RMI21 - Paths (DP reroot - hard)

//Make CSP great again
//Vengeance
#include <bits/stdc++.h>
#define TASK "TESTCODE"
#define Log2(x) 31 - __builtin_clz(x)
using namespace std;
const int N = 1e5;
vector<pair<int, int> > adj[N + 1];
int n, k;
long long dp[N + 1], g[N + 1], res[N + 1], val = 0;
multiset<long long> in, out;
void add(long long a)
{
    val += a;
    in.insert(a);
    if (in.size() > k)
    {
        val -= *in.begin();
        out.insert(*in.begin());
        in.erase(in.begin());
    }
}
void del(long long a)
{
    auto it = out.find(a);
    if (it != out.end())
    {
        out.erase(it);
        return ;
    }
    it = in.find(a);
    assert(it != in.end());
    val -= a;
    in.erase(it);
    if (!out.empty())
    {
        val += *out.rbegin();
        in.insert(*out.rbegin());
        it = out.end();
        --it;
        out.erase(it);
    }
}
void DFS_down(int u, int p)
{
    for (auto &x : adj[u])
    {
        if (x.first == p)
        {
            continue;
        }
        DFS_down(x.first, u);
        dp[u] = max(dp[u], dp[x.first] + x.second);
    }
}
void DFS_up(int u, int p)
{
    long long s[2], f[2];
    s[0] = s[1] = -1;
    f[0] = f[1] = 0;
    for (auto &x : adj[u])
    {
        int v = x.first, w = x.second;
        if (v == p)
        {
            continue;
        }
        for (int i = 1; i >= 0; -- i)
        {
            if (dp[v] + w > f[i])
            {
                for (int j = 0; j < i; ++ j)
                {
                    f[j] = f[j + 1];
                    s[j] = s[j + 1];
                }
                f[i] = dp[v] + w;
                s[i] = v;
                break;
            }
        }
    }
    for (auto &x : adj[u])
    {
        int v = x.first, w = x.second;
        if (v == p)
        {
            continue;
        }
        g[v] = g[u];
        for (int i = 1; i >= 0; -- i)
        {
            if (s[i] != v)
            {
                g[v] = max(g[v], f[i]);
                break;
            }
        }
        g[v] += w;
        DFS_up(v, u);
        if (v != s[1])
        {
            add(dp[v] + w);
        }
    }
    //cerr << u << ' ' << dp[u] << ' ' << g[u] << '\n';
}
void DFS(int u, int p)
{
    res[u] = val;
    for (auto &x : adj[u])
    {
        int v = x.first, w = x.second;
        if (v == p)
        {
            continue;
        }
        add(dp[v]);
        del(dp[v] + w);
        add(g[v]);
        del(g[v] - w);
        DFS(v, u);
        del(dp[v]);
        add(dp[v] + w);
        del(g[v]);
        add(g[v] - w);
    }
}
void read()
{
    cin >> n >> k;
    for (int i = 1; i < n; ++ i)
    {
        int u, v, w;
        cin >> u >> v >> w;
        adj[u].push_back({v, w});
        adj[v].push_back({u, w});
    }
}
void solve()
{
    DFS_down(1, 0);
    DFS_up(1, 0);
    add(dp[1]);
    add(0);
    DFS(1, 0);
    for (int u = 1; u <= n; ++ u)
    {
        cout << res[u] << '\n';
    }
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    if (fopen(TASK".INP", "r"))
    {
        freopen(TASK".INP", "r", stdin);
        //freopen(TASK".OUT", "w", stdout);
    }
    int t = 1;
    bool typetest = false;
    if (typetest)
    {
        cin >> t;
    }
    for (int __ = 1; __ <= t; ++ __)
    {
        //cout << "Case " << __ << ": ";
        read();
        solve();
    }
}