#include "cyberland.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define fst first
#define snd second
#define pb push_back
#define forn(i,a,b) for(int i = a; i < b; i++)
#define ALL(x) x.begin(),x.end()
#define SZ(x) (int)x.size()
#define mset(a,v) memset((a),(v),sizeof(a))
#define FIN ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define dbg(v) cout<<"Line("<<__LINE__<<"): "<<#v<<" = "<<v<<'\n';
#define pi pair<int,int>
#define pll pair<ll,ll>
typedef int ll;
using namespace std;
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> indexed_set;
typedef tree<int,null_type,less_equal<int>,rb_tree_tag,tree_order_statistics_node_update> indexed_multiset;
ll n,m,k,h;
vector<pll> adj[(ll)1e5+5];
ll type[(ll)1e5+5];
bool disp[(ll)1e5+5];
void dfs(ll nd){
if(disp[nd]) return;
disp[nd]=1;
if(nd==h) return;
for(auto i:adj[nd]) dfs(i.fst);
}
double Dijkstra(){
vector<vector<double>> dist(n+1,vector<double>(k+1,-1));
priority_queue<pair<double,pair<double,ll>>> pq;
pq.push({0,{0,0}});
dist[0][0]=0;
forn(i,0,n){
if(type[i]==0&&disp[i]){
pq.push({0,{0,i}});
dist[i][0]=0;
//forn(j,0,k+1) dist[i][j]=0;
}
}
type[0]=0;
double cost;
ll nd;
ll p2;
ll ndV;
double nCost;
while(!pq.empty()){
cost = pq.top().snd.fst*-1;
nd = pq.top().snd.snd;
p2 = pq.top().fst*-1;
pq.pop();
if(cost>dist[nd][p2]) continue;
if(nd==h) continue;
for(auto i:adj[nd]){
ndV = i.fst;
nCost = i.snd+cost;
if(type[ndV]==0) continue;
if(nCost<dist[ndV][p2]||dist[ndV][p2]==-1){
dist[ndV][p2]=nCost;
pq.push({p2*-1,{dist[ndV][p2]*-1,ndV}});
}
if(type[ndV]==2&&p2+1<min((ll)k+1,(ll)k+1)){
nCost/=2;
if(nCost<dist[ndV][p2+1]||dist[ndV][p2+1]==-1){
dist[ndV][p2+1]=nCost;
pq.push({(p2+1)*-1,{dist[ndV][p2+1]*-1,ndV}});
}
}
}
}
double res = -1;
forn(i,0,k+1) if(dist[h][i]!=-1&&(res>dist[h][i]||res==-1)) res = dist[h][i];
return (double)res;
}
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){
n=N;m=M;k=min((ll)K,(ll)70);h=H;
forn(i,0,n) disp[i]=0,adj[i].clear(),type[i]=arr[i];
forn(i,0,m) adj[x[i]].pb({y[i],c[i]}),adj[y[i]].pb({x[i],c[i]});
dfs(0);
return Dijkstra();
}
