// IOI 2011 - Race
// Lúcio Cardoso
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e5+10;
const int MAXD = 1e6+10;
const int MAXL = 20;
typedef pair<int, int> pii;
int n, k, size[MAXN], ans;
set<int> S[MAXD];
bool mark[MAXN];
vector<pii> grafo[MAXN];
int DFS(int u, int p)
{
size[u] = 1;
for (int i = 0; i < (int) grafo[u].size(); i++)
{
int v = grafo[u][i].first;
if (v == p || mark[v]) continue;
size[u] += DFS(v, u);
}
return size[u];
}
int centroid(int u, int x, int p)
{
for (int i = 0; i < (int) grafo[u].size(); i++)
{
int v = grafo[u][i].first;
if (v == p || mark[v]) continue;
if (size[v] > x/2) return centroid(v, x, u);
}
return u;
}
void upd(int u, int p, int d, int deep, int ok)
{
if (d > k) return;
if (ok) S[d].insert(deep);
else S[d].erase(deep);
for (int i = 0; i < (int) grafo[u].size(); i++)
{
int v = grafo[u][i].first;
if (v == p || mark[v]) continue;
upd(v, u, d+grafo[u][i].second, deep+1, ok);
}
}
int get(int u, int p, int d, int deep)
{
if (d > k) return 1e9;
int aux = 1e9;
if (S[k-d].size() > 0)
{
set<int>::iterator it = S[k-d].begin();
aux = deep+*it;
}
for (int i = 0; i < (int) grafo[u].size(); i++)
{
int v = grafo[u][i].first;
if (v == p || mark[v]) continue;
aux = min(aux, get(v, u, d+grafo[u][i].second, deep+1));
}
return aux;
}
void decompose(int u)
{
DFS(u, 0);
int c = centroid(u, size[u], 0);
mark[c] = 1;
upd(c, 0, 0, 0, 1);
int aux = 1e9;
for (int i = 0; i < (int) grafo[c].size(); i++)
{
int v = grafo[c][i].first;
if (mark[v]) continue;
upd(v, c, grafo[c][i].second, 1, 0);
aux = min(aux, get(v, c, grafo[c][i].second, 1));
upd(v, c, grafo[c][i].second, 1, 1);
}
ans = min(ans, aux);
upd(c, 0, 0, 0, 0);
for (int i = 0; i < (int) grafo[c].size(); i++)
{
int v = grafo[c][i].first;
if (!mark[v]) decompose(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 a = H[i][0]+1, b = H[i][1]+1, c = L[i];
grafo[a].push_back(make_pair(b, c));
grafo[b].push_back(make_pair(a, c));
}
ans = 1e9;
decompose(1);
return (ans==1e9)?(-1):ans;
}
