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

#define QwQ330AwA return 0
#define ll long long

const int N = 3005 + 5;
int n, k;
vector < pair <int, int> > e[N];
ll f[N][N][4], g[N][4];
int siz[N];

void ckmin(ll &u, ll v) {
	u = min(u, v);
}

ll merge(ll u, ll v, ll a) {
	return u + v + a;
}

void dfs(int u, int fa) {
	for (int i = 0; i <= n; i++) {
		for (int op = 0; op < 4; op++) f[u][i][op] = 1e18;
	}
	f[u][0][0] = 0;
	f[u][1][1] = 0;
	f[u][1][2] = 0;
	siz[u] = 1;
	for (auto qwq : e[u]) {
		int v = qwq.first, w = qwq.second;
		if (v == fa) continue;
		dfs(v, u);
		for (int i = 0; i <= siz[u] + siz[v]; i++) {
			for (int j = 0; j < 4; j++) {
				g[i][j] = 1e18;
			}
		}
		for (int i = 0; i <= siz[u]; i++) {
			for (int j = 0; j <= siz[v]; j++) {
				ckmin(g[i + j][0], merge(f[u][i][0], f[v][j][0], 0));
				ckmin(g[i + j][1], merge(f[u][i][1], f[v][j][0], 0));
				ckmin(g[i + j][1], merge(f[u][i][0], f[v][j][1], 2 * w));
				ckmin(g[i + j][1], merge(f[u][i][1], f[v][j][1], 2 * w));
				ckmin(g[i + j][2], merge(f[u][i][0], f[v][j][2], w));
				ckmin(g[i + j][2], merge(f[u][i][1], f[v][j][2], w));	
				ckmin(g[i + j][2], merge(f[u][i][2], f[v][j][1], 2 * w));
				ckmin(g[i + j][2], merge(f[u][i][2], f[v][j][0], 0));
				ckmin(g[i + j][3], merge(f[u][i][2], f[v][j][2], w));
				ckmin(g[i + j][3], merge(f[u][i][3], f[v][j][0], 0));
				ckmin(g[i + j][3], merge(f[u][i][3], f[v][j][1], 2 * w));
				ckmin(g[i + j][3], merge(f[u][i][0], f[v][j][3], 2 * w));
				ckmin(g[i + j][3], merge(f[u][i][1], f[v][j][3], 2 * w));				
			}
		}
		siz[u] += siz[v];
		for (int i = 0; i <= siz[u]; i++) {
			for (int j = 0; j< 4; j++) f[u][i][j] = g[i][j];
		}
	}
}
signed main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n >> k;
	for (int i = 1, u, v, w; i < n; i++) {
		cin >> u >> v >> w;
		e[u].push_back({v, w});
		e[v].push_back({u, w});
	}
	dfs(1, 0);
	ll ans = 1e18;
	for (int i = 1; i <= n; i++) ans = min(ans, f[i][k][3]);
	cout << ans;
	QwQ330AwA;
}