#include "bits/stdc++.h"
#include "cyberland.h"
using namespace std;
const char nl = '\n';
#include <vector>
struct UFDS{
int n; vector<int> lnk, sz;
UFDS(int N) {
n = N;
lnk.resize(n);
iota(lnk.begin(), lnk.end(), 0);
sz.resize(n, 1);
}
int find(int a) {
return (a == lnk[a] ? a : lnk[a] = find(lnk[a]));
}
bool same(int a, int b) {
return (find(a) == find(b));
}
void unite(int a, int b) {
a = find(a); b = find(b);
if(a == b) return;
if(sz[a] < sz[b]) swap(a, b);
lnk[b] = a;
sz[a] += sz[b];
}
};
double solve(int N, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr) {
K = min(K, 70);
vector<pair<int, double>> adj[N];
/* UFDS uf(N); */
for(int i = 0; i < M; ++i) {
adj[x[i]].emplace_back(y[i], c[i]);
adj[y[i]].emplace_back(x[i], c[i]);
/* if(x[i] != H && y[i] != H) uf.unite(x[i], y[i]); */
}
int S = 0, hf = -1; double wt = 1e9 + 1;
for(int i = 1; i < H; ++i) if(arr[i] == 0) S = i;
for(int i = 1; i < H; ++i) if(arr[i] == 2) hf = i;
if(hf > -1) for(auto [i, w] : adj[hf]) if(i != H && w < wt) wt = w;
double res = 0;
for(int i = S; i < H; ++i) {
for(auto [j, w]: adj[i]) {
if(j < i) continue;
res += w;
if(i != hf) continue;
double opt = res;
for(int rep = 0; rep < K; ++rep) {
opt = (opt + w) / 2;
res = min(res, opt);
}
}
}
return res;
/* cout << N << " cities" << nl; */
/* cout << M << " edges" << nl; */
/* cout << H << " destination" << nl; */
/* for(int i = 0; i < M; ++i) { */
/* cout << i << " : "; */
/* for(auto u : adj[i]) { */
/* cout << "(" << u.first << ", " << u.second << ") "; */
/* } */
/* cout << nl; */
/* } */
/* double dist[N][K + 1]; */
/* for(int i = 0; i < N; ++i) { */
/* for(int j = 0; j <= K; ++j) { */
/* dist[i][j] = -1; */
/* } */
/* } */
/* priority_queue<pair<double, pair<int, int>>> pq; */
/* dist[0][0] = 0; */
/* pq.push({-dist[0][0], {0, 0}}); */
/* for(int i = 0; i < N; ++i) { */
/* if(uf.same(i, 0) && arr[i] == 0) { */
/* dist[i][0] = 0; */
/* pq.push({-dist[i][0], {0, i}}); */
/* } */
/* } */
/* while(!pq.empty()) { */
/* int a = pq.top().second.second; */
/* int st = -pq.top().second.first; */
/* double d = -pq.top().first; */
/* pq.pop(); */
/* if(dist[a][st] < d || a == H) { */
/* continue; */
/* } */
/* for(auto [b, w] : adj[a]) { */
/* if(arr[b] == 0) { */
/* dist[b][st] = 0; */
/* pq.push({-dist[b][st], {-st, b}}); */
/* continue; */
/* } */
/* if(dist[b][st] == -1 || d + w < dist[b][st]) { */
/* dist[b][st] = d + w; */
/* pq.push({-dist[b][st], {-st, b}}); */
/* } */
/* if(arr[b] == 2 && st < K) { */
/* ++st; */
/* if(dist[b][st] == -1 || (d + w) / 2 < dist[b][st]) { */
/* dist[b][st] = (d + w) / 2; */
/* pq.push({-dist[b][st], {-st, b}}); */
/* } */
/* --st; */
/* } */
/* } */
/* } */
/* double ans = -1; */
/* for(int i = 0; i <= K; ++i) { */
/* if(ans == -1 || (dist[H][i] != -1 && ans > dist[H][i])) */
/* ans = dist[H][i]; */
/* } */
/* return ans; */
}
