/**************************************************************

    Problem: 3784

    User: BeiYu

    Language: C++

    Result: Accepted

    Time:4540 ms

    Memory:26660 kb

****************************************************************/

#include <bits/stdc++.h>

using namespace std;

#define debug(a) cout<<#a<<"="<<a<<" "

#define mpr make_pair

typedef pair< int,int > pr;

typedef pair< int,pr > prr;

const int N = 100500;

int n,k,rt,rtt;

int d[N],sz[N],ud[N];

int vis[N<<1];

int cnte;

struct Edge { int to,w; }edge[N<<2];

vector< int > g[N];

priority_queue< pr > qq;

priority_queue< pr > q[N];

vector< int > nxt[N];

vector< int > tmp[N][2];

inline int in(int x=0,char ch=getchar()) { while(ch>'9' || ch<'0') ch=getchar();

    while(ch>='0' && ch<='9') x=x*10+ch-'0',ch=getchar();return x; }

void AddEdge(int fr,int to,int w) { g[fr].push_back(cnte);edge[cnte++]=(Edge){ to,w }; }

void Print() {

    cout<<"start"<<endl;

    for(int i=1;i<=n;i++) {

        cout<<i<<"-->";

        for(int j=0;j<(int)g[i].size();j++) cout<<"id:"<<g[i][j]<<" "<<edge[g[i][j]].to<<" ";

        cout<<endl;

    }

    cout<<"-------------------------"<<endl;

}

void ReBuild(int u,int fa) {

    int cnt=0,id=-1,lst=0,fst=0;

    if(g[u].size()>3) for(int i=g[u].size()-1,v;i>=1;i--)

        if((v=edge[g[u][i]].to)!=fa) {

            if(cnt&1) {

                g[n].push_back(g[u][i]);

            }else {

                g[++n].push_back(g[u][i]);

                if(lst) {

                    AddEdge(lst,n,0);

                    AddEdge(n,lst,0);

                }else {

                    fst=n;

                }lst=n;

            }

            cnt^=1;

            edge[g[u][i]^1].to=n;

            g[u].pop_back();

        }else id=g[u][i],g[u].pop_back();

    if(id!=-1) g[u].push_back(id);

    if(fst) AddEdge(u,fst,0),AddEdge(fst,u,0);

    for(int i=0;i<(int)g[u].size();i++) if(edge[g[u][i]].to!=fa) ReBuild(edge[g[u][i]].to,u);

}

void GetSize(int u,int fa) {

    d[u]=d[fa]+1,sz[u]=1;

    for(int i=g[u].size()-1,v;~i;i--) if((v=edge[g[u][i]].to)!=fa && !vis[g[u][i]]) {

        GetSize(v,u),sz[u]+=sz[v];

    }

}

void GetRoot(int u,int nn) {

    rt=-1,rtt=N;GetSize(u,u);

//  for(int i=1;i<=n;i++) cout<<sz[i]<<" ";cout<<endl;

//  for(int i=1;i<=n;i++) cout<<d[i]<<" ";cout<<endl;

    queue< pr > q;q.push(mpr(u,u));

    for(pr x;!q.empty();) {

        x=q.front(),q.pop();

        int u=x.first,tmp;

        for(int i=0,v;i<(int)g[u].size();i++) if((v=edge[g[u][i]].to)!=x.second && !vis[g[u][i]]){

            if(d[u]>d[v]) tmp=max(sz[u],nn-sz[u]);

            else tmp=max(sz[v],nn-sz[v]);

//          debug(u),debug(v),debug(tmp),debug(g[u][i])<<endl;

            if(tmp<rtt) rtt=tmp,rt=g[u][i];

            q.push(mpr(v,u));

        }

    }

//  debug(u),debug(rt)<<endl;

}

void GetDep(int u,int fa,int w,vector< int > &vv) {

    vv.push_back(w);

    for(int i=0,v;i<(int)g[u].size();i++) if((v=edge[g[u][i]].to)!=fa && !vis[g[u][i]]) {

        GetDep(v,u,w+edge[g[u][i]].w,vv);

    }

}

void GetAns(int x,int nn) {

    vis[x]=vis[x^1]=1;

    int u=edge[x].to,v=edge[x^1].to;

    GetDep(u,u,0,tmp[x][0]),GetDep(v,v,0,tmp[x][1]);

    sort(tmp[x][0].begin(),tmp[x][0].end(),greater< int >());

    sort(tmp[x][1].begin(),tmp[x][1].end(),greater< int >());

//  cout<<"---------------------"<<endl;

//  debug(x),debug(nn),debug(u),debug(v)<<endl;

//  for(int i=0;i<(int)tmp[x][0].size();i++) cout<<tmp[x][0][i]<<" ";cout<<endl;

//  for(int i=0;i<(int)tmp[x][1].size();i++) cout<<tmp[x][1][i]<<" ";cout<<endl;

    nxt[x].resize(tmp[x][0].size());

    for(int i=0;i<(int)tmp[x][0].size();i++) nxt[x][i]=0;

    for(int i=0;i<(int)tmp[x][0].size();i++) q[x].push(mpr(tmp[x][0][i]+tmp[x][1][0]+edge[x].w,i));

//  debug(tmp[x][0][i]+tmp[x][1][0]+edge[x].w)

//  debug(q[x].top().first)<<endl;

    qq.push(mpr(q[x].top().first,x));

    if(d[u]<d[v]) swap(u,v);

    int ss=sz[u];

    GetRoot(u,ss);

    if(rt!=-1) GetAns(rt,ss);

    GetRoot(v,nn-ss);

    if(rt!=-1) GetAns(rt,nn-ss);

}

void init() {

    n=in(),k=in();

    for(int i=1,u,v,w;i<n;i++)

        u=in(),v=in(),w=in(),AddEdge(u,v,w),AddEdge(v,u,w);

//  ReBuild(1,1);

//  Print();

//  cout<<"qwq"<<endl;

    GetRoot(1,n);

//  debug(rt)<<endl;

    GetAns(rt,n);

}

void Del(int x) {

    pr r=q[x].top();

    q[x].pop();

    int u=r.second;

    if(nxt[x][u]+1<(int)tmp[x][1].size()) nxt[x][u]++,q[x].push(mpr(tmp[x][0][u]+tmp[x][1][nxt[x][u]]+edge[x].w,u));

    qq.push(mpr(q[x].top().first,x));

}

int Query() {

    pr x=qq.top();qq.pop();

    int r=x.first,u=x.second;

    Del(u);

    return r;

}

int main() {

//  freopen("in.in","r",stdin);

//  ios::sync_with_stdio(false);

    init();

    for(;k--;) {

        printf("%d\n",Query());

    }

    return 0;

}