#include "highway.h"
#define int long long
#define fi first
#define se second
#define ll int
using namespace std;
// progression
// solve sub2 (done!), sub4 (done!) then try sub6
vector<int> dist, parEdge, col, colVertex, heavy;
vector<vector<pair<int, int>>> adj, adj_t;
void dfs(int u, int d, int c, int par = -1){
colVertex[u] = c;
dist[u] = d;
for (pair<int, int> pa: adj[u]){
int v = pa.fi;
if (v == par) continue;
parEdge[v] = pa.se;
col[pa.se] = c;
dfs(v, d+1, c, u);
}
}
int sub2(int n, int m, int a, int b, int inSub, int base){
vector<signed> w(m, 0), cand;
vector<vector<int>> subtree(n+5, vector<int>());
int maxDist = 0;
for (int i = 0; i < n; i++){
if (colVertex[i] == inSub){
maxDist = max(maxDist, dist[i]);
subtree[dist[i]].push_back(i);
}
}
for (int d = maxDist; d >= 0; d--) {
for (int u : subtree[d]) cand.push_back(u);
}
// 2. Binary Search over the flattened list
int l = 0, r = (int)cand.size() - 1;
int res = subtree[0][0];
while (l <= r) {
int mid = (l + r) / 2;
fill(w.begin(), w.end(), 0);
for (int i = 0; i <= mid; i++) {
w[parEdge[cand[i]]] = 1;
}
if (ask(w) > base) {
res = cand[mid];
r = mid - 1;
} else {
l = mid + 1;
}
}
return res;
}
void find_pair(signed n, vector<signed> u, vector<signed> v, signed ap, signed bp) {
int a = (int)ap, b = (int) bp;
int m = u.size();
vector<signed> w(m, 0);
int base = ask(w);
int totLen = base / (int)a;
col.assign(m, 0);
colVertex.assign(n, 0);
dist.assign(n, 0);
parEdge.assign(n, 0);
heavy.assign(m, 1);
adj.assign(n, vector<pair<int, int>>());
adj_t.assign(n, vector<pair<int, int>>());
// binary search for the edge on
int l = 0, r = m-1;
while(l < r){
int mid = (l + r)/2;
// for l to mid, check if increase or not
for (int i = 0; i < m; i++){
w[i] = 0;
}
for (int i = l; i <= mid; i++){
w[i] = 1;
}
int chck = ask(w);
if (chck > totLen*a){
// move to r
r = mid;
// cout << "move r to " << mid << endl;
}
else{
l = mid+1;
// cout << "move l to " << mid+1 << endl;
}
}
// r is the edge confirmed to be in the path
int st1 = u[r], st2 = v[r];
for (int i = 0; i < m; i++){
adj_t[u[i]].push_back({v[i], i});
adj_t[v[i]].push_back({u[i], i});
}
// bfs-tree building ()
vector<int> q, vis(n, 0);
heavy[r] = 0;
q.push_back(u[r]);
vis[u[r]] = 1;
vis[v[r]] = 1;
while (!q.empty()){
int un = q.back();
q.pop_back();
for (pair<int, int> pa: adj_t[un]){
int vn = pa.fi;
if (vis[vn]) continue;
vis[vn] = 1;
heavy[pa.se] = 0;
// insert edge from u->v
adj[un].push_back({vn, pa.se});
adj[vn].push_back({un, pa.se});
q.push_back(vn);
}
}
vis[v[r]] = 0;
q.push_back(v[r]);
vis[u[r]] = 1;
vis[v[r]] = 1;
while (!q.empty()){
int un = q.back();
q.pop_back();
for (pair<int, int> pa: adj_t[un]){
int vn = pa.fi;
if (vis[vn]) continue;
vis[vn] = 1;
heavy[pa.se] = 0;
// insert edge from u->v
adj[un].push_back({vn, pa.se});
adj[vn].push_back({un, pa.se});
q.push_back(vn);
}
}
// dfs to seperate into 2 subtrees
dfs(st1, 0, 1, st2);
dfs(st2, 0, 2, st1);
int s = sub2(n, m, a, b, 1, base);
int t = sub2(n, m, a, b, 2, base);
answer(s, t);
}
