#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define per(i,a,b) for(int i=a;i>=b;i--)
ll rd() {
	ll now = 0, f = 1;
	char c = getchar();
	while ('0' > c || c > '9') {
		if (c == '-') f = -1;
		c = getchar();
	}
	while ('0' <= c && c <= '9') now = now * 10 + c - 48, c = getchar();
	return now * f;
}
void wr(ll x) {
	if (x < 0) x = -x, putchar('-');
	if (x > 9) wr(x / 10);
	putchar(x % 10 + 48);
	return ;
}
const int N = 3005, inf = 1e9;
struct E {
	int to, nxt, w;
} e[N << 1];
int n, k, sz[N], dp[N][N][3], head[N], cnt;
void add(int x, int y, int z) {
	e[++cnt] = {y, head[x], z};
	head[x] = cnt;
}
void merge(int x, int y, int len) {
	rep(i, sz[x] + 1, sz[x] + sz[y]) dp[x][i][0] = dp[x][i][1] = dp[x][i][2] = inf;
	per(i, sz[x], 1) rep(j, 1, sz[y]) {
		dp[x][i + j][0] = min(dp[x][i + j][0], dp[x][i][0] + dp[y][j][0] + len * 2);
		dp[x][i + j][1] = min(dp[x][i + j][1], dp[x][i][1] + dp[y][j][0] + len * 2);
		dp[x][i + j][1] = min(dp[x][i + j][1], dp[x][i][0] + dp[y][j][1] + len);
		dp[x][i + j][2] = min(dp[x][i + j][2], dp[x][i][2] + dp[y][j][0] + len * 2);
		dp[x][i + j][2] = min(dp[x][i + j][2], dp[x][i][1] + dp[y][j][1] + len);
		dp[x][i + j][2] = min(dp[x][i + j][2], dp[x][i][0] + dp[y][j][2] + len * 2);
	}
	sz[x] += sz[y];
}
void dfs(int x, int fa) {
	sz[x] = 1;
	for (int i = head[x]; i; i = e[i].nxt) {
		int v = e[i].to;
		if (v == fa) continue;
		dfs(v, x);
		merge(x, v, e[i].w);
	}
}
signed main() {
	n = rd(), k = rd();
	rep(i, 2, n) {
		int x = rd(), y = rd(), z = rd();
		add(x, y, z), add(y, x, z);
	}
	dfs(1, 1);
	int ans = inf;
	rep(i, 1, n) if (sz[i] >= k) ans = min(ans, dp[i][k][2]);
	cout << ans;
	return 0;
}