#include<bits/stdc++.h>
using namespace std;
const int N=1e5+10;
int n,k;
vector<pair<int,int>>to[N];
int TT,rt[N],stk[N*4],top;
int fa[N*4],son[N*4][2],sz[N*4],w[N*4];
long long val[N*4],tD[N*4],tC[N*4];
inline int NEW(long long x)
{
    int p;if(top)p=stk[top--];else p=++TT;
    fa[p]=son[p][0]=son[p][1]=tD[p]=tC[p]=0,
    w[p]=sz[p]=1,val[p]=x;return p;
}
inline void pu(int p){sz[p]=sz[son[p][0]]+sz[son[p][1]]+w[p];}
inline void TG(int p,long long D,long long C){if(!p)return;val[p]+=C+1ll*D*sz[son[p][0]];tD[p]+=D,tC[p]+=C;}
inline void PD(int p){if(tD[p]&&tC[p])TG(son[p][0],tD[p],tC[p]),TG(son[p][1],tD[p],(sz[son[p][0]]+w[p])*tD[p]+tC[p]),tD[p]=tC[p]=0;}
inline bool gc(int p){return son[fa[p]][1]==p;}
void check(int p,int o=0)
{
    if(!o)cerr<<"CHECK: "<<p<<endl;
    if(!p)return;
    assert(!son[p][0]||fa[son[p][0]]==p);
    assert(!son[p][1]||fa[son[p][1]]==p);
    assert(!son[0][0]&&!son[0][1]);
    check(son[p][0],1),check(son[p][1],1);
}
inline void ro(int p)
{
    int f=fa[p],gf=fa[f],o=gc(p);
    if(gf)son[gf][gc(f)]=p;fa[p]=gf;
    fa[son[f][o]=son[p][!o]]=f;
    fa[son[p][!o]=f]=p;
    pu(f),pu(p);
}
inline void splay(int&RT,int p,int goal=0)
{
    #ifdef DOQ
    cerr<<"SPALY: "<<RT<<" "<<p<<"\n";
    check(RT);
    #endif
    while(fa[p]!=goal)
    {
        int f=fa[p],gf=fa[f];
        if(gf!=goal)ro(gc(p)!=gc(f)?f:p);
        ro(p);
    }
    if(!goal)RT=p;
    #ifdef DOQ
    cerr<<"ED\n";
    #endif
}
inline void ins(int&RT,long long va)
{
    #ifdef DOQ
    cerr<<"INS: "<<RT<<" "<<va<<endl;
    check(RT);
    #endif
    if(!RT){RT=NEW(va);return;}
    int p=RT;
    while(1)
    {
        PD(p);int o=va<val[p];
        // cerr<<p<<" "<<va<<" "<<val[p]<<" "<<o<<" "<<son[p][o]<<endl;
        if(son[p][o])p=son[p][o];
        else
        {
            int x=NEW(va);
            fa[son[p][o]=x]=p;
            return splay(RT,p);
        }
    }
}
inline void del(int p){stk[++top]=p;}
void merge(int&A,int B)
{
    #ifdef DOQ
    cerr<<"merge: "<<A<<" "<<B<<endl;
    #endif
    if(!B)return;PD(B);
    merge(A,son[B][0]);
    ins(A,val[B]);
    merge(A,son[B][1]);
    del(B);
}
int s[N],so[N],W[N];
void dfs(int u,int f)
{
    s[u]=1;
    for(auto k:to[u])
    {
        int v=k.first;if(v==f)continue;
        dfs(v,u),s[u]+=s[v];
        if(s[so[u]]<s[v])so[u]=v,W[u]=k.second;
    }
}
void dfs1(int u,int f)
{
    #ifdef DOQ
    cerr<<"DFS1: "<<u<<" "<<f<<endl;
    #endif
    rt[u]=NEW(0);
    if(!so[u])return;
    dfs1(so[u],u);long long w=W[u];
    TG(rt[so[u]],-2ll*w,1ll*w*(k-1));
    merge(rt[u],rt[so[u]]);
    for(auto o:to[u])
    {
        int v=o.first;if(v==f||v==so[u])continue;
        dfs1(v,u);w=o.second;
        #ifdef DOQ
        cerr<<"_MERGE: "<<u<<" "<<v<<endl;
        #endif
        TG(rt[v],-2ll*w,1ll*w*(k-1));
        #ifdef DOQ
        check(rt[u]);check(rt[v]);
        #endif
        merge(rt[u],rt[v]);
        #ifdef DOQ
        cerr<<"ED\n";
        #endif
    }
}
long long ans[N];
int tt;
void pia(int p)
{
    if(!p)return;pia(son[p][0]);
    ans[++tt]=val[p];pia(son[p][1]);
}
int main()
{
    cin.tie(0)->sync_with_stdio(0);
    cin>>n>>k;
    for(int i=1,u,v,w;i<n;++i)
    {
        cin>>u>>v>>w;
        to[u].emplace_back(v,w);
        to[v].emplace_back(u,w);
    }
    dfs(1,0);dfs1(1,0);pia(rt[1]);
    for(int i=1;i<=k;++i)ans[i]+=ans[i-1];
    cout<<ans[k]<<"\n";
    return 0;
}