#include <bits/stdc++.h>
using namespace std;
vector<vector<size_t>> adj;
vector<vector<pair<size_t, int>>> graph;
const int oo = INT_MAX / 3;
int& rd(unordered_map<int, int>& m, int key)
{
auto it = m.find(key);
if(it == m.end()) it = m.emplace_hint(it, key, +oo);
return it->second;
}
void mini(unordered_map<int, int>& m, int key, int value)
{
rd(m, key) = min(rd(m, key), value);
}
void dfs_map_paths(size_t u, int s, int d, unordered_map<int, int>& m,
size_t glock = SIZE_MAX, size_t lock = SIZE_MAX)
{
if(d > +oo) return;
mini(m, s, d);
for(auto [v, w] : graph[u])
if(v != lock and v != glock)
dfs_map_paths(v, s + w, d + 1, m, glock, u);
}
size_t gl_vertices;
vector<size_t> gl_parent, gl_subsize;
vector<bool> gl_lock;
void dfs_root(size_t u, size_t glock = SIZE_MAX, size_t lock = SIZE_MAX)
{
gl_vertices++;
gl_subsize[u] = 1;
for(auto v : adj[u])
if(v != lock and not gl_lock[v])
gl_parent[v] = u, dfs_root(v, glock, u), gl_subsize[u] += gl_subsize[v];
}
size_t subtree_size(size_t from, size_t to)
{
return from == gl_parent[to] ? gl_subsize[to] : gl_vertices - gl_subsize[from];
}
size_t find_centroid(size_t init)
{
gl_vertices = 0;
dfs_root(init);
gl_parent[init] = SIZE_MAX;
size_t u = init;
while(true)
{
bool any = false;
for(auto v : adj[u])
if(not gl_lock[v] and subtree_size(u, v) > subtree_size(v, u))
{ any = true; u = v; break; }
if(not any) break;
}
return u;
}
int solve(size_t init, int k)
{
auto fix = find_centroid(init);
int result = +oo;
unordered_map<int, int> pre = {{0, 0}};
pre.reserve(4 * gl_vertices);
for(auto [v, w] : graph[fix])
if(not gl_lock[v])
{
unordered_map<int, int> cur;
cur.reserve(4 * subtree_size(fix, v));
dfs_map_paths(v, w, 1, cur, fix);
for(auto [s, d] : cur)
result = min(result, d + rd(pre, k - s));
for(auto [s, d] : cur)
mini(pre, s, d);
}
gl_lock[fix] = true;
for(auto v : adj[fix])
if(not gl_lock[v])
result = min(result, solve(v, k));
return result;
}
int best_path(int _n, int k, int H[][2], int L[])
{
const size_t n = _n;
graph.resize(n);
adj.resize(n);
for(size_t i = 0; i < n - 1; i++)
{
graph[H[i][0]].emplace_back(H[i][1], L[i]);
graph[H[i][1]].emplace_back(H[i][0], L[i]);
adj[H[i][0]].push_back(H[i][1]);
adj[H[i][1]].push_back(H[i][0]);
}
gl_lock.resize(n);
gl_parent.resize(n);
gl_subsize.resize(n);
int result = solve(0, k);
return result >= +oo ? -1 : result;
}
