#include<time.h>
#include<random>
#include<cstdio>
#define MAX 100005
#define max(a,b) (a>b?a:b)
#define min(a,b) (a<b?a:b)
typedef long long ll;
using namespace std;
mt19937 rnd(time(0));

namespace Treap{
    int tot,pos[MAX],siz[MAX];
    int son[MAX][2];
    ll v[MAX],tag1[MAX],tag2[MAX];
    void down(int x)
    {
        if(!tag1[x]&&!tag2[x])return;
        v[x]+=tag2[x]+tag1[x]*siz[son[x][0]];
        if(son[x][0])
        {
            tag1[son[x][0]]+=tag1[x];
            tag2[son[x][0]]+=tag2[x];
        }
        if(son[x][1])
        {
            tag1[son[x][1]]+=tag1[x];
            tag2[son[x][1]]+=tag2[x]+tag1[x]*(siz[son[x][0]]+1);
        }
        tag1[x]=tag2[x]=0;
    }
    void pus(int x)
    {
        siz[x]=siz[son[x][0]]+siz[son[x][1]]+1;
    }
    int build(int x)
    {
        v[++tot]=x,siz[tot]=1,pos[tot]=rnd();
        return tot;
    }
    int merge(int x,int y)
    {
        if(!x||!y)return x|y;
        down(x);down(y);
        if(pos[x]<pos[y])
        {
            son[x][1]=merge(son[x][1],y);
            pus(x);
            return x;
        }
        son[y][0]=merge(x,son[y][0]);
        pus(y);
        return y;
    }
    void split(int i,ll k,int&x,int&y)
    {
        if(!i)
        {
            x=y=0;
            return;
        }
        down(i);
        if(v[i]>=k)
        x=i,split(son[i][1],k-siz[son[i][0]]-1,son[i][1],y);
        else
        y=i,split(son[i][0],k,x,son[i][0]);
        pus(i);
    }
    void split1(int i,int k,int&x,int&y)
    {
        if(!i)
        {
            x=y=0;
            return;
        }
        down(i);
        if(siz[son[i][0]]<k)
        x=i,split(son[i][1],k-siz[son[i][0]]-1,son[i][1],y);
        else
        y=i,split(son[i][0],k,x,son[i][0]);
        pus(i);
    }
    void add(int&rt,ll x)
    {
        int a,b=build(x),c;
        split(rt,x,a,c);
        rt=merge(a,merge(b,c));
    }
    void add1(int&rt,int x)
    {
        int a,c;
        split(rt,v[x],a,c);
        rt=merge(a,merge(x,c));
    }
    void merge1(int x,int&y)
    {
        down(x);
        if(son[x][0])merge1(son[x][0],y),son[x][0]=0;
        if(son[x][1])merge1(son[x][1],y),son[x][1]=0;
        siz[x]=1;
        add1(y,x);
    }
    ll ask(int x)
    {
        down(x);
        if(son[x][0])v[x]+=ask(son[x][0]);
        if(son[x][1])v[x]+=ask(son[x][1]);
        return v[x];
    }
};

int n,k,head[100001],s[200001],nxt[200001],v[200001];

int dfs(int x,int fa)
{
    int rt=Treap::build(0);
    for(int i=head[x];i;i=nxt[i])
        if(s[i]!=fa)
        {
            int son=dfs(s[i],x);
            Treap::tag2[son]+=v[i]*ll(k-1);
            Treap::tag1[son]-=v[i]*2ll;
            if(Treap::siz[rt]<Treap::siz[son])
                Treap::merge1(rt,son),rt=son;
            else
                Treap::merge1(son,rt);
        }
    int r;
    Treap::split1(rt,k,rt,r);
    return rt;
}

int main()
{
    scanf("%d%d",&n,&k);
    for(int i=1;i<n;++i)
    {
        int x,y,w;
        scanf("%d%d%d",&x,&y,&w);
        s[i]=y;nxt[i]=head[x];head[x]=i;
        s[i+n-1]=x;nxt[i+n-1]=head[y];head[y]=i+n-1;
        v[i]=v[i+n-1]=w;
    }
    int rt=dfs(1,-1);
    printf("%lld",Treap::ask(rt));
}