#include <bits/stdc++.h>
#include "cyberland.h"
using namespace std;
typedef long long ll;
double solve(int N, int M, int K, int H, vector<int> x, vector<int>
y, vector<int> c, vector<int> arr) {
vector<vector<pair<int,int>>> g(N);
for(int i = 0; i < M; i++) {
g[x[i]].push_back({y[i], c[i]});
g[y[i]].push_back({x[i], c[i]});
}
priority_queue<pair<double,int>> pq;
vector<double> dd(N, 1e18);
{
dd[0] = 0;
pq.push({0, 0});
while(!pq.empty()) {
auto [x, v] = pq.top(); pq.pop();
x = -x;
if(dd[v] < x) continue;
for(auto [u, w] : g[v]) {
if(dd[u] > x + w && u != H) {
dd[u] = x + w;
pq.push({-dd[u], u});
}
}
}
}
vector<array<double, 2>> d(N, {1e18, 1e18});
arr[0] = 0;
for(int i = 0; i < N; i++) if(!arr[i] && dd[i] == 1e18) arr[i] = 1;
{
for(int i = 0; i < N; i++) {
if(!arr[i] && dd[i] != 1e18) {
d[i][1] = 0;
pq.push({0, i});
}
}
while(!pq.empty()) {
auto [x, v] = pq.top(); pq.pop();
x = -x;
if(d[v][1] < x) continue;
for(auto [u, w] : g[v]) {
if(d[u][1] > x + w && u != H) {
d[u][1] = x + w;
pq.push({-d[u][1], u});
}
}
}
}
double res = 1e18;
for(auto [u, w] : g[H]) {
res = min(res, d[u][1] + w);
}
for(int k = 1; k <= min(85, K); k++) {
vector<array<double,2>> nd(N, {1e18, 1e18});
priority_queue<pair<double,pair<int, int>>> pq;
for(int i = 0; i < N; i++) {
nd[i][0] = min(d[i][0], d[i][1]);
if(arr[i] == 2 && nd[i][0] != 1e18) {
nd[i][0] = min(nd[i][0], d[i][1] / 2);
}
if(nd[i][0] != 1e18) pq.push({-nd[i][0], {i, 0}});
}
while(!pq.empty()) {
auto [x, p] = pq.top();
auto [v, c] = p;
pq.pop();
x = -x;
if(nd[v][c] < x) continue;
for(auto [u, w] : g[v]) {
if(nd[u][c | 1] > x + w && u != H) {
nd[u][c | 1] = x + w;
pq.push({-nd[u][c | 1], {u, c | 1}});
}
}
}
swap(nd, d);
for(auto [u, w] : g[H]) {
res = min(res, min(d[u][0], d[u][1]) + w);
}
}
if(res == 1e18) res = -1;
return res;
}
// int main() {
// cin.tie(0); ios_base::sync_with_stdio(0);
// // cout << fixed << setprecision(1) << solve(4, 4, 30, 3, {0, 0, 1, 2}, {1, 2, 3, 3}, {5, 4, 2, 4}, {1, 0, 2, 1}) << '\n';
// // cout << fixed << setprecision(1) << solve(3, 2, 30, 2, {1, 2}, {2, 0}, {12, 4}, {1, 2, 1}) << '\n';
// cout << fixed << setprecision(1) << solve(4, 3, 3, 3, {0, 1, 2}, {1, 2, 3}, {11, 1, 10}, {1, 1, 2, 1}) << '\n';
// }
