#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll INF = 1e18;
int n, k;
vector<pair<int,ll>> adj[200005]; // cây
// =================== Subtask 1: Brute Force (n <= 20) ===================
ll distSmall[25][25];
ll subtask1() {
// Floyd-Warshall để tính dist[u][v]
for (int i=1; i<=n; i++)
for (int j=1; j<=n; j++)
distSmall[i][j] = (i==j?0:INF);
for (int u=1; u<=n; u++) {
for (auto [v,w]: adj[u]) {
distSmall[u][v] = min(distSmall[u][v], w);
}
}
for (int m=1; m<=n; m++)
for (int i=1; i<=n; i++)
for (int j=1; j<=n; j++)
distSmall[i][j] = min(distSmall[i][j], distSmall[i][m] + distSmall[m][j]);
vector<int> nodes(n);
iota(nodes.begin(), nodes.end(), 1);
ll ans = INF;
vector<int> mask;
// sinh tổ hợp
vector<int> choose(n,0);
fill(choose.begin(), choose.begin()+k, 1);
do {
vector<int> S;
for (int i=0; i<n; i++) if (choose[i]) S.push_back(i+1);
ll val = 0;
for (int u=1; u<=n; u++) {
ll best = INF;
for (int v: S) best = min(best, distSmall[u][v]);
val = max(val, best);
}
ans = min(ans, val);
} while (prev_permutation(choose.begin(), choose.end()));
return ans;
}
// =================== Subtask 2: k = 1 (radius of tree) ===================
pair<int,ll> dfs_far(int u, int p, ll d) {
pair<int,ll> res = {u,d};
for (auto [v,w]: adj[u]) if (v!=p) {
auto cur = dfs_far(v,u,d+w);
if (cur.second > res.second) res = cur;
}
return res;
}
ll subtask2() {
auto A = dfs_far(1,-1,0);
auto B = dfs_far(A.first,-1,0);
ll diameter = B.second;
return (diameter+1)/2;
}
// =================== Subtask 3: Path tree (line) ===================
ll subtask3() {
// Tính prefix khoảng cách
vector<ll> prefix(n+1,0);
for (int i=2; i<=n; i++) {
for (auto [v,w]: adj[i]) if (v==i-1) {
prefix[i] = prefix[i-1] + w;
}
}
// binary search đáp án
ll lo=0, hi=prefix[n], ans=hi;
auto check = [&](ll X)->bool {
int used=0;
int pos=1;
while (pos<=n) {
used++;
ll reach = prefix[pos] + 2*X; // cover trong khoảng cách X
int nxt=pos;
while (nxt<=n && prefix[nxt]-prefix[pos]<=2*X) nxt++;
pos=nxt;
if (used>k) return false;
}
return true;
};
while (lo<=hi) {
ll mid=(lo+hi)/2;
if (check(mid)) { ans=mid; hi=mid-1; }
else lo=mid+1;
}
return ans;
}
// =================== Subtask 4: General tree (binary search + greedy) ===================
int usedCenters;
ll limitX;
bool dfs_cover(int u, int p) {
ll maxNeed = -INF;
for (auto [v,w]: adj[u]) if (v!=p) {
if (dfs_cover(v,u)) return true;
}
// giả sử ta check từ lá lên (thực tế cần coding chi tiết hơn),
// ở đây mình viết dạng khung cho sub4.
return false;
}
bool check_general(ll X) {
// TODO: viết DFS greedy chuẩn
// Đếm số trạm cần <= k
return true; // placeholder
}
ll subtask4() {
ll lo=0, hi=1e15, ans=hi;
while (lo<=hi) {
ll mid=(lo+hi)/2;
if (check_general(mid)) { ans=mid; hi=mid-1; }
else lo=mid+1;
}
return ans;
}
// =================== MAIN ===================
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> k;
for (int i=1; i<n; i++) {
int a,b; ll c;
cin >> a >> b >> c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
ll ans=0;
if (n<=20) ans = subtask1();
else if (k==1) ans = subtask2();
else {
bool isPath=true;
for (int i=1; i<=n; i++) {
if (adj[i].size()>2) { isPath=false; break; }
}
if (isPath) ans = subtask3();
else ans = subtask4();
}
cout << ans << "\n";
return 0;
}
