#include <bits/stdc++.h>
using namespace std;
#define int long long
#define sz(x) (int)x.size()
#define all(x) x.begin() , x.end()
const int N = 1e5 + 7;
const int inf = 1e18 + 7;
struct SEGT{
vector < pair<int,int> > t;
int tree_size;
const pair<int,int> identity_element = {-inf,-inf};// value , index
pair<int,int> merge(pair<int,int> &x , pair<int,int> &y){
return max(x,y);
}
void init(int x){
tree_size = x+3;
t.assign(2*tree_size , identity_element);
}
void modify(int p, pair<int,int> value) { // set value at position p
for (t[p += tree_size] = value; p > 1; p >>= 1){
t[p>>1] = merge(t[p] , t[p^1]);
}
}
pair<int,int> query(int l, int r) { // sum on interval [l, r]
pair<int,int> res = identity_element;
for (r+=1 , l += tree_size, r += tree_size; l < r; l >>= 1, r >>= 1) {
if (l&1) res = merge(res , t[l++]);
if (r&1) res = merge(res , t[--r]);
}
return res;
}
} segt;
int n,k;
int ans[N];
vector<pair<int,int>>tree[N];
int heavy[N];
int set_heavy(int node , int par){
int maxi = -1;
for(auto itr : tree[node]){
if(itr.first == par)continue;
int val = set_heavy(itr.first , node) + itr.second;
if(maxi < val){
heavy[node] = itr.first;
maxi = val;
}
}
if(maxi == -1)heavy[node] = -1;
return maxi == -1 ? 0ll : maxi;
}
vector<pair<int , int>>leafs;// path cevabi , node
int mini[N] , maxi[N];
void retrieve(int node , int par , int cumans){
if(heavy[node] == -1){
mini[node] = maxi[node] = sz(leafs);
// cout << "MINI/MAXI " << node+1 << " : " << mini[node] << " " << maxi[node] << endl;
leafs.push_back({cumans , node});
return;
}
mini[node] = -1;
for(auto itr : tree[node]){
if(itr.first == par)continue;
if(heavy[node] == itr.first){
retrieve(itr.first , node , cumans + itr.second);
}
else{
retrieve(itr.first , node , itr.second);
}
if(mini[node] == -1)mini[node] = mini[itr.first];
maxi[node] = maxi[itr.first];
}
// cout << "MINI/MAXI " << node+1 << " : " << mini[node] << " " << maxi[node] << endl;
}
multiset<int>ste1 , ste2;
int sum1 = 0;
void rebalance(){
while(sz(ste1) > k){
sum1 -= *ste1.begin();
ste2.insert(*ste1.begin());
ste1.erase(ste1.begin());
}
while(sz(ste1) < k and !ste2.empty()){
sum1 += *--ste2.end();
ste1.insert(*--ste2.end());
ste2.erase(--ste2.end());
}
while(!ste1.empty() and !ste2.empty() and *ste1.begin() < *--ste2.end()){
int tmp1 = *ste1.begin() , tmp2 = *--ste2.end();
sum1 -= tmp1;
ste1.erase(ste1.begin());
ste2.erase(--ste2.end());
sum1 += tmp2;
ste1.insert(tmp2);
ste2.insert(tmp1);
}
}
void add(int x){
ste2.insert(x);
rebalance();
}
void del(int x){
if(ste2.count(x)){
ste2.erase(ste2.find(x));
}
else if(ste1.count(x)){
sum1 -= x;
ste1.erase(ste1.find(x));
}
else assert(false);
rebalance();
}
pair<int,int> MAX(pair<int,int> A , pair<int,int> B){
if(A > B)return A;
return B;
}
void dfs(int node , int par){
ans[node] = sum1;
// cout << "DFS : " << node+1 << " , " << ans[node] << endl;
// cout << "leafs : ";for(auto itr : leafs)cout << itr.second+1 << " ";cout << endl;
// cout << "SEGT : ";for(int i = 0;i<sz(leafs);i++)cout << segt.query(i,i).first << " ";cout << endl;
// cout << "ste1 : ";for(auto itr : ste1)cout << itr << " ";cout << endl;
// cout << "ste2 : ";for(auto itr : ste2)cout << itr << " ";cout << endl;
// cout << endl;
for(auto itr : tree[node]){
if(itr.first == par)continue;
// cout << node+1 << " -> " << itr.first+1 << " : " << mini[itr.first] << " " << maxi[itr.first] << endl;
auto tmp1 = segt.query(mini[itr.first] , maxi[itr.first]);
del(tmp1.first);
segt.modify(tmp1.second , {tmp1.first - itr.second , tmp1.second});
add(tmp1.first - itr.second);
auto tmp2 = pair<int,int>{-inf,-inf};
if(mini[itr.first] != 0){
tmp2 = MAX(tmp2 , segt.query(0 , mini[itr.first]-1));
}
if(maxi[itr.first] != sz(leafs)-1){
tmp2 = MAX(tmp2 , segt.query(maxi[itr.first]+1 , sz(leafs)-1));
}
if(tmp2 != pair<int,int>{-inf,-inf}){
del(tmp2.first);
segt.modify(tmp2.second , {tmp2.first + itr.second , tmp2.second});
add(tmp2.first + itr.second);
}
dfs(itr.first , node);
if(tmp2 != pair<int,int>{-inf,-inf}){
del(tmp2.first + itr.second);
segt.modify(tmp2.second , tmp2);
add(tmp2.first);
}
del(tmp1.first - itr.second);
segt.modify(tmp1.second , tmp1);
add(tmp1.first);
}
}
void solve(){
cin >> n >> k;
if(n == 1){
cout << 0 << '\n';
cout << endl;
return;
}
else if(n == 2){
int a,b,c;
cin >> a >> b >> c;
cout << c << '\n';
cout << c << '\n';
cout << endl;
return;
}
for(int i = 1;i<n;i++){
int x,y,c;
cin >> x >> y >> c;
x-- , y--;
tree[x].push_back({y , c});
tree[y].push_back({x , c});
}
int root = 0;
while(sz(tree[root]) == 1)root++;
set_heavy(root , root);
retrieve(root , root , 0ll);
segt.init(sz(leafs));
for(int i = 0;i<sz(leafs);i++){
segt.modify(i , {leafs[i].first , i});
add(leafs[i].first);
}
// cout << "leafs : ";for(auto itr : leafs)cout << itr.first << "," << itr.second+1 << " ";cout << endl;
dfs(root , root);
for(int i = 0;i<n;i++){
cout << ans[i] << '\n';
}
cout << endl;
}
signed main(){
ios_base::sync_with_stdio(0);cin.tie(0);
int testcase=1;//cin >> testcase;
while(testcase--)solve();
cerr << 1000.0 * clock() / CLOCKS_PER_SEC << " ms" << endl;
}
