//#pragma GCC optimize("Ofast", "unroll-loops")
//#pragma GCC target("sse", "sse2", "sse3", "ssse3", "sse4")
#ifdef LOCAL
#include <iostream>
#include <cmath>
#include <algorithm>
#include <stdio.h>
#include <cstdint>
#include <cstring>
#include <string>
#include <cstdlib>
#include <vector>
#include <bitset>
#include <map>
#include <queue>
#include <ctime>
#include <stack>
#include <set>
#include <list>
#include <random>
#include <deque>
#include <functional>
#include <iomanip>
#include <sstream>
#include <fstream>
#include <complex>
#include <numeric>
#include <cassert>
#include <array>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <thread>
#else
#include <bits/stdc++.h>
#endif

#define all(a) a.begin(),a.end()
#define len(a) (int)(a.size())
#define mp make_pair
#define pb push_back
#define fir first
#define sec second
#define fi first
#define se second

using namespace std;

typedef pair<int, int> pii;
typedef long long ll;
typedef long double ld;

template<typename T>
inline bool umin(T &a, T b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

template<typename T>
inline bool umax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

#ifdef LOCAL
#define D for (bool _FLAG = true; _FLAG; _FLAG = false)
#define LOG(...) print(#__VA_ARGS__" ::", __VA_ARGS__) << endl
template <class ...Ts> auto &print(Ts ...ts) { return ((cerr << ts << " "), ...); }
#else
#define D while (false)
#define LOG(...)
#endif // LOCAL

const int max_n = 1e5 + 11, inf = 1000111222;


//struct point {
//    int x, y;
//};
//
//inline bool cmp (point a, point b) {
//    return a.x < b.x || a.x == b.x && a.y < b.y;
//}
//
//inline bool cw (point a, point b, point c) {
//    return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) < 0;
//}
//
//inline bool ccw (point a, point b, point c) {
//    return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) > 0;
//}
//
//void convex_hull (vector<point> & a) {
//    if (len(a) <= 1) {
//        return;
//    }
//    sort (a.begin(), a.end(), cmp);
//    point p1 = a[0],  p2 = a.back();
//    vector<point> up = {p1}, down = {p1};
//    for (int i = 1; i < len(a); i++) {
//        if (i == len(a) - 1 || cw (p1, a[i], p2)) {
//            while (len(up) >= 2 && !cw(up[len(up) - 2], up.back(), a[i])) {
//                up.pop_back();
//            }
//            up.pb(a[i]);
//        }
//        if (i == len(a) - 1 || ccw (p1, a[i], p2)) {
//            while (len(down) >= 2 && !ccw(down[len(down) - 2], down.back(), a[i])) {
//                down.pop_back();
//            }
//            down.pb(a[i]);
//        }
//    }
//    a = up;
////    for (int i = len(down) - 2; i > 0; i--) {
////        a.pb(down[i]);
////    }
//}
//
//
//
//int dp[max_n][max_n], n, k, cnt[max_n];
//
//ll area(const vector<point>& fig) {
//    ll res = 0;
//    for (unsigned i = 0; i < fig.size(); i++) {
//        point p = i ? fig[i - 1] : fig.back();
//        point q = fig[i];
//        res += (p.x - q.x) * (p.y + q.y);
//    }
//    return abs(res);
//}


//inline void dfs (int v, int p = -1) {
//    cnt[v] = 1;
//    for (auto [to, len] : edge[v]) {
//        if (to == p) {
//            continue;
//        }
//        dfs(to, v);
//        for (int i1 = k; i1 >= 0; i1--) {
//            for (int j = min(cnt[to], k - i1); j >= 0; j--) {
//                umax(dp[v][i1 + j], dp[to][j] + dp[v][i1] + len * j * (k - j));
//                if (i1 + j + 1 <= k) {
//                    umax(dp[v][i1 + j + 1], dp[to][j] + dp[v][i1] + len * j * (k - j));
//                }
//            }
//        }
//        cnt[v] += cnt[to];
//    }
//    vector <point> have;
////    LOG(cnt[v]);
//    for (int i = 0; i <= min(k, cnt[v]); i++) {
//        have.pb(point{i, dp[v][i]});
////        LOG(i, dp[v][i]);
//    }
//    auto h = have;
//    convex_hull(h);
////    LOG(len(have), len(h), area(have), area(h));
////    assert(area(have) == area(h));
//    if (area(have) != area(h)) {
//        exit(3);
//    }
//}

struct dsu {
public:
    int n;
    vector <int> p, cnt;

    inline void make_set (int v) {
        p[v] = v;
    }

    dsu (int n) : n(n) {
        p.resize(n);
        cnt.assign(n, 1);
        for (int i = 0; i < n; i++) {
            make_set(i);
        }
    }

    inline int get (int v) {
        if (p[v] == v) return v;
        return p[v] = get(p[v]); /// compressing path
    }

    inline bool unite (int a, int b) {
        a = get(a);
        b = get(b);
        if (a == b) return false;
        if (cnt[a] > cnt[b]) {
            swap(a, b);
        }
        p[a] = b;
        cnt[b] += cnt[a];
        return true;
    }
};

const int debug = 0;
vector <pii> edge[max_n];

mt19937 rng(228);
template<typename T = int>
inline T randll(T l = INT_MIN, T r = INT_MAX) {
    return uniform_int_distribution<T>(l, r)(rng);
}

inline ld randld(ld l = INT_MIN, ld r = INT_MAX) {
    return uniform_real_distribution<ld>(l, r)(rng);
}


