#include<bits/stdc++.h>
#define ll long long
#define int long long
#define fr(i,j,k) for(register int i=j;i<=k;++i)
#define rf(i,j,k) for(register int i=j;i>=k;--i)
#define foredge(i,j) for(register int i=head[j];i;i=e[i].nxt)
#define pb push_back
#define Times printf("Time:%.3lf\n",clock()/CLOCKS_PER_SEC)
#define pii pair<int,int>
#define mk make_pair
using namespace std;
inline int read(){
	int x=0;
	bool f=0;
	char c=getchar();
	while(!isdigit(c)) f|=(c=='-'),c=getchar();
	while(isdigit(c)) x=(x<<3)+(x<<1)+(c^48),c=getchar();
	return f?-x:x;
}
inline void write(int x){
    if(x<0){putchar('-');x=-x;}
    if(x>9)write(x/10);
    putchar(x%10+'0');
}
inline void writeln(int x){write(x); puts("");}
inline void writepl(int x){write(x); putchar(' ');}
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
inline int randfind(int l,int r){return rnd()%(r-l+1)+l;}
//inline void init(){
//	int t=read();
//	while(t--) work();
//}
const int Maxn=2e3+10;
struct node{int nxt,to,d;}e[Maxn<<1];
int cnt,head[Maxn];
inline void add(int u,int v,int w){++cnt;e[cnt]=(node){head[u],v,w};head[u]=cnt;}
inline void chkmin(int &x,int y){if(x>y) x=y;}
inline void chkmax(int &x,int y){if(x<y) x=y;}
int f[Maxn][Maxn],g[Maxn][Maxn],h[Maxn][Maxn];
int siz[Maxn];
inline void dfs(int x,int fa){
    siz[x]=1;
    for(register int I=head[x];I;I=e[I].nxt) if(e[I].to!=fa){
        int y;y=e[I].to;dfs(y,x);
        rf(i,siz[x],1) rf(j,siz[y],1){
            chkmax(h[x][i+j],h[x][i]+h[y][j]+e[I].d);
            chkmax(h[x][i+j-1],h[x][i]+f[y][j]);
            chkmax(h[x][i+j-1],f[x][i]+h[y][j]);
            chkmax(h[x][i+j-1],g[x][i]+g[y][j]+e[I].d);
        }
        rf(i,siz[x],1) rf(j,siz[y],1){
            chkmax(g[x][i+j],g[x][i]+g[y][j]+e[I].d);
            chkmax(g[x][i+j-1],g[x][i]+f[y][j]);
            chkmax(g[x][i+j-1],f[x][i]+g[y][j]+e[I].d);
        }
        rf(i,siz[x],1) rf(j,siz[y],1){
            chkmax(f[x][i+j],f[x][i]+h[y][j]+e[I].d);
            chkmax(f[x][i+j-1],f[x][i]+f[y][j]);
        }siz[x]+=siz[y];
    }
}
int n,k;
inline void init(){
    n=read();k=read();
    fr(i,1,n-1){
        int x,y,z;
        x=read();y=read();z=read();
        add(x,y,z);add(y,x,z);
    }
}
inline void work(){
    dfs(1,0);
    fr(i,1,k+1) writepl(h[1][min(i,n)]);puts("");
}
signed main(){
	// freopen("input.in","r",stdin);
	// freopen("output.out","w",stdout);
    init();work();
    // printf("\nTIME:%.3lf",(double)clock()/CLOCKS_PER_SEC);
	return 0;
}