//#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];

mt19937 generator;

struct treap {
    int sz, value, prior;
    treap *left, *right;
    ll push_k,push_b;
    treap(int v) {
        value = v;
        sz = 1;
        prior = generator();
        left = NULL;
        right = NULL;
        push_k=0;
        push_b=0;
    }
};

treap* make_treap_leaf_copy(treap* v)
{
    assert(v->left==0);
    assert(v->right==0);
    treap *nt = new treap(v->value);
    return nt;
}

int get_size(treap *t) {
    if (t == NULL) {
        return 0;
    }
    return t->sz;
}

void update(treap *&t) {
    if (t == NULL) {
        return;
    }
    t->sz = 1 + get_size(t->left) + get_size(t->right);
}

void add_push(treap* t,ll k,ll b)
{
    assert(t!=0);
    t->value+=get_size(t->left)*k+b;
    t->push_k+=k;
    t->push_b+=b;
}

void make_push(treap *t)
{
    assert(t!=0);
    if (t->left){
        add_push(t->left,t->push_k,t->push_b);
    }
    if (t->right){
        add_push(t->right,t->push_k,t->push_b+(get_size(t->left)+1)*(t->push_k));
    }
}

treap *merge(treap *t1, treap *t2) {
    if (t1 == NULL) {
        return t2;
    }
    if (t2 == NULL) {
        return t1;
    }
    make_push(t1);
    make_push(t2);
    if (t1->prior <= t2->prior) {
        t2->left = merge(t1, t2->left);
        update(t2);
        return t2;
    } else {
        t1->right = merge(t1->right, t2);
        update(t1);
        return t1;
    }
}

void split_size(treap *our, int sz, treap *&l, treap *&r) {
    if (our == NULL) {
        l = NULL;
        r = NULL;
        return;
    }
    make_push(our);
    if (get_size(our->left) + 1 == sz) {
        l = our;
        r = our->right;
        l->right = NULL;
    } else {
        if (get_size(our->left) >= sz) {
            r = our;
            split_size(r->left, sz, l, r->left);
        } else {
            l = our;
            split_size(l->right, sz - get_size(l->left) - 1, l->right, r);
        }
    }
    update(l);
//    make_push(l);
    update(r);
//    make_push(r);
}

//void add(treap *&t, int x) {
//    treap *q = new treap(x);
//    t = merge(t, q);
//}

/// >= goes l, < goes r
void explicit_split(treap *our, int key, treap *&l, treap *&r) {
    if (our == NULL) {
        l = NULL;
        r = NULL;
        return;
    }
    make_push(our);
    if (our->value < key) {
        r = our;
        explicit_split(r->left, key, l, r->left);
    } else {
        l = our;
        explicit_split(l->right, key, l->right, r);
    }
    update(l);
    update(r);
}

typedef treap* barik_set;

void add_element(barik_set&t, int x) {
    treap *nt = new treap(x);
    treap *buf1, *buf2;
    explicit_split(t, x, buf1, buf2);
    t = merge(buf1, merge(nt, buf2));
}

//void explicit_erase(treap *&t, int x) {
//    treap *buf1, *buf2, *buf3, *buf4;
//    split(t, x, buf1, buf2);
//    split(buf2, x + 1, buf3, buf4);
//    t = merge(buf1, buf4);
//}

void do_naive_dfs_merge(barik_set &A,barik_set &B)
{
    if (!A){
        return;
    }
    make_push(A);
    add_element(B,A->value);
    do_naive_dfs_merge(A->left,B);
    do_naive_dfs_merge(A->right,B);
}

barik_set merge_two_sets(barik_set A,barik_set B)
{
    if (get_size(A)<get_size(B)){
        do_naive_dfs_merge(A,B);
        return B;
    }
    else{
        do_naive_dfs_merge(B,A);
        return A;
    }
}

void barik_push_kx_plus_b(barik_set &A,ll k,ll b)
{
    add_push(A,k,b);
}

void shift_right(barik_set& A)
{
    treap *buf1, *buf2;
    explicit_split(A, 0, buf1, buf2);
//    if (buf2!=0){
//        treap* t1,*t2;
//        split_size(buf2,1,t1,t2);
//        buf2=t2;
//    }
    {
        assert(buf1!=0);
        treap* t1,*t2;
        split_size(buf1,get_size(buf1)-1,t1,t2);
        treap* t3=make_treap_leaf_copy(t2);
        buf1=merge(t1,merge(t2,t3));
    }
    A = merge(buf1, buf2);
}

ll do_naive_dfs_sum(barik_set A,int& k)
{
    if (!A || !k){
        return 0ll;
    }
    make_push(A);
    ll res=0;
    res+=do_naive_dfs_sum(A->left,k);
    if (k!=0){
        res+=A->value;
        k--;
    }
    res+=do_naive_dfs_sum(A->right,k);
    return res;
}

ll sum_first_k(barik_set A,int k)
{
    return do_naive_dfs_sum(A,k);
}

barik_set dp[max_n];

void print_into_cerr_dfs(barik_set A)
{
    return;
    if (!A){
        return;
    }
    make_push(A);
    print_into_cerr_dfs(A->left);
    cerr<<A->value<<" ";
    print_into_cerr_dfs(A->right);
}

void print_into_cerr(barik_set A)
{
    return;
    cerr<<"barik set :: ";
    print_into_cerr_dfs(A);
    cerr<<"\n";
}

inline void dfs (int v, int p = -1) {
    LOG(v);
    cnt[v] = 1;
    for (auto [to, len] : edge[v]) {
        if (to == p) {
            continue;
        }
        dfs(to, v);
        LOG(to, v);
//        for (int j = 0; j < len(dp[to]); j++) {
//            dp[to][j] += len * 1ll * j * (k - j);
//        }
        ll B = k - 1;
        ll K = -2;
//        dp[to].add(K, B);
//        LOG(K * len, B * len);
        barik_push_kx_plus_b(dp[to], K * len, B * len);
//        gg.pb(to);
        cnt[v] += cnt[to];
//        dp[v].merge(dp[to]);
//        LOG(to, v, "finish 2");
        LOG("v");
        print_into_cerr(dp[v]);
        LOG("to");
        print_into_cerr(dp[to]);
        dp[v] = merge_two_sets(dp[v], dp[to]);
        LOG("merge");
        print_into_cerr(dp[v]);
//        LOG(to, v, "finish");
    }
    if (cnt[v] == 1) {
//        LOG("here");
        add_element(dp[v], 0);
//        LOG("here 2");
    }
    else {
//        dp[v].shift();
//        LOG("shift");
        shift_right(dp[v]);
//        LOG("shift 2");
    }
    LOG(v, "start");
    print_into_cerr(dp[v]);
}


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

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

    m1:
    n = 1e4;
    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);
    ll ans = 0;
    for (int i = 0; i < k; i++) {
        /// add a[i]
    }
    ans = sum_first_k(dp[0], k);
//    ans /= 2;
    cout << ans << '\n';
}