#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
const int maxn=1e5+10;
const ll llinf=0x3f3f3f3f3f3f3f3f;

inline int read(){
    int x=0,w=1;char c=getchar();
    while(c<'0'||c>'9'){x=(x<<3)+(x<<1)+c-'0';c=getchar();}
    while(c<='9'&&c>='0'){x=(x<<3)+(x<<1)+c-'0';c=getchar();}
    return x*w;
}

int n,k;
struct edge{
    int to,nxt,w;
}e[maxn<<1];
int head[maxn],cnt;
inline void add_edge(int u,int v,int w){
    e[++cnt].to=v,e[cnt].nxt=head[u],head[u]=cnt,e[cnt].w=w;
    e[++cnt].to=u,e[cnt].nxt=head[v],head[v]=cnt,e[cnt].w=w;
}

ll ans[maxn];
int p;

struct Splay{
    int tot,Q[maxn<<2],head,tail;
    int fa[maxn<<2],ch[maxn<<2][2];
    int cnt[maxn<<2],siz[maxn<<2];
    ll val[maxn<<2];
    ll tagD[maxn<<2],tagC[maxn<<2];
    Splay(){
        head=1,tail=0;
    }
    inline int new_node(ll k){
        int x;
        if(head<=tail){
            x=Q[head++];
            if(head>tail) head=1,tail=0;
        }
        else x=++tot;
        fa[x]=0,ch[x][0]=ch[x][1]=0,cnt[x]=1,siz[x]=1,val[x]=k,tagD[x]=0,tagC[x]=0;
        if(k==llinf||k==-llinf) cnt[x]=0,siz[x]=0;
        return x;
    }
    inline void push_up(int x){
        siz[x]=siz[ch[x][0]]+siz[ch[x][1]]+cnt[x];
    }
    inline void push_tag(int x,int D,int C){
        if(cnt[x]) val[x]+=1ll*D*siz[ch[x][0]]+C;
        tagD[x]+=D,tagC[x]+=C;
    }
    inline void push_down(int x){
        if(tagD[x]){
            if(ch[x][0]) push_tag(ch[x][0],tagD[x],tagC[x]);
            if(ch[x][1]) push_tag(ch[x][1],tagD[x],1ll*(siz[ch[x][0]]+cnt[x])*tagD[x]+tagC[x]);
            tagD[x]=0,tagC[x]=0;
        }
    }
    inline int build(){
        int x=new_node(0),y=new_node(llinf),z=new_node(-llinf);
        fa[y]=x,ch[x][0]=y,fa[z]=x,ch[x][1]=z;
        push_up(x);
        return x;
    }
    inline bool chkson(int x){
        return ch[fa[x]][1]==x;
    }
    inline void rotate(int x){
        int y=fa[x],z=fa[y];
        bool chk=chkson(x);
        if(z) ch[z][chkson(y)]=x;
        fa[x]=z;
        ch[y][chk]=ch[x][chk^1],fa[ch[x][chk^1]]=y;                                                                                                                                
        ch[x][chk^1]=y,fa[y]=x;
        push_up(y),push_up(x);
    }
    inline void splay(int &rt,int x,int goal=0){
        while(fa[x]!=goal){
            int y=fa[x],z=fa[y];
            if(z!=goal) rotate(chkson(x)==chkson(y)?y:x);
            rotate(x);
        }
        if(!goal) rt=x;
    }
    inline void insert(int &rt,ll k){
        // cerr<<k<<endl;
        int x=rt;
        while(1){
            push_down(x);
            if(k>=val[x]){
                if(ch[x][0]) x=ch[x][0];
                else{
                    int y=new_node(k);
                    fa[y]=x,ch[x][0]=y;
                    splay(rt,y);
                    // output1(rt);
                    // cerr<<endl;
                    return;
                }
            }
            else{
                if(ch[x][1]) x=ch[x][1];
                else{
                    int y=new_node(k);
                    fa[y]=x,ch[x][1]=y;
                    splay(rt,y);
                    // output1(rt);
                    // cerr<<endl;
                    return;
                }
            }
        }
    }
    inline void erase(int x){
        Q[++tail]=x;
        fa[x]=0,ch[x][0]=ch[x][1]=0,val[x]=0,tagD[x]=0,tagC[x]=0;
    }
    void merge(int &rt,int x){
        // cerr<<"x:"<<x<<" val:"<<val[x]<<endl;
        push_down(x);
        if(ch[x][0]) merge(rt,ch[x][0]);
        if(cnt[x]) insert(rt,val[x]);
        if(ch[x][1]) merge(rt,ch[x][1]);
        erase(x);
    }
    void dfs(int x){
        push_down(x);
        if(ch[x][0]) dfs(ch[x][0]);
        if(cnt[x]) ans[++p]=val[x];
        if(ch[x][1]) dfs(ch[x][1]);
    }
    void output1(int x){
        push_down(x);
        if(ch[x][0]) output1(ch[x][0]);
        cerr<<val[x]<<" ";
        if(ch[x][1]) output1(ch[x][1]);
    }
}S;

