#include <bits/stdc++.h>

using namespace std;
using ll = long long;

const int N = 3e5 + 10;

struct Edge
{
	int par;
	int child;
	int weight;
	Edge() {}
	Edge(int par, int child, int weight) : par(par), child(child), weight(weight){}
	bool operator < (const Edge &o) const {
		return weight < o.weight;
	}
};


vector<pair<int, int>>  tree[N];
vector<Edge> edges;
int weights[N];

int mi[N], dsu[N];

int find(int x) {
	if (x == dsu[x]) return x;
	return dsu[x] = find(dsu[x]);
}

int uni(int x, int y) {
	x = find(x), y = find(y);
	if (x == y) return mi[x];
	int val = max(mi[x], mi[y]);
	dsu[x] = y;
	mi[y] = min(mi[x], mi[y]);
	return val;
}

int main() {
	cin.tie(0) -> sync_with_stdio(0);
	int n, k;
	cin >> n >> k;
	for (int i = 1; i < n; i++) {
		dsu[i] = mi[i] = i;
		int x, y, w;
		cin >> x >> y >> w;
		edges.emplace_back(x, y, w);
	}
	dsu[n] = mi[n] = n;
	sort(edges.begin(), edges.end());
	for (auto &[l, r, w] : edges) {
		int val = uni(l, r);
		assert(weights[val] == 0);
		weights[val] = w;
	}
	ll sum = 0;
	priority_queue<int, vector<int>, greater<int>> topk;
	cout << "0\n";
	for (int i = 2; i <= n; i++) {
		topk.push(weights[i]);
		sum += weights[i];
		if (topk.size() > k) {
			sum -= topk.top();
			topk.pop();
		}
		cout << sum << "\n";
	}


}