// Code by Heratino & Nelofus
// ???????????
// ???????????

#include <bits/stdc++.h>
using i64 = long long;

//{{{
template<typename Ta, typename Tb>
inline void chkmax(Ta &a, const Tb &b) {if (a < b)	a = b;}
template<typename Ta, typename Tb>
inline void chkmin(Ta &a, const Tb &b) {if (a > b)	a = b;}
//}}}

constexpr int N = 3e5 + 10;
std::vector<std::array<int, 2>> G[N];
int n, k;

std::array<std::array<i64, 2>, 3> f[N];

std::array<i64, 2> operator + (std::array<i64, 2> a, i64 val) {return {a[0] + val, a[1]};}
std::array<i64, 2> operator + (std::array<i64, 2> a, std::array<i64, 2> b) {return {a[0] + b[0], a[1] + b[1]};}
inline void chkmax(std::array<i64, 2> &a, const std::array<i64, 2> &b) {
	if (a[0] < b[0])
		a = b;
	else if (a[0] == b[0] && a[1] > b[1])
		a = b;
}

void dfs(int u, int fa, i64 slope) {
	f[u][0] = f[u][1] = f[u][2] = {0, 0};
	for (const auto &[v, w] : G[u]) {
		if (v == fa)
			continue;
		dfs(v, u, slope);
		chkmax(f[u][2], f[u][2] + f[v][0]);
		chkmax(f[u][2], f[u][1] + f[v][1] + (std::array<i64, 2>){w + slope, 1});
		chkmax(f[u][1], f[u][1] + f[v][0]);
		chkmax(f[u][1], f[u][0] + f[v][1] + w);
		f[u][0] = f[u][0] + f[v][0];
	}
	chkmax(f[u][0], f[u][1] + (std::array<i64, 2>){slope, 1});
	chkmax(f[u][0], f[u][2]);
}

bool check(i64 x) {
	dfs(1, 0, x);
	return f[1][0][1] <= k;
}

int main() {
#ifdef HeratinoNelofus
	freopen("input.txt", "r", stdin);
#endif
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);

	std::cin >> n >> k;
	k++;
	for (int i = 1; i < n; i++) {
		int u, v, w;
		std::cin >> u >> v >> w;
		G[u].push_back({v, w});
		G[v].push_back({u, w});
	}
	i64 l = -1e9 - 10, r = 1e9 + 10;
	while (l < r) {
		i64 mid = l + r >> 1;
		if (check(mid))
			l = mid + 1;
		else
			r = mid;
	}
	i64 slope = l - 1;
	check(slope);
	std::cout << f[1][0][0] - k * slope << '\n';
	return 0;
}