int siz[maxn],son[maxn];
int rt[maxn];
void dfs1(int u,int fa){
    siz[u]=1;
    int maxson=-1;
    for(int i=head[u],v;i;i=e[i].nxt){
        v=e[i].to;
        if(v==fa) continue;
        dfs1(v,u);
        siz[u]+=siz[v];
        if(siz[v]>maxson) son[u]=v,maxson=siz[v];
    }
}
void dfs2(int u,int fa){
    rt[u]=S.build();
    // cerr<<"u:"<<u<<endl;
    // S.output1(rt[u]);
    // cerr<<endl;
    if(!son[u]) return;
    int tmp;
    for(int i=head[u],v,w;i;i=e[i].nxt){
        v=e[i].to,w=e[i].w;
        if(v==son[u]) tmp=w;
    }
    dfs2(son[u],u);
    // cerr<<"u:"<<u<<" son:"<<son[u]<<endl;
    S.push_tag(rt[son[u]],-2ll*tmp,1ll*tmp*(k-1));
    // cerr<<"D:"<<-2ll*tmp<<" C:"<<1ll*tmp*(k-1)<<endl;
    // cerr<<"son:"<<son[u]<<endl;
    S.merge(rt[son[u]],rt[u]);
    rt[u]=rt[son[u]];
    // S.output1(rt[u]);
    // cerr<<endl;
    for(int i=head[u],v,w;i;i=e[i].nxt){
        v=e[i].to,w=e[i].w;
        if(v==fa||v==son[u]) continue;
        dfs2(v,u);
        S.push_tag(rt[v],-2ll*w,1ll*w*(k-1));
        S.merge(rt[u],rt[v]);
        // cerr<<"u:"<<u<<" v:"<<v<<endl;
        // S.output1(rt[u]);
        // cerr<<endl;
    }
    // cerr<<"u:"<<u<<endl;
    // S.output1(rt[u]);
    // cerr<<endl;
}

int main(){
    // freopen("h.in","r",stdin);
    n=read(),k=read();
    for(int i=1,u,v,w;i<n;++i){
        u=read(),v=read(),w=read();
        add_edge(u,v,w);
    }
    dfs1(1,0);
    dfs2(1,0);
    S.dfs(rt[1]);
    // for(int i=1;i<=n;++i) cerr<<ans[i]<<" ";
    // cerr<<endl;
    for(int i=1;i<=k;++i) ans[i]+=ans[i-1];
    printf("%lld\n",ans[k]);
    return 0;
}


/*
f(u,i+j) <-- f(u,i) + f(v,j) + w(u,v)*j*(k-j) 

w(u,v)[j(k-j)-(j-1)(k-j+1)]

g(x)=x(k-x) \Delta g(x)=(xk-x^2)-(xk-x^2+x-k+x-1)=-2x+(k+1)

\Delta g(1)=k-1 \Delta^2 g(x)=-2

a_1=w(u,v)(k-1),d=-2w(u,v)
*/