#include "cyberland.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
const int N = 1e5+5;
int n, h;
ll mn[N], dis[3][N];
vector<int> arr;
vector<pair<int, ll>> adj[N];
void dijkstra(int x, int idx) {
priority_queue<pair<ll, int>> pq;
if (idx == 2) {
for (int i = 0; i < n; i++) {
if (arr[i] || dis[0][i] == -1) continue;
pq.push(make_pair(-0, i));
}
}
else {
pq.push(make_pair(-0, x));
}
while (!pq.empty()) {
ll d = -pq.top().first;
int y = pq.top().second;
pq.pop();
if (dis[idx][y] != -1) continue;
dis[idx][y] = d;
if (idx != 1 && y == h) continue;
for (auto& [z, d2] : adj[y]) {
if (dis[idx][z] != -1) continue;
pq.push(make_pair(-(d+d2), z));
}
}
}
double solve(int N, int m, int k, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> ARR) {
n = N;
h = H;
arr.clear();
arr = ARR;
for (int i = 0; i < n; i++) {
adj[i].clear();
}
for (int i = 0; i < m; i++) {
adj[x[i]].push_back(make_pair(y[i], c[i]));
adj[y[i]].push_back(make_pair(x[i], c[i]));
}
for (int i = 0; i < n; i++) {
dis[0][i] = dis[1][i] = dis[2][i] = -1;
mn[i] = -1;
for (auto& [j, d] : adj[i]) {
if (j == h) continue;
if (mn[i] == -1) mn[i] = d;
else mn[i] = min(mn[i], d);
}
}
dijkstra(0, 0);
dijkstra(h, 1);
dijkstra(-1, 2);
// nada
ld ans = dis[0][h];
// solo 0
if (dis[2][h] != -1) ans = min(ans, (ld)dis[2][h]);
// solo 2
for (int i = 0; i < n; i++) {
if (arr[i] != 2 || dis[0][i] == -1 || dis[1][i] == -1) continue;
ld div = 2;
ld x = dis[0][i] / div;
if (mn[i] != -1) {
int cnt = k-1;
while (cnt > 0) {
ld nwX = (x + mn[i]) / div;
if (nwX > x) break;
x = nwX;
cnt--;
}
}
ans = min(ans, (ld)(x + dis[1][i]));
}
// 0 y 2
for (int i = 0; i < n; i++) {
if (arr[i] != 2 || dis[0][i] == -1 || dis[1][i] == -1 || dis[2][i] == -1) continue;
ld div = 2;
ld x = dis[2][i] / div;
if (mn[i] != -1) {
int cnt = k-1;
while (cnt > 0) {
ld nwX = (x + mn[i]) / div;
if (nwX > x) break;
x = nwX;
cnt--;
}
}
ans = min(ans, (ld)(x + dis[1][i]));
}
return ans;
}
