#include <bits/stdc++.h>
#define FOR(i,j,k) for(int i=j, r##i=k; i<=r##i; ++i)
#define ROF(i,j,k) for(int i=j, l##i=k; i>=l##i; --i)
inline int read (void) {
  int x = 0, f = 1, ch = getchar();
  while(!isdigit(ch)) { if(ch == '-') f = -f; ch = getchar(); }
  while(isdigit(ch)) { x = x * 10 + ch - '0'; ch = getchar(); }
  return x * f;
}
using ll = long long;
inline ll _max (ll p, ll q) { return p > q ? p : q; }
const int maxn = 2005;
int tot_edge, head[maxn], to[maxn<<1], link[maxn<<1], cost[maxn<<1];
inline void add_edge (int x, int y, int c) {
  to[++tot_edge] = y;
  cost[tot_edge] = c;
  link[tot_edge] = head[x];
  head[x] = tot_edge;
}
ll f[maxn][maxn][3], g[maxn][3]; int K, sz[maxn];
void dfs (int x, int fa=0) {
  sz[x] = 1;
  for(int now=head[x]; now; now=link[now]) {
    if(to[now] == fa) continue;
    dfs (to[now], x);
    FOR(i,0,sz[x]-1) FOR(j,0,sz[to[now]]-1) {
      FOR(k,0,2) g[i+j+1][k] = _max (g[i+j+1][k], f[x][i][k] + cost[now] + f[to[now]][j][2]);
      FOR(k1,0,2) FOR(k2,0,2) if(k1 + k2 <= 2)
        g[i+j][k1+k2] = _max (g[i+j][k1+k2], f[x][i][k1] + f[to[now]][j][k2] + (k2 == 1) * cost[now]);
    }
    std::swap (f[x], g); memset (g, 0, sizeof(g));
    sz[x] += sz[to[now]];
    FOR(i,0,sz[x]-1) FOR(j,1,2)
      f[x][i][j] = _max (f[x][i][j], f[x][i][j-1]);
  }
}
int main (void) {
  int n = read(); K = read();
  FOR(i,2,n) {
    int x = read(), y = read(), c = read();
    add_edge (x, y, c);
    add_edge (y, x, c);
  }
  dfs (1);
  FOR(i,0,K) printf("%lld%c", f[1][i][2], i==K?10:32);
  return 0;
}