#include<bits/stdc++.h>
#define ll long long
#define pii pair<int,int>
#define fi first
#define se second
using namespace std;
long long read(){
	long long x=0,f=1;char ch=getchar();
	while(!isdigit(ch))
	{if(ch=='-') f=-1;ch=getchar();}
	while(isdigit(ch)){x=x*10+ch-48;ch=getchar();}
	return x*f;
}
void write(long long x){
    if(x<0) putchar('-'),x=-x;
    if(x>9) write(x/10);
    putchar(x%10+'0');
}
const int N=4010;
int n,k;
int head[N],ver[N<<1],nxt[N<<1],tot;
ll edge[N<<1],dep[N];
set<pair<pii,ll> >sedge;
void add(int x,int y,ll z){
	ver[++tot]=y,edge[tot]=z,nxt[tot]=head[x],head[x]=tot;
}
int eul[N<<1],red[N<<1],nume;
int mu,mv,mx,my;
ll mw,me;
struct ST{
    int f[N<<1][14];
    int Log[N<<1];
    int op(int x,int y){
        return dep[x]<dep[y]?x:y;
    }
    void init(int n,int *a){
        Log[0]=-1;
        for(int i=1;i<=n;i++)f[i][0]=a[i],Log[i]=Log[i>>1]+1;
        for(int i=1;i<14;i++)
            for(int j=1;j+(1<<i)-1<=n;j++)
                f[j][i]=op(f[j][i-1],f[j+(1<<(i-1))][i-1]);
    }
    int ask(int l,int r){
        int k=Log[r-l+1];
        return op(f[l][k],f[r-(1<<k)+1][k]);
    }
}st;
void dfs1(int x,int fa){
    if(x==1)dep[x]=0;
    //printf("dep[%d]=%lld\n",x,dep[x]);
    red[eul[x]=++nume]=x;
    for(int i=head[x];i;i=nxt[i]){
        int y=ver[i];
        if(y==fa)continue;
        dep[y]=dep[x]+edge[i];
        dfs1(y,x);
        red[++nume]=x;
    }
}
ll dist(int x,int y){
    return dep[x]+dep[y]-(dep[st.ask(min(eul[x],eul[y]),max(eul[x],eul[y]))]<<1);
}
struct Diam{
    int x,y;
    ll z;
    Diam(int xx=0,int yy=0){
        x=xx,y=yy;
        if(x)z=dist(x,y);else z=-1;
    }
    bool operator <(const Diam p)const{
        return z<p.z;
    }
}f[N];
Diam operator +(const Diam p,const Diam q){
    return max(max(p,q),max(max(Diam(p.x,q.x),Diam(p.x,q.y)),max(Diam(p.y,q.x),Diam(p.y,q.y))));
}
void dfs2(int x,int fa){
    f[x]=Diam(x,x);
    for(int i=head[x];i;i=nxt[i]){
        int y=ver[i];
        if(y==fa)continue;
        dfs2(y,x);
        f[x]=f[x]+f[y];
    }
    //printf("f[%d]=(%d,%d) %lld\n",x,f[x].x,f[x].y,f[x].z);
}
void init(){
	memset(head,0,sizeof(head));
	tot=nume=0;
	for(auto u:sedge){
		add(u.fi.fi,u.fi.se,u.se);add(u.fi.se,u.fi.fi,u.se);
	}
    dfs1(1,0);
    st.init(nume,red);
    dfs2(1,0);
    mu=mv=mx=my=me=0;mw=-1;
}
void dfs3(int x,int fa){
    vector<int>son;
    vector<ll>val;
    vector<Diam>pre,suf;
    son.clear();pre.clear();suf.clear();
    for(int i=head[x];i;i=nxt[i]){
        int y=ver[i];
        son.push_back(y);
        val.push_back(edge[i]);
        pre.push_back(f[y]);
        suf.push_back(f[y]);
    }
    for(int i=1;i<son.size();i++){
        pre[i]=pre[i-1]+pre[i];
    }
    for(int i=son.size()-2;i>=0;i--)
        suf[i]=suf[i+1]+suf[i];
    Diam now,e;
    for(int i=0;i<son.size();i++){
        int y=son[i];
        if(y==fa)continue;
        now=Diam(x,x);
        if(i>0)now=now+pre[i-1];
        if(i<son.size()-1)now=now+suf[i+1];
        f[x]=now;e=f[y];
        ll w=f[x].z+f[y].z+val[i];
        if(w>mw){
            mw=w;mu=x;mv=y;me=val[i];mx=f[x].x;my=f[y].y;
        }
        f[y]=f[y]+now;
        dfs3(y,x);
        f[y]=e;
    }
}
int main(){
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	n=read();k=read();
	for(int i=1;i<n;i++){
		pair<pii,ll> u;
		u.fi.fi=read();u.fi.se=read();u.se=read();
		sedge.insert(u);
	}
    init();
    write(f[1].z);putchar(' ');
    while(k--){
        dfs3(1,0);
        write(mw);putchar(' ');
        if(mu>mv)swap(mu,mv);
        if(mx>my)swap(mx,my);
        sedge.erase(make_pair(make_pair(mu,mv),me));
        sedge.insert(make_pair(make_pair(mx,my),me));
        init();
    }
    puts("");
	return 0;
}