#include "race.h"
#include <bits/stdc++.h>
#define fastio ios_base::sync_with_stdio(0), cin.tie(0)
#define fi first
#define se second
#define endl '\n'
#define sz(v) (int)(v).size()
#define all(v) (v).begin(), (v).end()
#define compress(v) sort(all(v)), (v).erase(unique(all((v))), v.end())
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using ld = long double;
const int N = 2e5 + 5;
const int K = 1e6 + 5;
int n, k;
vector<pii> adj[N];
bool fin[N];
int sz[N];
int d[K];
int get_cent(int t_size, int cur, int pv = -1) {
int minx = N;
for (auto &next : adj[cur]) {
if (pv == next.first || fin[next.first]) continue;
if (sz[next.first] > t_size / 2)
return get_cent(t_size, next.first, cur);
minx = min(minx, sz[next.first]);
}
if (minx <= t_size / 2) return cur;
return -1;
}
void get_sz(int cur, int pv = -1) {
sz[cur] = 1;
for (auto &next : adj[cur]) {
if (next.first == pv || fin[next.first]) continue;
get_sz(next.first, cur);
sz[cur] += sz[next.first];
}
}
void assign(int cur, int w, int pv = -1, int cnt = 1) {
if (w > k) return;
d[w] = min(d[w], cnt);
for (auto &next : adj[cur]) {
if (next.first == pv || fin[next.first]) continue;
assign(next.first, next.second + w, cur, cnt + 1);
}
}
int get(int cur, int w, int pv = -1, int cnt = 1) {
int ret = N;
if (w > k) return ret;
ret = min(ret, cnt + d[k - w]);
for (auto &next : adj[cur]) {
if (next.first == pv || fin[next.first]) continue;
ret = min(get(next.first, w + next.second, cur, cnt + 1), ret);
}
return ret;
}
int calc(int node) {
int ret = N;
// Find Centroid
memset(sz, 0, sizeof sz);
get_sz(node);
int cent = get_cent(sz[node], node);
//cout << node << ' ' << cent << endl;
if (cent == -1) {
fin[node] = true;
return ret;
}
fin[cent] = true;
// Find Minimum nodes of length K
memset(d, 0x3f, sizeof d);
d[0] = 0;
for (auto &next : adj[cent]) {
if (fin[next.first]) continue;
ret = min(ret, get(next.first, next.second));
assign(next.first, next.second);
}
// call calc for subtrees
for (auto &next : adj[cent]) {
if (fin[next.first]) continue;
ret = min(ret, calc(next.first));
}
return ret;
}
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], w = L[i];
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
}
int ans = calc(0);
return (ans != ::N ? ans : -1);
}
