#include <bits/stdc++.h>
#include "cyberland.h"
#pragma GCC optimize("O3")
#pragma GCC target("lzcnt", "popcnt")
using namespace std;
typedef double dbl;
typedef vector<int> vi;
typedef long long i64;
typedef pair<int, int> pii;
#define ff first
#define ss second
#define MP make_pair
const int mxk = 32;
const int mxn = 1e5 + 10;
vector<pii> adj[mxn];
dbl dis[mxk][mxn];
bool vis[mxn];
int H;
template<typename T> void ono_min(T &MIN, T CMP) { if(MIN > CMP) MIN = CMP; }
const bool operator < (pair<pair<dbl, int>, int> L, pair<pair<dbl, int>, int> R) {
if(L.ff != R.ff) return L.ff < R.ff;
if(L.ss == H) return 1;
if(R.ss == H) return 0;
return L.ss < R.ss;
}
double solve(int N, int M, int K, int H, vi x, vi y, vi c, vi arr) {
::H = H;
for(int i = 0; i < N; i++)
adj[i].clear();
for(int i = 0; i < M; i++) {
adj[x[i]].push_back(MP(y[i], c[i]));
adj[y[i]].push_back(MP(x[i], c[i]));
}
priority_queue<pair<pair<dbl, int>, int>> pq;
for(int i = 0; i < N; i++)
for(int j = 0; j <= K && j < mxk; j++)
dis[j][i] = -1.0;
for(int i = 0; i < N; i++)
vis[i] = 0;
queue<int> q;
vis[0] = 1;
q.push(0);
pq.push(MP(MP(0.0, 0), 0));
while(q.size()) {
int u = q.front();
q.pop();
if(arr[u] == 0)
pq.push(MP(MP(0.0, 0), u));
for(pii p : adj[u]) {
int v = p.ff;
if(!vis[v]) {
vis[v] = 1;
q.push(v);
}
}
}
while(pq.size()) {
dbl d = -pq.top().ff.ff;
int k = pq.top().ff.ss;
int u = pq.top().ss;
pq.pop();
if(dis[k][u] > -1.0) continue;
if(u == H) return d;
dis[k][u] = d;
for(pii p : adj[u]) {
int v = p.ff;
dbl c = p.ss;
// cout << " " << v;
if(v == 0 || arr[v] == 0) continue;
if(dis[k][v] == -1.0)
pq.push(MP(MP(-(d + c), k), v));
if(arr[v] == 2 && k < K && k < mxk)
if(dis[k + 1][v] == -1.0)
pq.push(MP(MP(-(d + c) / 2.0, k + 1), v));
}
// cout << endl;
}
// dbl ans = 1e18;
// for(int k = 0; k < mxk; k++)
// if(dis[k][H] != -1)
// ono_min(ans, dis[k][H]);
// if(ans != -1) return ans;
return -1;
}
