#pragma GCC optimize("unroll-loops,O3")
#include <bits/stdc++.h>
using i64 = long long;
#undef DEBUG
#ifdef DEBUG
#include "debug.h"
#else
#define debug(...) void(23)
#endif
std::random_device rd;
std::mt19937 rng(rd());
struct node {
i64 val = 0;
i64 sum = 0;
int siz = 1;
node* lv = nullptr;
node* rv = nullptr;
unsigned long int wei = rng();
node() {}
node(i64 x) : val(x), sum(x) {}
};
int size(node* v) { return v ? v->siz : 0; }
i64 sum(node* v) { return v ? v->sum : 0; }
void pull(node*& v) {
if (!v) {
return;
}
v->siz = size(v->lv) + size(v->rv) + 1;
v->sum = sum(v->lv) + sum(v->rv) + v->val;
}
void merge(node*& v, node* lv, node* rv) {
if (!lv || !rv) {
v = (lv ? lv : rv);
return;
}
if (lv->wei > rv->wei) {
merge(lv->rv, lv->rv, rv);
v = lv;
} else {
merge(rv->lv, lv, rv->lv);
v = rv;
}
pull(v);
}
void split(node* v, node*& lv, node*& rv, int k) {
if (!v) {
lv = nullptr;
rv = nullptr;
return;
}
if (size(v->lv) >= k) {
split(v->lv, lv, v->lv, k);
rv = v;
} else {
split(v->rv, v->rv, rv, k - size(v->lv) - 1);
lv = v;
}
pull(lv);
pull(rv);
}
int count(node* v, i64 x) {
if (!v) {
return 0;
}
if (v->val <= x) {
return size(v->lv) + 1 + count(v->rv, x);
} else {
return count(v->lv, x);
}
}
node* root = nullptr;
void debug_dfs(node* v) {
if (!v) {
return;
}
debug_dfs(v->lv);
std::cerr << v->val << ' ';
debug_dfs(v->rv);
}
void debug_treap(node* v) {
#ifdef DEBUG
std::cerr << "treap: ";
debug_dfs(v);
std::cerr << '\n';
#endif
}
void add(i64 x) {
debug("add:", x);
int s = count(root, x);
node* nd = new node(x);
node *a;
split(root, root, a, s);
merge(root, root, nd);
merge(root, root, a);
debug_treap(root);
}
void del(i64 x) {
debug("del: ", x);
int s = count(root, x);
node *a, *b;
split(root, root, a, s - 1);
split(a, a, b, 1);
merge(root, root, b);
debug_treap(root);
}
int N, K;
std::vector<std::vector<int>> adj;
std::vector<std::array<int, 3>> E;
std::vector<i64> dep;
std::vector<std::set<std::pair<i64, int>, std::greater<std::pair<i64, int>>>> comes;
std::vector<i64> ans;
std::vector<int> saver;
int dfs1(int v, int pr) {
debug(v, pr);
if (int(adj[v].size()) == 1) {
comes[v].emplace(0, v);
}
for (auto i : adj[v]) {
int u = E[i][0] ^ E[i][1] ^ v;
if (u == pr) {
continue;
}
int x = dfs1(u, v);
saver[u] = x;
del(dep[x]);
dep[x] += E[i][2];
add(dep[x]);
comes[v].emplace(dep[x], x);
}
return comes[v].begin()->second;
}
i64 calc() {
// auto cd = dep;
// std::sort(cd.begin(), cd.end(), std::greater());
// i64 res = 0;
// for (int i = 0; i < K; ++i) {
// res += cd[i];
// }
node *a, *b;
split(root, a, b, N - K);
i64 res = sum(b);
merge(root, a, b);
return res;
}
void dfs2(int v, int pr) {
debug(v, pr, dep);
for (auto i : adj[v]) {
int u = E[i][0] ^ E[i][1] ^ v;
if (u == pr) {
continue;
}
int vtx = saver[u];
std::pair<i64, int> mxx = {-1, -1};
for (auto[d, vv] : comes[v]) {
if (vv != vtx) {
mxx = {d, vv};
break;
}
}
del(dep[vtx]);
del(dep[mxx.second]);
dep[vtx] -= E[i][2];
dep[mxx.second] += E[i][2];
add(dep[vtx]);
add(dep[mxx.second]);
ans[u] = calc();
comes[u].emplace(mxx.first + E[i][2], mxx.second);
dfs2(u, v);
del(dep[mxx.second]);
del(dep[vtx]);
dep[mxx.second] -= E[i][2];
dep[vtx] += E[i][2];
add(dep[mxx.second]);
add(dep[vtx]);
}
}
int main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cin >> N >> K;
adj.resize(N);
E.resize(N);
comes.resize(N);
ans.resize(N);
saver.resize(N);
dep.resize(N);
for (int i = 0; i < N; ++i) {
add(0);
}
for (int i = 1; i < N; ++i) {
int A, B, C;
std::cin >> A >> B >> C;
--A, --B;
E[i] = {A, B, C};
adj[A].emplace_back(i);
adj[B].emplace_back(i);
}
dfs1(0, 0);
ans[0] = calc();
dfs2(0, 0);
for (int i = 0; i < N; ++i) {
std::cout << ans[i] << '\n';
}
return 0;
}
