#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fi first
#define se second
#define pb push_back
const int N = 1e6 + 5;
int n, k, mx, ans = 1e9;
bool centroid[N];
int dp[N], sz[N];
vector<pair<int, int>> g[N];
int dfs(int u, int par, int h) {
sz[u] = 1;
mx = max(mx, h);
for (auto b : g[u]) {
int v = b.fi;
if (v != par && !centroid[v]) {
sz[u] += dfs(v, u, h + 1);
}
}
return sz[u];
}
int find_centroid(int u, int par, int n) {
for (auto b : g[u]) {
int v = b.fi;
if (v != par && !centroid[v] && sz[v] > n / 2) {
return find_centroid(v, u, n);
}
}
return u;
}
void count_path(int u, int par, int h, int e) {
if (h <= k) {
ans = min(ans, e + dp[k - h]);
}
//cout << u << " " << h << " " << e << " " << k - h << " " << dp[k - h] << "\n";
for (auto b : g[u]) {
int v = b.fi, w = b.se;
if (v != par && !centroid[v] && h + w <= k) {
count_path(v, u, h + w, e + 1);
}
}
}
void update(int u, int par, int h, int e) {
if (h <= k) {
dp[h] = min(dp[h], e);
}
for (auto b : g[u]) {
int v = b.fi, w = b.se;
if (v != par && !centroid[v] && h + w <= k) {
count_path(v, u, h + w, e + 1);
}
}
}
void solve_centroid(int u) {
mx = 0;
int n = dfs(u, 0, 0);
int c = find_centroid(u, 0, n);
centroid[c] = 1;
for (int i = 1; i <= min(k, mx * 10); ++i) {
dp[i] = 1e9;
}
dp[0] = 0;
for (auto b : g[c]) {
int v = b.fi;
int w = b.se;
if (!centroid[v] && w <= k) {
count_path(v, c, w, 1);
update(v, c, w, 1);
}
}
for (auto b : g[c]) {
int v = b.fi;
if (!centroid[v]) {
solve_centroid(v);
}
}
}
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] + 1;
int v = H[i][1] + 1;
int w = L[i];
g[u].pb({v, w});
g[v].pb({u, w});
}
solve_centroid(1);
if (ans == 1e9) return -1;
return ans;
}
