#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pii pair<int,int>
#define x first
#define y second
mt19937 rnd(time(0));
inline int read(){
	int x=0;bool f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=0;ch=getchar();}
	while(ch>='0'&&ch<='9')x=(x<<1)+(x<<3)+ch-'0',ch=getchar();
    if(f)return x;return ~(x-1);
}
int n,k,tot;
vector<pii> g[100005];
int rt[100005];
struct{
	int l,r,val,sz;
	ll key,a,d;
}t[3000005];
int newn(ll v){
	t[++tot]={0,0,rnd(),1,v,0,0};
	return tot;
}
void pushup(int p){t[p].sz=t[t[p].l].sz+t[t[p].r].sz+1;}
void mdf(int p,ll a,ll d){
	if(!p)return;
	t[p].key+=a+d*t[t[p].r].sz;
	t[p].a+=a,t[p].d+=d;
}
void pushdown(int p){
	if(!t[p].a&&!t[p].d)return;
	mdf(t[p].l,t[p].a+(1+t[t[p].r].sz)*t[p].d,t[p].d),mdf(t[p].r,t[p].a,t[p].d);
	t[p].a=t[p].d=0;
}
void split(int p,int key,int &x,int &y){
	if(!p){
		x=y=0;return;
	}
	pushdown(p);
	if(t[p].key<=key)x=p,split(t[p].r,key,t[p].r,y);
	else y=p,split(t[p].l,key,x,t[p].l);
	pushup(p);
}
int merge(int x,int y){
    if(!x||!y)return x|y;
    pushdown(x),pushdown(y);
    if(t[x].val>t[y].val){t[x].r=merge(t[x].r,y),pushup(x);return x;}
    else{t[y].l=merge(x,t[y].l),pushup(y);return y;}
}
void ins(int p,ll v){
	int nw=newn(v),x,y;
	split(rt[p],v,x,y);
	x=merge(x,merge(nw,y));
	rt[p]=x;
}
void dfs(int x,int y){
	if(!x)return;
	ins(y,t[x].key);
	pushdown(x);
	dfs(t[x].l,y),dfs(t[x].r,y);
}
void calc(int x,int fa){
	rt[x]=newn(0);
	for(auto i:g[x])if(i.x!=fa){
		calc(i.x,x);
		mdf(rt[i.x],1ll*(k-1)*i.y,-2ll*i.y);
		int a=rt[x],b=rt[i.x];
		if(t[a].sz<t[b].sz)swap(a,b);
		rt[x]=a,dfs(b,x);
	}
}
int rk;
ll ans=0;
void find(int x){
	if(!x)return;
	pushdown(x);
	find(t[x].r),++rk;
	if(rk<=k)ans+=t[x].key;
	find(t[x].l);
}
int main(){
	n=read(),k=read();
	for(int i=1;i<n;i++){
		int x=read(),y=read(),z=read();
		g[x].push_back({y,z}),g[y].push_back({x,z});
	}
	calc(1,0);
	find(rt[1]);
	cout<<ans;
}