#include <bits/stdc++.h>

using namespace std;

const int N = 2005;

int m;
long long f[N][N][3];
vector< pair<int, int> > G[N];

int dfs(int x, int fa = -1, long long lst = -1e18) {
    int sz = 0;
    for (auto [v, w] : G[x]) {
        if (v == fa) continue;
        int tsz = dfs(v, x, w);
        for (int i = 2; ~i; --i) {
            for (int j = 2 - i; ~j; --j) {
                for (int p = min(m, sz); ~p; --p) {
                    for (int q = min(m - p, tsz); ~q; --q) {
                        f[x][p + q][i + j] = max(f[x][p + q][i + j], f[x][p][i] + f[v][q][j] + (j == 1 ? w : 0));
                    }
                }
            }
        }
        sz += tsz;
    }
    for (int i = 0; i < m && i <= sz; ++i) {
        f[x][i + 1][0] = max(f[x][i + 1][0], f[x][i][2] + lst);
    }
    return sz + 1;
}

signed main() {
    int n; scanf("%d%d", &n, &m);
    for (int i = 1, x, y, v; i < n; ++i) {
        scanf("%d%d%d", &x, &y, &v);
        G[x].push_back({y, v});
        G[y].push_back({x, v});
    }
    dfs(1);
    for (int i = 0; i <= m; ++i) {
        printf("%lld%c", *max_element(f[1][min(i, n)], f[1][min(i, n)] + 3), " \n"[i == m]);
    }
    return 0;
}