#include "race.h"
#include <vector>
#include <array>
using namespace std;
using ll = long long;
struct CentroidDecomposition
{
int n, k;
vector<bool> used;
vector<vector<pair<int, ll>>> adj;
vector<int> sizes, del1, del2;
array<int, 1000001> counter1{}, counter2{};
int res = -1;
int calc(int v, int p)
{
sizes[v] = 1;
for (auto [u, w] : adj[v]) if (u != p && !used[u]) sizes[v] += calc(u, v);
return sizes[v];
}
int findCentroid(int v, int p, int all)
{
for (auto [u, w] : adj[v]) if (u != p && !used[u] && sizes[u] > all / 2) return findCentroid(u, v, all);
return v;
}
void dfs(int v, int p, int l, ll d)
{
if (d <= k)
{
counter2[d] = min(counter2[d], l);
del1.push_back(d);
del2.push_back(d);
}
for (auto [u, w] : adj[v]) if (u != p && !used[u]) dfs(u, v, l + 1, d + w);
}
int build(int v)
{
int all = calc(v, 0);
int centroid = findCentroid(v, 0, all);
//calc res
int res = 1e9;
counter1[0] = 0;
del1.push_back(0);
for (auto [u, w]: adj[centroid])
{
if (!used[u])
{
dfs(u, centroid, 1, w);
for (int i : del2) if (k - i >= 0) res = min(res, counter2[i] + counter1[k - i]);
for (int i : del2)
{
counter1[i] = min(counter1[i], counter2[i]);
counter2[i] = 1e9;
}
del2.clear();
}
}
for (int i : del1) counter1[i] = 1e9;
del1.clear();
used[centroid] = true;
for (auto [u, w] : adj[centroid]) if (!used[u]) res = min(res, build(u));
return res;
}
CentroidDecomposition(vector<vector<pair<int, ll>>> adj, int k) : adj(adj), k(k)
{
int n = (int)adj.size() - 1;
used.resize(n + 1);
sizes.resize(n + 1);
counter1.fill(1e9);
counter2.fill(1e9);
res = build(0);
if (res == 1e9) res = -1;
}
int operator()()
{
return res;
}
};
int best_path(int n, int k, int H[][2], int L[])
{
vector<vector<pair<int, ll>>> adj(n + 1);
for (int i = 0; i + 1 < n; ++i)
{
adj[H[i][0]].emplace_back(H[i][1], L[i]);
adj[H[i][1]].emplace_back(H[i][0], L[i]);
}
return CentroidDecomposition(adj, k)();
}
