/**
  * created     : 12.10.2024 22:19:00
  * author      : wzj33300
  */

#include <bits/stdc++.h>
using namespace std;

#ifdef DEBUG
#include <algo/debug.h>
#else
#define debug(...) 42
#define assert(...) 42
#endif

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using db = long double;  // or double, if TL is tight
using str = string;      // yay python!

// pairs
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
#define mp make_pair
#define fi first
#define se second

// ^ lol this makes everything look weird but I'll try it
template <class T>
using vc = vector<T>;
template <class T, size_t SZ>
using AR = array<T, SZ>;
using vi = vc<int>;
using vb = vc<bool>;
using vl = vc<ll>;
using vd = vc<db>;
using vs = vc<str>;
using vpi = vc<pi>;
using vpl = vc<pl>;
using vpd = vc<pd>;

// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep1(i, n) for (int i = 1; i < (n); ++i)
#define rep1n(i, n) for (int i = 1; i <= (n); ++i)
#define repr(i, n) for (int i = (n) - 1; i >= 0; --i)

#define rep_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))

#define lb lower_bound
#define ub upper_bound
template <class T>
int lwb(vc<T> &a, const T &b) {
  return int(lb(all(a), b) - bg(a));
}
template <class T>
int upb(vc<T> &a, const T &b) {
  return int(ub(all(a), b) - bg(a));
}
// const int MOD = 998244353;  // 1e9+7;
const int Big = 1e9;  // not too close to INT_MAX
const ll BIG = 1e18;  // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4]{1, 0, -1, 0}, dy[4]{0, 1, 0, -1};  // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

int pct(int x) { return __builtin_popcount(x); }
int pct(u32 x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int pct(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <class T>
bool ckmin(T &a, const T &b) {
  return b < a ? a = b, 1 : 0;
}  // set a = min(a,b)
template <class T>
bool ckmax(T &a, const T &b) {
  return a < b ? a = b, 1 : 0;
}  // set a = max(a,b)

template <class T, class U>
T fstTrue(T lo, T hi, U f) {
  ++hi;
  assert(lo <= hi);  // assuming f is increasing
  while (lo < hi) {  // find first index such that f is true
    T mid = lo + (hi - lo) / 2;
    f(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U f) {
  --lo;
  assert(lo <= hi);  // assuming f is decreasing
  while (lo < hi) {  // find first index such that f is true
    T mid = lo + (hi - lo + 1) / 2;
    f(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}

// signed main() {
int main() {
  // freopen(".in", "r",stdin);
  // freopen(".out","w",stdout);
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  std::cin >> n >> m;
  ++m;
  vc<vpi> e(n);
  for (int i = 1; i < n; i++) {
    int u, v, w;
    std::cin >> u >> v >> w;
    --u, --v;
    e[u].eb(v, w), e[v].eb(u, w);
  }
  /*
  wqs ?? k ???
  */
  vc f(n, AR<pl, 3>{});
  auto check = [&](ll add_val) {
    vc(n, AR<pl, 3>{}).swap(f);
    auto dfs = [&](auto &&dfs, int x, int fa) -> void {
      auto &fu = f[x];
      fu.fill({-BIG, -BIG});
      fu[0] = {0, 0};
      fu[1] = {add_val, 1};
      for (auto [v, w] : e[x]) {
        if (v == fa) continue;
        dfs(dfs, v, x);
        auto &fv = f[v];
        AR<pl, 3> nf;
        nf.fill({-BIG, -BIG});
        for (int i = 0; i < 3; i++) {
          for (int j = 0; j < 3; j++) {
            pl now(fu[i].first + fv[j].first, fu[i].second + fv[j].second);
            ckmax(nf[i], now);
          }
        }
        for (int i = 0; i < 2; i++) {
          for (int j = 0; j < 2; j++) {
            /*
          i+j=2 -1
          i+j=1 0
          i+j=0 1
          */
            pl now(fu[i].first + fv[j].first + w + add_val * (1 - (i + j)), fu[i].second + fv[j].second + 1 - (i + j));
            ckmax(nf[i + 1], now);
          }
        }
        fu = nf;
      }
    };
    dfs(dfs, 0, -1);
    debug(f);
    return std::max_element(all(f[0]))->second >= m;
  };
  ll d = fstTrue(-1'000'000'000'000LL, 1'000'000'000'000LL, check);
  debug(d);
  check(d);
  std::cout << std::max_element(all(f[0]))->first - d * m;
  return 0;
}