#include<bits/stdc++.h>
#define re register
typedef long long ll;
typedef unsigned long long ull;
template<class T>
inline void read(T &x)
{
	x=0;
	char ch=getchar(),t=0;
	while(ch<'0'||ch>'9') t|=ch=='-',ch=getchar();
	while(ch>='0'&&ch<='9') x=(x<<3)+(x<<1)+(ch^48),ch=getchar();
	if(t) x=-x;
}
template<class T,class ...Arc>
inline void read(T &x,Arc &...arc){ read(x),read(arc...); }
template<class T>
inline void write(T x)
{
	if(x<0) putchar('-'),x=-x;
	if(x>9) write(x/10);
	putchar(x%10+48);
}
inline void write(char c){ putchar(c); }
inline void write(bool x){ putchar(x?'1':'0'); }
inline void write(char *s){ while(*s!='\0') putchar(*s++); }
inline void write(const char *s){ while(*s!='\0') putchar(*s++); }
template<class T,class ...Arc>
inline void write(T x,Arc ...arc){ write(x),write(arc...); }
template<class T>
inline bool checkMax(T &x,T y){ return x<y?x=y,1:0; }
template<class T>
inline bool checkMin(T &x,T y){ return x>y?x=y,1:0; }
using Pir=std::pair<int,int>;
#define fir first
#define sec second
#define Mkr std::make_pair
const int MAXN=2e5+10;
int N,K;
std::vector<Pir>Edges[MAXN];
std::mt19937 rnd(time(NULL));
struct FHQ
{
	#define ls(p) Tr[p].lc
	#define rs(p) Tr[p].rc
	struct Treap
	{
		int lc,rc,siz,rd;
		ll val,k,b;
	}Tr[MAXN<<4];
	int Idx;
	std::stack<int>Pool;
	inline int newNode(ll v)
	{
		int p=Pool.empty()?++Idx:Pool.top();
		if(!Pool.empty()) Pool.pop();
		Tr[p].k=Tr[p].b=Tr[p].lc=Tr[p].rc=0;
		Tr[p].val=v,Tr[p].siz=1,Tr[p].rd=rnd();
		return p;
	}
	inline void pushUp(int p)
	{ Tr[p].siz=Tr[ls(p)].siz+Tr[rs(p)].siz+1; }
	inline void upDate(int p,ll k,ll b)
	{
		Tr[p].val+=k*(Tr[ls(p)].siz+1)+b;
		Tr[p].k+=k,Tr[p].b+=b;
	}
	inline void pushDown(int p)
	{
		if(Tr[p].k||Tr[p].b)
		{
			if(Tr[p].lc) upDate(ls(p),Tr[p].k,Tr[p].b);
			if(Tr[p].rc) upDate(rs(p),Tr[p].k,Tr[p].k*(Tr[ls(p)].siz+1)+Tr[p].b);
			Tr[p].k=Tr[p].b=0;
		}
	}
	void split(int p,ll val,int &u,int &v)
	{
		if(!p) u=v=0;
		else
		{
			pushDown(p);
			if(Tr[p].val<val) v=p,split(ls(p),val,u,ls(p));
			else u=p,split(rs(p),val,rs(p),v);
			return pushUp(p);
		}
	}
	int merge(int u,int v)
	{
		if(!u||!v) return u^v;
		pushDown(u),pushDown(v);
		if(Tr[u].rd<Tr[v].rd)
		{
			rs(u)=merge(rs(u),v);
			return pushUp(u),u;
		}
		else
		{
			ls(v)=merge(u,ls(v));
			return pushUp(v),v;
		}
	}
	inline void insert(int &p,ll v)
	{
		int x=0,y=0;
		split(p,v,x,y);
		p=merge(merge(x,newNode(v)),y);
	}
	void flatten(int p,std::vector<ll>&vec)
	{
		Pool.push(p);pushDown(p);
		if(Tr[p].lc) flatten(ls(p),vec);
		vec.push_back(Tr[p].val);
		if(Tr[p].rc) flatten(rs(p),vec);
	}
	#undef ls
	#undef rs
}Tr;
int Rt[MAXN],Siz[MAXN];
void dfsTree(int x,int last)
{
	Siz[x]=1;
	int s=0;
	for(auto e:Edges[x])
	{
		int v=e.fir,vl=e.sec;
		if(v==last) continue;
		dfsTree(v,x);
		Tr.upDate(Rt[v],-2ll*vl,1ll*vl*(K+1));
		Siz[x]+=Siz[v];
		if(Siz[v]>Siz[s]) s=v;
	}
	if(s) Rt[x]=Rt[s];
	Tr.insert(Rt[x],0);
	for(auto e:Edges[x])
	{
		int v=e.fir;
		if(v==last||v==s) continue;
		std::vector<ll>vec;
		Tr.flatten(Rt[v],vec);
		for(ll val:vec) Tr.insert(Rt[x],val);
	}
}
int main()
{
	// freopen("memory.in","r",stdin); 	
	// freopen("memory.out","w",stdout);
	read(N,K);
	for(int i=2,u,v,w;i<=N;++i)
	{
		read(u,v,w);
		Edges[u].push_back(Mkr(v,w));
		Edges[v].push_back(Mkr(u,w));
	}
	dfsTree(1,0);
	ll ans=0;
	std::vector<ll>vec;
	Tr.flatten(Rt[1],vec);
	for(int i=0;i<K;++i) ans+=vec[i];
	write(ans*2);
	return 0;
}
/*

*/