#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
constexpr int M=1e5+5;vector<int>vec;
int n,m,x,y,z,rt[M],siz[M];LL ans;
vector<pair<int,int>>g[M];
namespace Treap{
	mt19937 mt(time(NULL));
	struct Treap{
		int ls,rs,rnd,siz;
		LL val,lazy1,lazy2;
	}tr[M]; int num;
	int new_node(int x){
		tr[++num].val=x;tr[num].siz=1;
		tr[num].rnd=mt();return num;
	}
	void pushup(int x){
		tr[x].siz=tr[tr[x].ls].siz+tr[tr[x].rs].siz+1;
	}
	void addtag(int x,LL k,LL b){
		tr[x].val+=(tr[tr[x].ls].siz+1)*k+b;
		tr[x].lazy1+=k;tr[x].lazy2+=b;
	}
	void pushdown(int x){
		if (tr[x].lazy1||tr[x].lazy2)
			addtag(tr[x].ls,tr[x].lazy1,tr[x].lazy2),
			addtag(tr[x].rs,tr[x].lazy1,tr[x].lazy1*(tr[tr[x].ls].siz+1)+tr[x].lazy2),
			tr[x].lazy1=tr[x].lazy2=0;
	}
	void split(int now,LL k,int &x,int &y){
		if (!now) return x=y=0,void(); pushdown(now);
		if (tr[now].val>k||tr[now].val==k&&mt()&1)
			x=now,split(tr[x].rs,k,tr[x].rs,y);
		else y=now,split(tr[y].ls,k,x,tr[y].ls);
		pushup(now);
	}
	int merge(int x,int y){
		if (!x||!y) return x|y;
		if (tr[x].rnd<tr[y].rnd){
			pushdown(x);
			tr[x].rs=merge(tr[x].rs,y);
			pushup(x); return x;
		}
		pushdown(y);
		tr[y].ls=merge(x,tr[y].ls);
		pushup(y); return y;
	}
	int Merge(int x,int y){
		if (!x||!y) return x|y;
		if (tr[x].rnd>tr[y].rnd) swap(x,y);
		pushdown(x);int a,b;
		split(y,tr[x].val,a,b);
		tr[x].ls=Merge(tr[x].ls,a);
		tr[x].rs=Merge(tr[x].rs,b);
		return pushup(x),x;
	}
	void solve(int x){
		if (!x) return ;
		pushdown(x);
		solve(tr[x].ls);
		vec.push_back(tr[x].val);
		solve(tr[x].rs);
	}
}
int read(){
	int x=0,f=1;char ch=getchar();
	while (!isdigit(ch)) {if (ch=='-') f=-1;ch=getchar();}
	while (isdigit(ch)) x=x*10+ch-48,ch=getchar();
	return x*f;
}
void dfs(int x,int f){
	siz[x]=1;
	rt[x]=Treap::new_node(0);
	for (auto [u,v]:g[x]){
		if (u==f) continue;
		dfs(u,x);siz[x]+=siz[u];
		Treap::addtag(rt[u],-2ll*v,1ll*(m+1)*v);
		rt[x]=Treap::Merge(rt[x],rt[u]);
	}
}
int main(){
	n=read();m=read();
	for (int i=1;i<n;i++){
		x=read();y=read();z=read();
		g[x].push_back({y,z});
		g[y].push_back({x,z});
	}
	dfs(1,0);Treap::solve(rt[1]);
	for (int i=0;i<m;i++)
		ans+=vec[i];
	printf("%lld\n",ans);
	return 0;
}