#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=4e5+5,M=N*30+5,K=1000+5,mod=998244353,Mod=mod-1;const db eps=1e-9;const int INF=1e9+7;mt19937 rnd(263082);
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
	Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
	Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
}using namespace Debug;
int n,k,rt[N];vector<pii> S[N];
ll ans;
namespace fhq{
	int l[N],r[N],siz[N],rd[N],cnt;ll val[N],t1[N],t2[N];
	void up(int v){siz[v]=siz[l[v]]+siz[r[v]]+1;}
	int newn(){rd[++cnt]=rnd();siz[cnt]=1;return cnt;}
	void Pg(int v,ll w1,ll w2){
		if(!v) return;
		t1[v]+=w1;t2[v]+=w2;
		val[v]+=t1[v]+t2[v]*siz[l[v]];
	}
	void P(int v){
		if(t1[v]||t2[v]) Pg(l[v],t1[v],t2[v]),Pg(r[v],t1[v]+(siz[l[v]]+1)*t2[v],t2[v]),t1[v]=t2[v]=0;
	}
	void split(ll x,int v,int &a,int &b){
		if(!v){a=b=0;return;}P(v);
		if(val[v]>=x) a=v,split(x,r[v],r[a],b);
		else b=v,split(x,l[v],a,l[v]);
		up(v);
	}
	int merge(int x,int y){
		if(!x||!y) return x|y;P(x);P(y);
		if(rd[x]>rd[y]) swap(x,y);
		int r1,r2;split(val[x],y,r1,r2);
		l[x]=merge(l[x],r1);r[x]=merge(r[x],r2);up(x);
		return x;
	}
	void print(int x){
		if(!x) return;P(x);
		print(l[x]);/*gdb(val[x]);*/if(k) k--,ans+=val[x];print(r[x]);
	}
}
void dfs(int x,int La){
	rt[x]=fhq::newn();
	for(auto i:S[x]) if(i.fi^La){
		dfs(i.fi,x);
		fhq::Pg(rt[i.fi],1ll*i.se*(k-1),-2*i.se);
		rt[x]=fhq::merge(rt[x],rt[i.fi]);
	}
}
void Solve(){
	int i,j;scanf("%d%d",&n,&k);
	for(i=1;i<n;i++){
		int x,y,z;scanf("%d%d%d",&x,&y,&z);
		S[x].emplace_back(y,z);S[y].emplace_back(x,z);
	}
	dfs(1,0);fhq::print(rt[1]);
	printf("%lld\n",ans);
}
int main(){
	int t=1;
	// scanf("%d",&t);
	while(t--) Solve();
	cerr<<clock()*1.0/CLOCKS_PER_SEC<<'\n';
}