ioi05p6.cpp

// Ivan Carvalho
// Solution to https://dmoj.ca/problem/ioi05p6
#include <bits/stdc++.h>
using namespace std;

typedef pair<int, int> ii;
const int MAXN = 102;
const int MAXK = 52;
const int INF = 2 * 1e9;

vector<ii> grafo[MAXN];
int dp[MAXN][MAXN][MAXK], dist[MAXN][MAXN], qtd[MAXN], N, K;
bool vis1[MAXN][MAXN], vis2[MAXN][MAXN];

void dfs_dist(int v, int p, int depth) {
    if (vis2[v][p]) return;
    vis2[v][p] = 1;
    dist[v][p] = depth;
    for (ii aresta : grafo[v]) {
        dfs_dist(aresta.first, aresta.first, 0);
        dfs_dist(aresta.first, p, depth + aresta.second);
    }
}

void solve(int v, int p) {
    if (vis1[v][p]) return;
    vis1[v][p] = 1;
    int embutido = dist[v][p] * qtd[v];
    int knapsack[MAXK];
    for (int i = 0; i <= K; i++) knapsack[i] = embutido;
    for (ii aresta : grafo[v]) {
        int u = aresta.first;
        solve(u, u);
        solve(u, p);
        int novo[MAXK];
        for (int i = 0; i <= K; i++) {
            novo[i] = INF;
        }
        for (int peso = 0; peso <= K; peso++) {
            for (int i = K; i >= peso; i--) {
                novo[i] = min(novo[i], knapsack[i - peso] + dp[u][p][peso]);
                if (peso >= 1)
                    novo[i] =
                        min(novo[i], knapsack[i - peso] + dp[u][u][peso - 1]);
            }
        }
        for (int i = 0; i <= K; i++) knapsack[i] = novo[i];
    }
    for (int i = 0; i <= K; i++) dp[v][p][i] = knapsack[i];
}

int main() {
    scanf("%d %d", &N, &K);
    for (int i = 1; i <= N; i++) {
        int w, v, d;
        scanf("%d %d %d", &w, &v, &d);
        grafo[v].push_back(ii(i, d));
        qtd[i] = w;
    }
    dfs_dist(0, 0, 0);
    solve(0, 0);
    printf("%d\n", dp[0][0][K]);
    return 0;
}