#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
#include <vector>
#define rr register
#define nn 50010
using namespace std;
int read() {
    int re = 0, sig = 1;
    char c = getchar();

    while (c < '0' || c > '9') {
        if (c == '-')
            sig = -1;

        c = getchar();
    }

    while (c >= '0' && c <= '9') {
        re = (re << 1) + (re << 3) + c - '0';
        c = getchar();
    }

    return re * sig;
}

struct node {
    int to, len, nxt;
} ed[nn * 2];
int head[nn];
void addedge(int u, int v, int len) {
    static int top = 1;
    ed[top].len = len, ed[top].to = v;
    ed[top].nxt = head[u], head[u] = top;
    top++;
    ed[top].len = len, ed[top].to = u;
    ed[top].nxt = head[v], head[v] = top;
    top++;
}

int n, m;
int lensum = 0;
bool vis[nn];
int f[nn];
int cnt;

void work1() {
    int k, maxn;
    int dis[nn];
    queue <int> q;
    memset(dis, -1, sizeof(dis));
    dis[1] = 0, q.push(1);

    while (!q.empty()) {
        k = q.front(), q.pop();

        for (int i = head[k] ; i ; i = ed[i].nxt) {
            if (dis[ed[i].to] == -1) {
                dis[ed[i].to] = dis[k] + ed[i].len;
                q.push(ed[i].to);
            }
        }
    }

    maxn = 0;

    for (int i = 1 ; i <= n ; i++)
        if (dis[i] > maxn)
            maxn = dis[i], k = i;


    memset(dis, -1, sizeof(dis));
    dis[k] = 0, q.push(k);

    while (!q.empty()) {
        k = q.front(), q.pop();

        for (int i = head[k] ; i ; i = ed[i].nxt) {
            if (dis[ed[i].to] == -1) {
                dis[ed[i].to] = dis[k] + ed[i].len;
                q.push(ed[i].to);
            }
        }
    }

    maxn = 0;

    for (int i = 1 ; i <= n ; i++)
        if (dis[i] > maxn)
            maxn = dis[i];

    printf("%d", maxn);
}

int tmp[nn], siz = 0;
bool cmp(int a, int b) {
    return a > b;
}
void dfs(rr int x, rr int maxn) {
    /*
        vis[x] = true;
        vector <int> tmp;
        for(int i = head[x] ; i ; i = ed[i].nxt)
            if(!vis[ed[i].to]){
                dfs(ed[i].to , maxn);
                if(f[ed[i].to] + ed[i].len >= maxn) cnt++;
                else tmp.push_back(f[ed[i].to] + ed[i].len);
            }
        int nowcnt = 0;
        if(tmp.empty())return;
        sort(tmp.begin() , tmp.end() , cmp);
        int i = 0 , j = tmp.size() - 1;
        for( ; i < j ; i++){
            while(tmp[i] + tmp[j] < maxn)
                j--;
            if(i >= j)
                break;
            cnt++;  nowcnt++;
            j--;
        }
        f[x] = 0;
        int l = 0 , r = tmp.size() - 1;
        int mid , res;
        while(l <= r){
            mid = (l + r) / 2;
            rr int cntt = 0;
            rr int i = 1 , j = siz;
            for( ; i < j ; i++){
                if(i == mid)continue;
                while(tmp[i] + tmp[j] < maxn || j == mid)
                    j--;
                if(i >= j)
                    break;
                cntt++;
                j--;
            }
            if(nowcnt == cntt)  r = mid - 1 , res = mid;
            else l = mid + 1;
        }
        f[x] = tmp[res];
    //  printf("%d\n" , tmp.size());
        return;
        /*/
    vis[x] = true;

    for (rr int i = head[x] ; i ; i = ed[i].nxt)
        if (!vis[ed[i].to]) {
            dfs(ed[i].to, maxn);
        }

    siz = 0;

    for (rr int i = head[x] ; i ; i = ed[i].nxt)
        if (!vis[ed[i].to]) {
            if (f[ed[i].to] + ed[i].len >= maxn)
                cnt++;
            else
                tmp[++siz] = f[ed[i].to] + ed[i].len;
        }

    //  if(siz == 0)return;
    sort(tmp + 1, tmp + siz + 1, cmp);

    int nowcnt = 0;

    for (rr int i = 1, j = siz ; i < j ; ++i) {
        while (tmp[i] + tmp[j] < maxn)
            --j;

        if (i >= j)
            break;

        ++nowcnt;
        --j;
    }

    f[x] = 0;

    rr int l = 1, r = siz;
    rr int mid;
    rr int res = 0;

    while (l <= r) {
        mid = (l + r) / 2;

        rr int cntt = 0;
        rr int i = 1, j = siz;

        for (; i < j ; i++) {
            if (i == mid)
                continue;

            while (tmp[i] + tmp[j] < maxn || j == mid)
                --j;

            if (i >= j)
                break;

            ++cntt;
            --j;
        }

        if (nowcnt == cntt)
            r = mid - 1, res = mid;
        else
            l = mid + 1;
    }

    cnt += nowcnt;
    f[x] = tmp[res];
    vis[x] = false;
    //*/
    /*  cout << x << ":\n";
        for(int i = 1 ; i <= siz ; i ++)
            cout << tmp[i] << '\t';
        cout << endl;*/
}
bool check(int maxn) {
    memset(f, 0, sizeof(f));
    memset(vis, 0, sizeof(vis));
    cnt = 0;
    dfs(1, maxn);
    return cnt >= m;
}

int main() {
    bool ty1, ty2;
    ty1 = ty2 = true;
    n = read();
    m = read();

    for (int i = 1 ; i < n ; i++) {
        int u, v, len;
        u = read(), v = read(), len = read();
        lensum += len;
        addedge(u, v, len);
    }

    if (m == 1) {
        work1();
        return 0;
    }

    rr int l = 1, r = lensum;
    r /= m;

    while (l < r) {
        int mid = (l + r) / 2;

        if ((l + r) & 1)
            mid++;

        if (check(mid))
            l = mid;
        else
            r = mid - 1;
    }

    printf("%d", l);
    return 0;
}