/**
____ ____ ____ ____ ____ ____
||l |||e |||i |||n |||a |||d ||
||__|||__|||__|||__|||__|||__||
|/__\|/__\|/__\|/__\|/__\|/__\|
**/
#include<bits/stdc++.h>
#define endl '\n'
using namespace std;
typedef long long ll;
void speed()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
}
const ll maxn = 1e5 + 10;
ll n, k, idx[maxn][2], go_up[maxn];
ll num[maxn], depth[maxn], ch[maxn][2], up[maxn], fin[maxn], in[maxn], out[maxn], timer;
vector < pair < ll, ll > > g[maxn];
void calc(ll ver, ll par)
{
idx[ver][0] = -1;
idx[ver][1] = -1;
ch[ver][0] = ch[ver][1] = -1;
in[ver] = ++ timer;
for (pair < ll, ll > nb : g[ver])
{
if (nb.first == par)
continue;
depth[nb.first] = depth[ver] + nb.second;
calc(nb.first, ver);
///cout << ver << " :: " << nb.first << " :: " << ch[nb.first][0] + nb.second << endl;
if (ch[nb.first][0] + nb.second > ch[ver][0])
{
ch[ver][1] = ch[ver][0];
idx[ver][1] = idx[ver][0];
ch[ver][0] = ch[nb.first][0] + nb.second;
idx[ver][0] = idx[nb.first][0];
}
else if (ch[nb.first][0] + nb.second > ch[ver][1])
{
ch[ver][1] = ch[nb.first][0] + nb.second;
idx[ver][1] = idx[nb.first][0];
}
}
if (ch[ver][0] == -1)
{
ch[ver][0] = 0;
idx[ver][0] = ver;
}
out[ver] = timer;
}
void trav(ll ver, ll par, ll dw)
{
if (par == -1)
{
up[ver] = 0;
go_up[ver] = 1;
}
else
{
up[ver] = up[par] + dw;
go_up[ver] = go_up[par];
ll path = ch[par][0], go_path = idx[par][0];
if (idx[par][0] == idx[ver][0])
path = ch[par][1], go_path = idx[par][1];
if (path + dw > up[ver])
up[ver] = path + dw, go_up[ver] = go_path;
}
for (pair < ll, ll > nb : g[ver])
{
if (nb.first == par)
continue;
trav(nb.first, ver, nb.second);
}
}
void calc_num(ll ver, ll par, ll far)
{
ll mx = -1;
bool leaf = true;
for (pair < ll, ll > nb : g[ver])
{
if (nb.first == par)
continue;
leaf = false;
if (idx[nb.first][0] == idx[ver][0])
calc_num(nb.first, ver, far + nb.second);
else
calc_num(nb.first, ver, nb.second);
}
if (leaf)
num[ver] = far;
}
set < pair < ll, ll > > lw, hg;
ll ans = 0;
void add(ll ver, ll val)
{
pair < ll, ll > cur = {num[ver], ver};
if (lw.find(cur) != lw.end())
lw.erase(cur);
else
{
ans -= num[ver];
hg.erase(cur);
}
cur.first += val;
num[ver] += val;
hg.insert(cur);
///cout << ans << endl;
ans += cur.first;
///cout << cur.first << " :: " << cur.second << endl;
if (hg.size() > k)
{
ans = ans - (*hg.begin()).first;
lw.insert(*hg.begin());
hg.erase(hg.begin());
}
///cout << "---------- " << ans << endl;
}
void rem(ll ver, ll val)
{
pair < ll, ll > cur = {num[ver], ver};
if (lw.find(cur) != lw.end())
lw.erase(cur);
else
{
ans -= num[ver];
hg.erase(cur);
}
cur.first -= val;
num[ver] -= val;
lw.insert(cur);
///cout << "rem " << cur.first << " " << cur.second << endl;
if (lw.size() > (n - k))
{
ans = ans + (*lw.rbegin()).first;
hg.insert(*lw.rbegin());
lw.erase(*lw.rbegin());
}
}
void dfs(ll ver, ll par, ll dw)
{
//cout << ver << " : " << par << " : " << dw << endl;
//cout << idx[ver][0] << " " << idx[ver][1] << " " << num[idx[ver][0]] << " " << go_up[ver] << endl;
if (par != -1)
{
if (go_up[ver] > 0)
add(go_up[ver], dw);
if (idx[ver][0] > 0)
rem(idx[ver][0], dw);
}
/**cout << "currently" << endl;
cout << ver << " " << ans << endl;
for (ll i = 1; i <= n; i ++)
cout << num[i] << " ";
cout << endl;*/
/**ll sum = 0;
vector < ll > d;
for (int i = 1; i <= n; i ++)
d.push_back(num[i]);
sort(d.begin(), d.end());
reverse(d.begin(), d.end());
for (int i = 0; i < k; i ++)
sum += d[i];
fin[ver] = sum;*/
fin[ver] = ans;
for (pair < ll, ll > nb : g[ver])
{
if (nb.first == par)
continue;
dfs(nb.first, ver, nb.second);
}
if (par != -1)
{
if (go_up[ver] > 0)
rem(go_up[ver], dw);
if (idx[ver][0] > 0)
add(idx[ver][0], dw);
} /**cout << "finito" << endl;
cout << ver << endl;
for (ll i = 1; i <= n; i ++)
cout << num[i] << " ";
cout << endl;*/
}
void solve()
{
cin >> n >> k;
for (ll i = 1; i < n; i ++)
{
ll v, u;
ll l;
cin >> v >> u >> l;
g[v].push_back({u, l});
g[u].push_back({v, l});
}
calc(1, -1);
trav(1, -1, 0);
calc_num(1, -1, 0);
/**for (int i = 1; i <= n; i ++)
{
if (go_up[i] <= 0)
continue;
if (in[go_up[i]] >= in[i] && out[go_up[i]] <= out[i])
cout << "FSAWRSF" << endl;
}*/
for (ll i = 1; i < k; i ++)
hg.insert({0, i});
for (ll i = k; i <= n; i ++)
lw.insert({0, i});
for (ll i = 1; i <= n; i ++)
{
if (num[i] != 0)
{
ll st = num[i];
num[i] = 0;
///cout << "here " << num[i] << " :: " << i << endl;
add(i, st);
}
}
dfs(1, -1, 0);
for (ll i = 1; i <= n; i ++)
cout << fin[i] << endl;
}
int main()
{
///freopen("test.txt", "r", stdin);
///freopen("output.txt", "w", stdout);
speed();
solve();
return 0;
}
