//（づ￣3￣）づ╭❤️～
// Huwng Lee ~_~
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
#define int long long
#define pl pair <ll, ll>
#define pll pair <pl, ll>
#define pi pair <int, int>
#define pb push_back
#define fi first
#define se second
#define ld long double
#define fti(i, x, y) for(int i = (x), _y = (y); i <= _y; ++ i)
#define ftd(i, x, y) for(int i = (x), _y = (y); i >= _y; -- i)
using namespace std;
typedef long long ll;
const int e = 2e5 + 2;
const ll oo = 1e18;
int n, k;
ll need[e], cover[e];
ll d1[e], d2[e], d[e], tmp;
vector <pi> a[e];
vector <int> ans;
bool park[e];
void lph()
{
freopen("park.inp", "r", stdin);
freopen("park.out", "w", stdout);
}
void inp()
{
cin >> n >> k;
fti(i, 1, n - 1)
{
int u, v, w;
cin >> u >> v >> w;
a[u].pb({v, w});
a[v].pb({u, w});
}
}
void reset(ll d[])
{
fti(i, 1, n)
d[i] = oo;
}
ll bfs(queue <int> &qu, ll d[])
{
while(qu.size())
{
int u = qu.front();
qu.pop();
for(auto [v, w]: a[u])
{
if(d[v] > d[u] + w)
{
d[v] = d[u] + w;
qu.push(v);
}
}
}
ll res = 0;
fti(i, 1, n)
res = max(res, d[i]);
return res;
}
void sub1()
{
int nmask = (1 << n);
ll res = oo;
fti(mask, 0, nmask - 1)
{
if(__builtin_popcount(mask) != k)
continue;
queue <int> qu;
vector <int> tmp;
reset(d);
fti(i, 1, n)
{
if((mask >> i - 1) & 1)
{
d[i] = 0;
qu.push(i);
tmp.pb(i);
}
}
ll mx = bfs(qu, d);
if(mx < res)
{
res = mx;
ans = tmp;
}
}
cout << res << "\n";
for(int u: ans)
cout << u << " ";
}
void dk(int u, int p, ll d[], int &node)
{
for(auto [v, w]: a[u])
{
if(v == p)
continue;
d[v] = d[u] + w;
if(d[v] > tmp)
tmp = d[v], node = v;
dk(v, u, d, node);
}
}
void sub2()
{
int st = 0, en = 0;
d[1] = 0;
dk(1, 0, d, st);
d1[st] = 0;
tmp = 0;
dk(st, 0, d1, en);
d2[en] = 0;
tmp = 0;
dk(en, 0, d2, st);
ll ans = oo, id = 0;
fti(i, 1, n)
{
ll mx = max(d1[i], d2[i]);
if(mx < ans)
ans = mx, id = i;
}
cout << ans << "\n" << id;
}
bool check1(ll x, vector <int> &tmp)
{
int cnt = 0, j = 0;
ll s = 0;
fti(i, 1, n)
{
if(d1[i] - s >= x)
{
++ cnt;
tmp.pb(i);
s = d1[i];
}
if(cnt > k)
return 0;
}
return cnt <= k;
}
void sub3()
{
reset(d);
queue <int> qu;
qu.push(1);
d[1] = 0;
bfs(qu, d1);
while(qu.size()) qu.pop();
d[n] = 1;
qu.push(n);
bfs(qu, d2);
ll l = 0, r = oo, res = 0;
while(l <= r)
{
ll mid = (l + r) >> 1;
vector <int> tmp;
if(check1(mid, tmp))
{
r = mid - 1;
res = mid;
ans = tmp;
}
else
l = mid + 1;
}
cout << res << "\n";
for(int u: ans)
cout << u << " ";
}
void dfs(int u, int p, int &cnt, vector <int> &tmp, ll R)
{
need[u] = 0;
cover[u] = oo;
for(auto [v, w]: a[u])
{
if(v == p)
continue;
dfs(v, u, cnt, tmp, R);
if(need[v] != -1)
{
if(need[v] + w > R)
{
++ cnt;
cover[u] = min(cover[u], 1ll * w);
tmp.pb(v);
park[v] = 1;
}
else
need[u] = max(need[u], need[v] + w);
}
else if(cover[v] != oo)
cover[u] = min(cover[u], cover[v] + w);
}
if(need[u] != -1 && cover[u] != oo && need[u] + cover[u] <= R)
need[u] = -1;
}
bool check(ll R, vector <int> &tmp)
{
fti(i, 1, n)
park[i] = 0;
int cnt = 0;
dfs(1, 0, cnt, tmp, R);
if(need[1] != -1)
{
++ cnt, tmp.pb(1);
park[1] = 1;
}
return cnt <= k;
}
void sub4()
{
ll l = 0, r = oo, res = oo;
while(l <= r)
{
ll mid = (l + r) >> 1;
vector <int> tmp;
if(check(mid, tmp))
{
r = mid - 1, res = mid;
ans = tmp;
}
else
l = mid + 1;
}
cout << res << "\n";
k -= ans.size();
fti(i, 1, n)
if(!park[i] && k)
ans.pb(i), -- k;
for(int u: ans)
cout << u << " ";
}
void proc()
{
// if(n <= 20)
// sub1();
// else if(k == 1)
// sub2();
// else
// sub3();
sub4();
}
main()
{
// lph();
ios_base::sync_with_stdio(0);cin.tie(nullptr);
inp();
proc();
return 0;
}
/*
9 3
1 2 5
1 3 1
3 4 10
3 5 9
5 6 8
2 7 1
2 8 2
8 9 7
*/
