#include <bits/stdc++.h>

using namespace std;

#define ll long long

typedef pair<int, int> P;
#define fi first
#define se second

const int N = 1e5 + 5;

int n, m;
vector<P> G[N];

mt19937 rng(time(0));
struct FHQ
{
	int ls[N], rs[N], siz[N], rnd[N];
	ll val[N], k[N], b[N];
	int cnt, st[N], tp;

	int New(int v)
	{
		int x = tp ? st[tp--] : ++cnt;
		ls[x] = rs[x] = 0, siz[x] = 1, rnd[x] = rng();
		val[x] = v, k[x] = b[x] = 0;
		return x;
	}

	void pushup(int p)
	{
		siz[p] = siz[ls[p]] + siz[rs[p]] + 1;
	}

	void push(int p, ll K, ll B)
	{
		val[p] += K * (siz[ls[p]] + 1) + B;
		k[p] += K, b[p] += B;
	}

	void pushdown(int p)
	{
		if(k[p] || b[p])
		{
			if(ls[p]) push(ls[p], k[p], b[p]);
			if(rs[p]) push(rs[p], k[p], k[p] * (siz[ls[p]] + 1) + b[p]);
			k[p] = b[p] = 0;
		}
		return;
	}

	void Split(int p, int v, int &x, int &y)
	{
		if(!p) return x = y = 0, void();
		pushdown(p);
		if(val[p] >= v) x = p, Split(rs[p], v, rs[x], y);
		else y = p, Split(ls[p], v, x, ls[y]);
		pushup(p);
		return;
	}

	int merge(int x, int y)
	{
		if(!x || !y) return x | y;
		if(rnd[x] < rnd[y])
		{
			pushdown(x);
			rs[x] = merge(rs[x], y);
			return pushup(x), x;
		} else {
			pushdown(y);
			ls[y] = merge(x, ls[y]);
			return pushup(y), y;
		}
	}

	void Insert(int &p, int v)
	{
		int x, y; Split(p, v, x, y);
		p = merge(merge(x, New(v)), y);
		return;
	}

	void Clear(int p, vector<ll> &vec)
	{
		pushdown(p);
		if(ls[p]) Clear(ls[p], vec);
		vec.push_back(val[p]); st[++tp] = p;
		if(rs[p]) Clear(rs[p], vec);
		return;
	}
} T;
int rt[N];

int siz[N];
void dfs(int u, int fa)
{
	int son = 0; siz[u] = 1;
	for(auto p : G[u]) if(p.fi != fa)
	{
		int v = p.fi, w = p.se;
		dfs(v, u); siz[u] += siz[v];
		if(siz[v] > siz[son]) son = v;
		T.push(rt[v], -2 * w, w * (m + 1));
	}
	if(son) rt[u] = rt[son];
	T.Insert(rt[u], 0);
	for(auto p : G[u]) if(p.fi != fa && p.fi != son)
	{
		int v = p.fi; vector<ll> vec;
		T.Clear(rt[v], vec);
		for(auto it : vec) T.Insert(rt[u], it);
	}
	return;
}

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr), cout.tie(nullptr);

	cin >> n >> m;
	for(int i = 1, u, v, w; i < n; i++)
		cin >> u >> v >> w, G[u].push_back({v, w}), G[v].push_back({u, w});
	dfs(1, 0);

	vector<ll> vec;
	T.Clear(rt[1], vec);

	ll ans = 0;
	for(int i = 0; i < m; i++) ans += vec[i];
	cout << ans << '\n';
	return 0;
}