#include <bits/stdc++.h>
using namespace std;
const int MAXN = 300005;
int n, k;
vector<pair<int, int>> e[MAXN];
mt19937 Rand(114514);
struct Treap {
    int lc[MAXN], rc[MAXN], rnd[MAXN];
    long long val[MAXN], k[MAXN], b[MAXN];
    int siz[MAXN];
    int tot;
    stack<int> s;
    int newNode(long long v) {
        int p = s.empty() ? ++tot : s.top();
        if (!s.empty()) s.pop();
        k[p] = b[p] = lc[p] = rc[p] = 0;
        val[p] = v, siz[p] = 1, rnd[p] = Rand();
        return p;
    }
    void pushUp(int p) {
        siz[p] = siz[lc[p]] + siz[rc[p]] + 1;
    }
    void tag(int p, long long K, long long B) {
        val[p] += K * (siz[lc[p]] + 1) + B;
        k[p] += K, b[p] += B;
    }
    void pushDown(int p) {
        if (k[p] || b[p]) {
            if (lc[p]) tag(lc[p], k[p], b[p]);
            if (rc[p]) tag(rc[p], k[p], k[p] * (siz[lc[p]] + 1) + b[p]);
            k[p] = b[p] = 0;
        }
    }
    void split(int v, int p, int &x, int &y) {
        if (!p) x = y = 0;
        else {
            pushDown(p);
            if (v > val[p]) {
                y = p;
                split(v, lc[p], x, lc[p]);
            } else {
                x = p;
                split(v, rc[p], rc[p], y);
            }
            pushUp(p);
        }
    }
    int merge(int x, int y) {
        if (!x || !y) return x + y;
        pushDown(x), pushDown(y);
        if (rnd[x] < rnd[y]) {
            rc[x] = merge(rc[x], y);
            pushUp(x);
            return x;
        } else {
            lc[y] = merge(x, lc[y]);
            pushUp(y);
            return y;
        }
    }
    void flatten(int p, vector<long long> &v) {
        s.push(p);
        pushDown(p);
        if (lc[p]) flatten(lc[p], v);
        v.push_back(val[p]);
        if (rc[p]) flatten(rc[p], v);
    }
    void insert(int &p, int v) {
        int x, y; split(v, p, x, y);
        p = merge(merge(x, newNode(v)), y);
    }
} t;
int root[MAXN];
int siz[MAXN];
void dfs(int u, int pre) {
    siz[u] = 1;
    int s = 0;
    for (auto p : e[u]) if (p.first != pre) {
        int v = p.first, w = p.second;
        dfs(v, u);
        t.tag(root[v], -2ll * w, 1ll * w * (k + 1));
        siz[u] += siz[v];
        if (siz[v] > siz[s]) s = v;
    }
    if (s) root[u] = root[s];
    t.insert(root[u], 0);
    for (auto p : e[u]) if (p.first != pre && p.first != s) {
        int v = p.first;
        vector<long long> val;
        t.flatten(root[v], val);
        for (long long w : val) {
            t.insert(root[u], w);
        }
    }
}
int main() {
    // freopen("H.in", "r", stdin);
    scanf("%d%d", &n, &k);
    for (int i = 1; i < n; i++) {
        int u, v, w; scanf("%d%d%d", &u, &v, &w);
        e[u].push_back({v, w});
        e[v].push_back({u, w});
    }
    dfs(1, 0);
    long long ans = 0;
    vector<long long> val;
    t.flatten(root[1], val);
    for (int i = 1; i <= k; i++) {
        ans += val[i - 1];
    }
    printf("%lld\n", ans);
    return 0;
}
/*
6 3
1 2 3
2 3 2
2 4 1
1 5 2
5 6 3

*/