#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <bits/stdc++.h>
#define LL long long
const int N = 2000;
using namespace std;

#define L(i, s, t) for(int i = s; i <= t; ++i)
#define R(i, t, s) for(int i = t; i >= s; --i)

void read(int &x) {
    x = 0; int w = 1; char c = getchar(); for(; c < '0' || c > '9'; c = getchar()) if (c == '-') w = -1;
    for(; c <= '9' && c >= '0'; c = getchar()) x = x * 10 + c - '0'; x *= w;
}

int n, k, h[N + 5], nxt[2 * N + 5], e[2 * N + 5], tot;

LL f[N + 5][N + 5][3]; int sz[N + 5];
LL g[N + 5][3], w[2 * N + 5];

void add(int x, int y, int ww) {
	nxt[++tot] = h[x]; e[tot] = y; w[tot] = ww; h[x] = tot;
}

const LL inf = 1ll << 60;

void dfs(int x, int ff) {
	// cou
	sz[x] = 1; // f[x][0] 代表， f[x][1] 代表两个儿子， f[x][2] 代表已经成形
	for(int i = h[x]; i; i = nxt[i]) {
		int v = e[i];
		if (v == ff) continue;
		dfs(v, x);
		for(int j = 0; j <= sz[x] + sz[v]; ++j)
			{g[j][0] = g[j][1] = g[j][2] = -inf;}
		for(int j = 0; j <= sz[x]; ++j)
			for(int k = 0; k <= sz[v]; ++k) {
				g[j + k + 1][0] = max(g[j + k + 1][0], f[x][j][0] + w[i] + f[v][k][2]);
				g[j + k + 1][1] = max(g[j + k + 1][1], f[x][j][1] + w[i] + f[v][k][2]);
				g[j + k + 1][2] = max(g[j + k + 1][2], f[x][j][2] + w[i] + f[v][k][2]);
				g[j + k][0] = max(g[j + k][0], f[x][j][0] + f[v][k][0]);
				g[j + k][1] = max(g[j + k][1], f[x][j][1] + f[v][k][0]);
				g[j + k][1] = max(g[j + k][1], f[x][j][0] + w[i] + f[v][k][1]);
				g[j + k][2] = max(g[j + k][2], f[x][j][1] + f[v][k][1] + w[i]);
				g[j + k][2] = max(g[j + k][2], f[x][j][2] + f[v][k][0]);
				g[j + k][2] = max(g[j + k][2], f[x][j][0] + f[v][k][2]);
			}
		sz[x] += sz[v];
		for(int j = 0; j < sz[x]; ++j) {
			f[x][j][0] = g[j][0];
			f[x][j][1] = max(g[j][1], f[x][j][0]);
			f[x][j][2] = max(g[j][2], f[x][j][1]);
		}
	}
}

int main() {
	// freopen("t.in", "r", stdin);
	read(n); read(k);
	for(int i = 1; i < n; ++i) {
		int x, y, w; read(x); read(y); read(w);
		add(x, y, w); add(y, x, w);
	}
	dfs(1, 0);
	for(int i = 0; i <= k; ++i)
		printf("%lld ", f[1][i][2]);
    return 0;
}
// dp u, sz, k