//#include "richest.h"
#pragma GCC optimize("Ofast,unroll-loops")
#include<bits/stdc++.h>
#define int   long long
#define ll long long
#define down cout<<'\n';
#define debug cout<<" cucuucucuuu",down
#define modwwe  int t;cin>>t; while(t--)
#define bit(i,j) (i>>j&1)
#define sobit(a) __builtin_popcountll(a)
#define task2 "top1apio"
#define task "test"
#define fin(x) freopen(x".inp","r",stdin)
#define fou(x) freopen(x".out","w",stdout)
#define pb push_back
#define mask(k) (1ll<<k)
#define checktime   cerr << (double)clock() / CLOCKS_PER_SEC * 1000  << " ms";
using namespace std;
#define getchar_unlocked getchar
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
using i128 = __int128;
int rand(int l,int r)
{
    return uniform_int_distribution<int>(l,r)(rd);
}
void phongbeo();
const ll inf=1e15;
const ll mod2 =1e9 + 7;
//const ll base=67;
ll  n, m, s1, s2, s4, s3, sf, k, s5, s6, s7, s8, s9, mx2, res, dem2 = 0, dem = 0, s33, dem3, dem4, mid, l2, r2, center;
ll  i, s10, s12,k1,k2,k3,s11,lim,w,l,r,dem5,dem6,dem7,dem9,now,root,q,en;
ll kk;
ll el = 19;
main()
{
    ///top1apio
    if(fopen(task2".inp","r"))
    {
        fin(task2);
        fou(task2);
    }
    ///top1apio
    if(fopen(task".inp","r"))
    {
        fin(task);
        fou(task);
    }
    ///top1apio
    ios_base::sync_with_stdio(0);
    cout.tie(0);
    cin.tie(0);
//   cin>>s1;
    //ll t;cin>>t;while(t--)
    phongbeo(),down
    ///  checktime
    ///top1apio
}
pair<int,int> dp[100001],mx[100001],pre[100003],suff[100003];
int cost[100001];
set<pair<int,int>>dc,ocl;
struct ib
{
    int a,b;
};
vector<ib> v[100001];
void del(pair<int,int> x)
{
    if(dc.find(x)!=dc.end())dc.erase(dc.find(x)),s4-=x.first;
    if(ocl.find(x)!=ocl.end())ocl.erase(ocl.find(x));
    while(ocl.size()&&dc.size()<k)
    {
        auto it=ocl.rbegin();
        dc.insert(*it);
        s4+=it->first;
        ocl.erase(*it);
    }
    while(ocl.size()&&dc.begin()->first<ocl.rbegin()->first)
    {
        auto it=ocl.rbegin();
        dc.insert(*it);
        s4+=it->first;
        ocl.erase(*it);
        auto itc=dc.begin();
        s4-=itc->first;
        ocl.insert(*itc);
        dc.erase(*itc);
    }
}
void add(pair<int,int> x)
{
    ocl.insert(x);
    while(ocl.size()&&dc.size()<k)
    {
        auto it=ocl.rbegin();
        dc.insert(*it);
        s4+=it->first;
        ocl.erase(*it);
    }
    while(ocl.size()&&dc.begin()->first<ocl.rbegin()->first)
    {
        auto it=ocl.rbegin();
        dc.insert(*it);
        s4+=it->first;
        ocl.erase(*it);
        auto itc=dc.begin();
        s4-=itc->first;
        ocl.insert(*itc);
        dc.erase(*itc);
    }
}
pair<int,int> mer(pair<int,int> a,pair<int,int> b)
{
    if(a.first>b.first)return a;
    return b;
}
void dfs(int x,int y)
{
    bool ok=0;
    for(auto [f,cost]:v[x])
        if(f^y)
        {
            ok=1;
            dfs(f,x);
            del(mx[f]);
            mx[f].first+=cost;
            add(mx[f]);
            mx[x]=mer(mx[x],mx[f]);
        }
}
void reroot(int x,int y)
{
    cost[x]=s4;
    dem=0;
    pre[0]=dp[x];
    for(auto [f,cost]:v[x])
        if(f^y)
        {
            dem++;
            pre[dem]=mer(mx[f],pre[dem-1]);
        }
    reverse(v[x].begin(),v[x].end());
    suff[dem+1]=dp[x];
    for(auto [f,cost]:v[x])
        if(f^y)
        {
            suff[dem]=mer(mx[f],suff[dem+1]);
            dp[f]=mer(pre[dem-1],suff[dem+1]);
            dem--;
        }
    reverse(v[x].begin(),v[x].end());
    for(auto [f,cost]:v[x])
        if(f^y)
        {
            del(dp[f]);
            dp[f].first+=cost;
            add(dp[f]);
            del(mx[f]);
            mx[f].first-=cost;
            add(mx[f]);
            reroot(f,x);
            del(dp[f]);
            dp[f].first-=cost;
            add(dp[f]);
            del(mx[f]);
            mx[f].first+=cost;
            add(mx[f]);
        }
}
void phongbeo()
{
    cin>>n>>k;
    for(int i=1; i<=n; i++)
    {
        add({0,i});
        mx[i]= {0,i};
    }
    for(int i=1; i<n; i++)
        cin>>l>>r>>s2,v[l].pb({r,s2}),v[r].pb({l,s2});
    dfs(1,0);
    dp[1]= {0,1};
    reroot(1,0);
    for(int i=1; i<=n; i++)
        cout<<cost[i],down
    }
Compilation message (stderr)
Main.cpp:34:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
   34 | main()
      | ^~~~
Main.cpp: In function 'int main()':
Main.cpp:13:23: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   13 | #define fin(x) freopen(x".inp","r",stdin)
      |                ~~~~~~~^~~~~~~~~~~~~~~~~~~
Main.cpp:39:9: note: in expansion of macro 'fin'
   39 |         fin(task2);
      |         ^~~
Main.cpp:14:23: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   14 | #define fou(x) freopen(x".out","w",stdout)
      |                ~~~~~~~^~~~~~~~~~~~~~~~~~~~
Main.cpp:40:9: note: in expansion of macro 'fou'
   40 |         fou(task2);
      |         ^~~
Main.cpp:13:23: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   13 | #define fin(x) freopen(x".inp","r",stdin)
      |                ~~~~~~~^~~~~~~~~~~~~~~~~~~
Main.cpp:45:9: note: in expansion of macro 'fin'
   45 |         fin(task);
      |         ^~~
Main.cpp:14:23: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   14 | #define fou(x) freopen(x".out","w",stdout)
      |                ~~~~~~~^~~~~~~~~~~~~~~~~~~~
Main.cpp:46:9: note: in expansion of macro 'fou'
   46 |         fou(task);
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