#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef array<int,2> pr;
const ll N = 2010,INF = 1e18;
template<typename T>void tomin(T& x,T y){x = min(x,y);}
template<typename T>void tomax(T& x,T y){x = max(x,y);}
//
int n,k;
vector<pr> e[N];

ll f[N][N][3],g[N][3]; int sz[N];
void dfs(int u,int fa){
    for(auto [v,w] : e[u])if(v != fa)dfs(v,u);
    sz[u] = 1; f[u][0][0] = f[u][0][1] = f[u][0][2] = 0;
    for(auto [v,w] : e[u])if(v != fa){
        for(int i=0;i<n;i++)for(int x=0;x<3;x++)g[i][x] = -INF;

        //case1. 断边
        for(int i=0;i<sz[u];i++)for(int x=0;x<3;x++){
            if(f[u][i][x] == -INF)continue;
            for(int j=0;j<sz[v];j++){
                if(f[v][j][2] == -INF)continue;
                tomax(g[i+j+1][x],f[u][i][x] + f[v][j][2] + w);
            }
        }
        //case2. 不断边
        for(int i=0;i<sz[u];i++)for(int x=0;x<3;x++){
            if(f[u][i][x] == -INF)continue;
            for(int j=0;j<sz[v];j++)for(int y=0;y<3-x;y++){
                if(f[v][j][y] == -INF)continue;
                tomax(g[i+j][x+y],f[u][i][x] + f[v][j][y] + (y==1) * w);
            }
        }

        sz[u] += sz[v];
        for(int i=0;i<sz[u];i++)for(int x=0;x<3;x++)f[u][i][x] = g[i][x];
    }
}

int main(){
    cin>>n>>k;
    for(int i=1,u,v,w;i<n;i++){
        cin>>u>>v>>w;
        e[u].push_back({v,w}); e[v].push_back({u,w});
    }
    for(int i=1;i<=n;i++)for(int j=0;j<n;j++)for(int x=0;x<3;x++)f[i][j][x] = -INF;
    dfs(1,0);

    ll ans = -INF;
    for(int i=0;i<=k;i++){
        if(i<n)tomax(ans,f[1][i][2]);
        cout<<ans<<" ";
    }

    return 0;
}