to, dis});
}
if(dis<k && d+dist/2<dp[to][dis+1]){
dp[to][dis+1]=d+dist/2;
pq.push({dp[to][dis+1], to, dis+1});
}
}
}
}
double ans=INF;
for(int i=0; i<=k; i++) ans=min(ans, dp[h][i]);
if(ans==INF) return -1;
else return ans;
}
*/
/*
int main(){
fast();
int n, m, k, h; cin>>n>>m>>k>>h;
vector<int> x(N+1), y(N+1), c(N+1), a(N+1);
for(int i=0; i<m; i++){
cin>>x[i]>>y[i]>>c[i];
}
for(int i=0; i<n; i++) cin>>a[i];
cout<<solve(n, m, k, h, x, y, c, a);
}
*/
