#include "cyberland.h"
#include<bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define rs resize
#define ft front()
#define bk back()
#define vi vector<int>
#define vvi vector<vector<int>>
#define pii pair<int, int>
#define vpii vector<pair<int, int>>
#define vc vector<char>
#define vb vector<bool>
#define mii map<int,int>
#define f0r(i,n) for(int i=0;i<n;i++)
#define FOR(i,k,n) for(int i=k;i<n;i++)
#define r0f(i,n) for(int i = n-1; i >= 0; i--)
#define R0F(i,k,n) for(int i = n-1; i >= k; i--)
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define in(a) int a; cin>>a
#define in2(a,b) int a,b; cin>>a>>b
#define in3(a,b,c) int a,b,c; cin>>a>>b>>c
#define in4(a,b,c,d) int a,b,c,d; cin>>a>>b>>c>>d
#define vin(v,n); vi v(n); f0r(i,n){cin>>v[i];}
#define out(a) cout<<a<<'\n'
#define out2(a,b) cout<<a<<' '<<b<<'\n'
#define out3(a,b,c) cout<<a<<' '<<b<<' '<<c<<'\n'
#define out4(a,b,c,d) cout<<a<<' '<<b<<' '<<c<<' '<<d<<'\n'
#define pout(a) cout<<a.first<<' '<<a.second<<'\n'
#define vout(v) for(auto u : v){cout<<u<<' ';} cout<<endl
#define dout(a) cout<<a<<' '<<#a<<endl
#define dout2(a,b) cout<<a<<' '<<#a<<' '<<b<<' '<<#b<<endl
#define yn(x); if(x){cout<<"YES"<<'\n';}else{cout<<"NO"<<'\n';}
#define p2(x) (1LL << (x))
#define pct(x) (__builtin_popcountll(x))
#define ist(x,y) ((x >> y) & 1)
template<class T, class U> bool ckmin(T& a, const U& b) { return (T)b < a ? a = (T)b, 1 : 0; }
template<class T, class U> bool ckmax(T& a, const U& b) { return a < (T)b ? a = (T)b, 1 : 0; }
const int leg = 1e9 + 7;
const int mod = 998244353;
using namespace std;
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) {
K = min(K, 62); vpii adj[N]; f0r(i, M){adj[x[i]].pb(mp(y[i], c[i])); adj[y[i]].pb(mp(x[i], c[i]));}
double dist[N][K+1]; f0r(i, N)f0r(j, K+1)dist[i][j] = 4e18; dist[0][0] = 0;
priority_queue<pair<double, pii>>q; q.push(mp(0, mp(0, 0)));
while(!q.empty()){
int node = q.top().second.first; int k = q.top().second.second; q.pop();
if(node == H)continue;
for(auto &[u,w] : adj[node]){
if(arr[u] == 0){
if(dist[u][k] > 0)dist[u][k] = 0, q.push(mp(-dist[u][k], mp(u,k)));
}
else if(arr[u] == 1){
if(dist[u][k] > dist[node][k] + w)dist[u][k] = dist[node][k] + w,q.push(mp(-dist[u][k], mp(u,k)));
}
else{
if(dist[u][k] > dist[node][k] + w)dist[u][k] = dist[node][k] + w,q.push(mp(-dist[u][k], mp(u,k)));
if(k < K && dist[u][k+1] > (dist[node][k] + w)/2)dist[u][k+1] = (dist[node][k] + w)/2, q.push(mp(-dist[u][k+1], mp(u,k+1)));
}
}
}
double mn = 4e18; f0r(i, K+1)mn = min(mn, dist[H][i]);
if(mn == 4e18)return -1;
else return mn;
}
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