#include <bits/stdc++.h>
using namespace std;
const int maxn = 200000;
int dp[maxn][2];
vector< pair<int,int> > E[maxn];
int n,k;
bool cmp(const pair<int,int> &a, const pair<int,int> &b){
return (a.first > b.first);
}
void dfs(int u, int p){
vector< pair<int,int> > c;
set<int> st;
for(auto e: E[u]){
int v = e.first;
int cst = e.second;
if(v == p) continue;
dfs(v,u);
c.push_back({dp[v][0] + cst,v});
}
sort(c.begin(), c.end(), cmp);
int tk = min(k-1, (int)(c.size()));
for(int i = 0; i < tk; i++){
dp[u][0] += c[i].first;
st.insert(c[i].second);
}
int extra = 0;
if(tk != (int)(c.size()))
extra = c[tk].first;
for(auto e: E[u]){
int v = e.first;
int cst = e.second;
if(v == p) continue;
if(st.count(v) == 0)
dp[u][1] = max(dp[u][1], dp[v][1] + dp[u][0] + cst);
else
dp[u][1] = max(dp[u][1], dp[u][0] - dp[v][0] + extra + dp[v][1]);
}
st.clear();
c.clear();
}
int main(){
scanf("%d%d", &n, &k);
for(int i = 1; i < n; i++){
int u,v,c;
scanf("%d%d%d", &u, &v, &c);
E[u].push_back({v,c});
E[v].push_back({u,c});
}
dfs(0,-1);
cout << max(dp[0][0], dp[0][1]) << "\n";
return 0;
}
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