#include<bits/stdc++.h>

#define ll long long
#define pi pair<ll,ll>
#define vi vector<ll>
#define cpy(x,y,s) memcpy(x,y,sizeof(x[0])*(s))
#define mset(x,v,s) memset(x,v,sizeof(x[0])*(s))
#define all(x) begin(x),end(x)
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define ary array
#define eb emplace_back

#define N 500005

using namespace std;
ll read(){
    ll x=0,f=1;char ch=getchar();
    while(ch<'0' || ch>'9')f=(ch=='-'?-1:f),ch=getchar();
    while(ch>='0' && ch<='9')x=(x<<1)+(x<<3)+(ch^48),ch=getchar();
    return x*f;
}
void write(ll x){
    if(x<0)x=-x,putchar('-');
    if(x/10)write(x/10);
    putchar(x%10+'0');
}

mt19937 rnd(20080623);

ll rt[N];
struct tg{
    ll k,b;
    tg(ll k=0,ll b=0):k(k),b(b){}
};

struct fhqtreap{
    ll ls[N<<2],rs[N<<2],pri[N<<2],v[N<<2],siz[N<<2];
    tg tag[N<<2];
    ll tot;
    stack<ll> st;
    ll newnode(ll w){
        ll pos=(st.size()?st.top():++tot);
        if(st.size())st.pop();
        tag[pos].k=tag[pos].b=0;ls[pos]=rs[pos]=0;
        v[pos]=w;pri[pos]=rnd();siz[pos]=1;return pos;
    }
    void ps(ll x,tg T){
        ll num=siz[ls[x]]+1;
        v[x]+=T.k*num+T.b;tag[x].k+=T.k;tag[x].b+=T.b;
    }
    void pd(ll x){
        tg T=tag[x];
        if(ls[x])ps(ls[x],T);
        if(rs[x])ps(rs[x],tg(T.k,T.b+(siz[ls[x]]+1)*T.k));
        tag[x].k=tag[x].b=0;
    }
    void upd(ll x){siz[x]=siz[ls[x]]+siz[rs[x]]+1;}
    ll merge(ll L,ll R){
        if(!L || !R)return L|R;
        pd(L);pd(R);
        if(pri[L]>pri[R]){rs[L]=merge(rs[L],R);upd(L);return L;}
        else {ls[R]=merge(L,ls[R]);upd(R);return R;}
    }
    void split(ll x,ll val,ll &L,ll &R){
        if(!x)return L=0,R=0,void();pd(x);
        if(val>v[x]){R=x;split(ls[x],val,L,ls[x]);upd(x);}
        else {L=x;split(rs[x],val,rs[x],R);upd(x);}
    }
    void insert(ll &p,ll x){
        ll L,R;split(p,v[x],L,R);
        L=merge(L,x);
        p=merge(L,R);
    }
    void flat(ll x,vector<ll> &res){
        pd(x);st.push(x);
        if(ls[x])flat(ls[x],res);
        res.pb(v[x]);
        if(rs[x])flat(rs[x],res);
    }
}T;

ll siz[N],n,k;
vector<pi> e[N];

void dfs(ll x,ll fa){
    siz[x]=1;ll son=0;
    for(auto _:e[x]){
        ll v=_.fi,w=_.se;
        if(v==fa)continue;dfs(v,x);
        if(siz[v]>siz[son])son=v;
        T.ps(rt[v],tg(-2*w,w*(k+1)));
    }
    if(son)rt[x]=rt[son];
    T.insert(rt[x],T.newnode(0));
    for(auto _:e[x]){
        ll v=_.fi,w=_.se;
        if(v==fa || v==son)continue;
        vector<ll> s;
        T.flat(rt[v],s);
        for(auto w:s)T.insert(rt[x],T.newnode(w));
    }
}

int main(){
    #ifdef EAST_CLOUD
    freopen("a.in","r",stdin);
    //freopen("a.out","w",stdout);
    #endif

    n=read(),k=read();
    for(ll i=1;i<n;i++){
        ll u=read(),v=read(),w=read();
        e[u].eb(v,w);e[v].eb(u,w);
    }
    dfs(1,0);
    vector<ll> res;
    T.flat(rt[1],res);
    ll ans=0;
    for(ll i=0;i<k;i++)ans+=res[i];
    write(ans);
    return 0;
}