vector <int> used;
inline int dfs (int v, int &center, int sz, int p = -1) {
    int cnt = 1;
    for (auto &i : edge[v]) {
        if (i.first != p && !used[i.first]) {
            cnt += dfs(i.first, center, sz, v);
        }
    }
    if (center == -1 && cnt + cnt > sz)
        center = v;
    return cnt;
}



struct point {
    ll x, y;
    point operator + (const point & p) const {
        return point{x + p.x, y + p.y};
    }
    point operator - (const point & p) const {
        return point{x - p.x, y - p.y};
    }
    ll cross(const point & p) const {
        return x * p.y - y * p.x;
    }
};

void reorder_polygon(vector<point> & P){
    size_t pos = 0;
    for(size_t i = 1; i < P.size(); i++){
        if(P[i].y < P[pos].y || (P[i].y == P[pos].y && P[i].x < P[pos].x))
            pos = i;
    }
    rotate(P.begin(), P.begin() + pos, P.end());
}

vector<point> minkowski(vector<point> P, vector<point> Q){
    // the first vertex must be the lowest
    reorder_polygon(P);
    reorder_polygon(Q);
    // we must ensure cyclic indexing
    P.push_back(P[0]);
    P.push_back(P[1]);
    Q.push_back(Q[0]);
    Q.push_back(Q[1]);
    // main part
    vector<point> result;
    size_t i = 0, j = 0;
    while(i < P.size() - 2 || j < Q.size() - 2){
//        LOG(i, j);
        result.push_back(P[i] + Q[j]);
        auto cross = (P[i + 1] - P[i]).cross(Q[j + 1] - Q[j]);
        if(cross >= 0 && i < P.size() - 2)
            ++i;
        if(cross <= 0 && j < Q.size() - 2)
            ++j;
    }
    return result;
}


vector <ll> dp[max_n];
int n, k;

vector <int> GG;


inline void convolve (int a, int b) {
    vector <point> A(len(dp[a])), B(len(dp[b]));
    for (int i = 0; i < len(dp[a]); i++) {
        A[i] = point{ dp[a][i], i};
    }
    for (int i = 0; i < len(dp[b]); i++) {
        B[i] = point{dp[b][i], i};
    }
    auto res = minkowski(A, B);
    dp[a].resize(min(k + 1, len(A) + len(B) - 1));
    int j = 1;
    ll last = 0, val = 0;
    if (res[0].y != 0 || res[0].x != 0) {
        exit(47);
    }
//    LOG("here");
//    for (auto &i : res) {
//        LOG(i.x, i.y);
//    }
    for (int i = 1; i < len(res); i++) {
//        LOG(i);
//        LOG(res[i].y);
        while (j < res[i].y && j < len(dp[a])) {
            dp[a][j] = (j - last) * (res[i].x - val) + val * (res[i].y - last);
            if (dp[a][j] % (res[i].y - last) != 0) {
                exit(48);
            }
            dp[a][j] /= (res[i].y - last);
//            LOG(j, dp[a][j]);
            ++j;
        }
        if (j < len(dp[a])) {
            if (j != res[i].y) {
                exit(49);
            }
            dp[a][j] = res[i].x;
            ++j;
        }
        if (last > res[i].y) {
            break;
        }
        last = res[i].y;
        val = res[i].x;
    }
    LOG(len(res));
    dp[b].clear();
//    LOG(j, len(dp[a]));
    if (j != len(dp[a])) {
        exit(50);
    }
//    for (auto &kk : dp[a]) {
//        LOG(kk);
//    }
}

inline int calc (int l, int r) {
    if (l == r) {
        return GG[r];
    }
    int x = (l + r) >> 1;
    int L = calc(l, x);
    int R = calc(x + 1, r);
    convolve(R, L);
    return R;
}

int cnt[max_n];

inline void dfs (int v, int p = -1) {
    cnt[v] = 1;
    vector <int> gg;
    for (auto [to, len] : edge[v]) {
        if (to == p) {
            continue;
        }
        dfs(to, v);
        for (int j = 0; j < len(dp[to]); j++) {
            dp[to][j] += len * 1ll * j * (k - j);
        }
        gg.pb(to);
        cnt[v] += cnt[to];
    }
    if (gg.empty()) {
        dp[v].resize(2);
    }
    else {
        GG = gg;
        int where = calc(0, len(GG) - 1);
        dp[where].swap(dp[v]);
        int need = min({cnt[v], k});
        dp[v].resize(need + 1);
        for (int j = len(dp[v]) - 1; j > 0; j--) {
            umax(dp[v][j], dp[v][j - 1]);
        }
    }
}


int main() {
//    freopen("input.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);

    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    m1:
    n = 1e5;
    for (int i = 0; i <= n; i++) {
        edge[i].clear();
//        for (int j = 0; j <= n; j++) {
//            dp[i][j] = 0;
//        }
    }
    k = n;
    if (!debug) {
        cin >> n >> k;
    }
    used.resize(n);
    dsu t(n);
    LOG("here");
    for (int i = 1, u, v, w; i < n; i++) {
        if (!debug) {
            cin >> u >> v >> w;
            --u, --v;
        }
        else {
            u = i, v = i - 1;
            w = randll(1, 100);
//            u = randll(0, n - 1);
//            v = randll(0, n - 1);
            while (!t.unite(u, v)) {
                u = randll(0, n - 1);
                v = randll(0, n - 1);
            }
        }
        edge[u].pb({v, w});
        edge[v].pb({u, w});
    }
    dfs(0);
    cout << dp[0][k] << '\n';
    LOG(n, k);
}