#include <bits/stdc++.h>
using namespace std ;
#define f(i,a,b) for(int i=int(a);i<int(b);++i)
#define pr pair
#define ar array
#define fr first
#define sc second
#define vt vector
#define pb push_back
#define eb emplace_back
#define LB lower_bound
#define UB upper_bound
#define PQ priority_queue
#define sz(x) ((int)(x).size())
#define all(a) (a).begin(),(a).end()
#define allr(a) (a).rbegin(),(a).rend()
#define mem(a,b) memset(a, b, sizeof(a))
template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
int best_path(int N, int K, int H[][2], int L[]) {
vt<ar<int,2>> g[N];
f(i,0,N-1){
int u = H[i][0], v = H[i][1], w = L[i];
g[u].pb({v,w});
g[v].pb({u,w});
}
int ans = N;
map<int,int> dp[N];
vt<int> ew(N), el(N); /* current dp[i] is actually {a + extra_weight, b + extra_length} */
function<void(int,int)> small_to_large_merging = [&](int i,int p){
dp[i][0] = ew[i] = el[i] = 0;
for(auto [j,w] : g[i]) if(j != p){
small_to_large_merging(j,i);
if(sz(dp[i]) > sz(dp[j])){
// update ans.
for(auto [w_j, l_j] : dp[j]){
int actual_w = w_j + ew[j] + w;
int actual_l = l_j + el[j] + 1;
int need_w = K - actual_w;
int put_i = need_w - ew[i];
if(dp[i].count(put_i)){
ckmin(ans,dp[i][put_i] + el[i] + actual_l);
}
}
// update dp[i].
for(auto [w_j, l_j] : dp[j]){
int actual_w = w_j + ew[j] + w;
int actual_l = l_j + el[j] + 1;
int put_i = actual_w - ew[i];
int put_l = actual_l - el[i];
if(dp[i].count(put_i)){
ckmin(dp[i][put_i], put_l);
}else{
dp[i][put_i] = put_l;
}
}
dp[j].clear();
}else{
// update ans.
for(auto [w_i,l_i] : dp[i]){
int actual_w = w_i + ew[i] + w;
int actual_l = l_i + el[i] + 1;
int need_w = K - actual_w;
int put_j = need_w - ew[j];
if(dp[j].count(put_j)){
ckmin(ans,dp[j][put_j] + el[j] + actual_l);
}
}
//update dp[j].
el[j] += 1;
ew[j] += w;
for(auto [w_i,l_i] : dp[i]){
int actual_w = w_i + ew[i];
int actual_l = l_i + el[i];
int put_j = actual_w - ew[j];
int put_l = actual_l - el[j];
if(dp[j].count(put_j)){
ckmin(dp[j][put_j],put_l);
}else{
dp[j][put_j] = put_l;
}
}
// swap
dp[i].swap(dp[j]);
dp[j].clear();
ew[i] = ew[j];
el[i] = el[j];
}
}
};
small_to_large_merging(0,0);
if(ans == N) ans = -1;
return ans;
}
