#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
using ll = long long;
struct node {
node* l = nullptr;
node* r = nullptr;
ll val = 0;
ll sm = 0;
};
node* copy(node* nd) {
node* v = new node();
v->l = nd->l;
v->r = nd->r;
v->val = nd->val;
return v;
}
node* merge(node* l, node* r) {
if (!l)
return r;
if (!r)
return l;
}
const int MAXN = 1e5 + 123;
vector<pair<int, int>> edg[MAXN];
ll cost[MAXN * 3];
pair<int, int> edges[MAXN * 3];
vector<ll> dp[MAXN * 3];
void get_dp(int e, int k) {
if (dp[e].size())
return;
auto [rt, v] = edges[e];
if (k == 1)
dp[e] = {0};
for (auto [u, ne] : edg[v]) {
if (u == rt)
continue;
get_dp(ne, k);
if (k == 1) {
dp[e][0] = max(dp[e][0], dp[ne][0]);
continue;
}
vector<ll> ndp(dp[e].size() + dp[ne].size());
merge(dp[e].rbegin(), dp[e].rend(), dp[ne].rbegin(), dp[ne].rend(), ndp.rbegin());
ndp.resize(min(int(ndp.size()), k));
dp[e] = ndp;
}
if (dp[e].empty()) {
dp[e] = {cost[e]};
} else {
dp[e][0] += cost[e];
}
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int n, k;
cin >> n >> k;
for (int i = 0; i + 1 < n; ++i) {
int u, v, c;
cin >> u >> v >> c;
--u, --v;
edg[u].push_back({v, i * 2});
edg[v].push_back({u, i * 2 + 1});
edges[i * 2] = {u, v};
edges[i * 2 + 1] = {v, u};
cost[i * 2] = cost[i * 2 + 1] = c;
}
for (int e = 2 * n; e < 3 * n; ++e) {
edges[e] = {n, e - 2 * n};
get_dp(e, k);
ll ans = 0;
for (auto x : dp[e])
ans += x;
cout << ans << '\n';
}
//for (int e = 0; e < n * 2 - 1; ++e)
//get_dp(e, k);
//for (int v = 0; v < n; ++v) {
//vector<ll> ans;
//for (auto [u, e] : edg[v]) {
//vector<ll> ndp(ans.size() + dp[e].size());
//merge(dp[e].rbegin(), dp[e].rend(), ans.rbegin(), ans.rend(), ndp.rbegin());
//ndp.resize(min(int(ndp.size()), k));
//ans = ndp;
//}
//ll anssm = 0;
//for (auto x : ans)
//anssm += x;
//cout << anssm << '\n';
//}
}
