#include <race.h>
#include <bits/stdc++.h>
#define taskname "test"
#define fi first
#define se second
#define pb push_back
#define faster ios_base::sync_with_stdio(0); cin.tie(0);
using namespace std;
using ll = long long;
using pii = pair <int, int>;
using pil = pair <int, ll>;
using pli = pair <ll, int>;
using pll = pair <ll, ll>;
using ull = unsigned ll;
mt19937 Rand(chrono::steady_clock::now().time_since_epoch().count());
ll min(const ll &a, const ll &b){
return (a < b) ? a : b;
}
ll max(const ll &a, const ll &b){
return (a > b) ? a : b;
}
//const ll Mod = 1000000009;
//const ll Mod2 = 999999999989;
//only use when required
const int maxN = 1e6 + 1;
const int inf = 0x3f3f3f3f;
int n, k;
bool visited[maxN];
int par[maxN];
int subtree_size[maxN];
int edge[maxN];
vector <pii> adj[maxN];
void centroid_dfs(int u, int p){
subtree_size[u] = 1;
for (const auto &v: adj[u]){
int i = v.fi;
if (visited[i] || i == p) continue;
centroid_dfs(i, u);
subtree_size[u] += subtree_size[i];
}
}
int find_centroid(int u, int p, int sz){
for (const auto &v: adj[u]){
int i = v.fi;
if (visited[i] || i == p) continue;
if (subtree_size[i] > n / 2){
return find_centroid(i, u, sz);
}
}
return u;
}
//check if there is any "best path" traversing through the ROOT of the subtree(this case: centroid)
int find_path(int u, int p, int d, int cnt){
int tem = min(edge[k - d] + cnt, inf);
for (const auto &i: adj[u]){
if (visited[i.fi] || i.fi == p || i.se + d > k) continue;
tem = min(tem, find_path(i.fi, u, i.se + d, cnt + 1));
}
edge[d] = min(edge[d], cnt);
return tem;
}
int ans = inf;
int build_centroid(int u){
centroid_dfs(u, 0);
int centroid = find_centroid(u, 0, subtree_size[u]);
visited[centroid] = 1;
memset(edge, 0x3f, sizeof(edge));
edge[0] = 0;
ans = min(ans, find_path(centroid, 0, 0, 0));
for (const auto &i: adj[centroid]){
if (visited[i.fi]) continue;
par[build_centroid(i.fi)] = centroid;
}
return centroid;
}
int best_path(int N, int K, int H[][2], int L[]){
n = N; k = K;
for (int i = 0; i < n - 1; ++i){
int u = H[i][0], v = H[i][1];
adj[u + 1].pb({v + 1, L[i]});
adj[v + 1].pb({u + 1, L[i]});
}
par[build_centroid(1)] = 0;
return ans;
}
