#include<bits/stdc++.h>
#define I using
#define love namespace
#define Elaina std
#define ll long long
I love Elaina;
const int N=100010;
ll read(){
	ll x=0,f=1;
	char ch=getchar();
	while(ch<'0'||ch>'9'){
		if(ch=='-')f=-1;
		ch=getchar();
	}
	while(ch>='0'&&ch<='9'){
		x=(x<<3)+(x<<1)+ch-'0';
		ch=getchar();
	}
	return x*f;
}
ll n,m,x,y,z,head[N],cnt,ans;
struct edge{
	int to,nxt;
	ll val;
}e[N<<1];
void addedge(int u,int v,ll w){e[++cnt].to=v,e[cnt].nxt=head[u],e[cnt].val=w,head[u]=cnt;}
namespace AyaseEli{
	int root[N];
	ll fa[N<<2],val[N<<2],siz[N<<2],ch[N<<2][2],tag1[N<<2],tag2[N<<2];
	vector<int>stk;
	void pushup(int k){siz[k]=siz[ch[k][0]]+siz[ch[k][1]]+1;}
	void pushdown(int k){
		if(ch[k][0])val[ch[k][0]]+=tag1[k]+(siz[ch[ch[k][0]][0]]+1)*tag2[k],tag1[ch[k][0]]+=tag1[k],tag2[ch[k][0]]+=tag2[k];
		if(ch[k][1])val[ch[k][1]]+=tag1[k]+(siz[ch[k][0]]+siz[ch[ch[k][1]][0]]+2)*tag2[k],tag1[ch[k][1]]+=tag1[k]+(siz[ch[k][0]]+1)*tag2[k],tag2[ch[k][1]]+=tag2[k];
		tag1[k]=tag2[k]=0;
	}
	void rotate(int x){
		int y=fa[x],z=fa[y];
		int k=x==ch[y][1];
		ch[y][k]=ch[x][k^1];
		if(ch[x][k^1])fa[ch[x][k^1]]=y;
		ch[x][k^1]=y,fa[y]=x,fa[x]=z;
		if(z)ch[z][y==ch[z][1]]=x;
		pushup(y),pushup(x);
	}
	void splay(int &rt,int x,int goal=0){
		for(int y=fa[x];y=fa[x],y!=goal;rotate(x)){
			int z=fa[y];
			if(z!=goal)rotate((x==ch[y][1])^(y==ch[z][1])?x:y);
		}
//		if(!goal)rt=x;
	}
	void dfs(int u){
		if(!u)return;
		pushdown(u);
		dfs(ch[u][0]);
		stk.push_back(u);
		dfs(ch[u][1]);
	}
	void insert(int &rt,int k){
		int v=val[k];
		if(!rt){
			rt=k,ch[rt][0]=ch[rt][1]=0,siz[rt]=1;
			pushup(rt);
			return;
		}
		int x=rt,y=0;
		while(1){
			pushdown(x);
			y=x,x=ch[y][v<val[y]];
			if(!x){
				x=k,ch[x][0]=ch[x][1]=0,siz[x]=1,fa[x]=y,ch[y][v<val[y]]=x;
				pushup(x),pushup(y),splay(rt,x);
				break;
			}
		}
	}
	void merge(int &rt,int x){
		stk.clear();
		dfs(x);
		for(int tmp:stk)insert(rt,tmp);
		rt=stk.back();
	}
}
I love AyaseEli;
void dfs1(int u,int fa){
	insert(root[u],u);
	for(int i=head[u];i;i=e[i].nxt){
		int v=e[i].to;
		if(v==fa)continue;
		dfs1(v,u);
		val[root[v]]+=1ll*(m+1)*e[i].val-2ll*(siz[ch[root[v]][0]]+1)*e[i].val,tag1[root[v]]+=1ll*(m+1)*e[i].val,tag2[root[v]]-=2ll*e[i].val;
		if(siz[root[u]]<siz[root[v]])swap(root[u],root[v]);
		merge(root[u],root[v]);
	}
}
int main(){
	n=read(),m=read();
	for(int i=1;i<n;i++){
		x=read(),y=read(),z=read();
		addedge(x,y,z),addedge(y,x,z);
	}
	dfs1(1,0);
	stk.clear();
	dfs(root[1]);
	for(int i=0;i<min(m,(ll)stk.size());i++)ans+=val[stk[i]];
	printf("%lld",ans);
	return 0;
}