#include<bits/stdc++.h>
#define ll long long
#define ls (rt<<1)
#define rs (rt<<1|1)
#define pb  push_back
#define mp make_pair
using namespace std;
const int LEN=1<<21;
char BUF[LEN],*Pin,*Pin_last,PUF[LEN],*Pout=PUF,*Pout_last=PUF+LEN-1;
inline char G(){return Pin==Pin_last&&(Pin_last=(Pin=BUF)+fread(BUF,1,LEN,stdin),Pin==Pin_last)?EOF:*Pin++;}
inline void P(char x){if(Pout==Pout_last)fwrite(PUF,1,Pout-PUF,stdout),Pout=PUF;*Pout++=x;}
inline int read(){int res=0,f=1,ch=' ';for(;(ch<'0'||ch>'9')&&ch!=EOF;ch=G())if(ch=='-')f=-1;for(;ch>='0'&&ch<='9';ch=G())res=(res<<3)+(res<<1)+ch-48;return res*f;}
inline ll readL(){ll res=0,f=1,ch=' ';for(;(ch<'0'||ch>'9')&&ch!=EOF;ch=G())if(ch=='-')f=-1;for(;ch>='0'&&ch<='9';ch=G())res=(res<<3)+(res<<1)+ch-48;return res*f;}
inline void wtL(ll a){if(a>9)wtL(a/10);P(a%10+'0');return;}
inline void writeL(ll a,char b){if(a<0)P('-'),a=-a;wtL(a),P(b);}
inline void wt(int a){if(a>9)wt(a/10);P(a%10+'0');return;}
inline void write(int a,char b){if(a<0)P('-'),a=-a;wt(a),P(b);}
inline void wt_str(char s[],int len=0){if(!len)len=strlen(s);for(int i=0;i<len;i++)P(s[i]);return;}
const int N=3e3+10;
struct Edge{int to,next,dis;}e[N<<1];
int head[N],num,n,k,siz[N],f[N][N][3],ans=2e9;
//f[i][j][k]  iµÄ×ÓÊ÷ÖÐÑ¡ÁËj¸ö£¬ÆðµãÖյ㹲k¸ö 
inline void add(int x,int y,int z){return e[++num]=(Edge){y,head[x],z},head[x]=num,void();}
inline void chkmin(int &x,int y){return (x>y?x=y:0),void();} 
void dfs(int now,int fa)
{
	f[now][1][0]=f[now][1][1]=0,siz[now]=1;
	for(int p=head[now],to,vl;p;p=e[p].next)
		if((to=e[p].to)!=fa)
		{
			dfs(to,now),vl=e[p].dis;
			for(int j=siz[now];j;j--)
				for(int z=siz[to];z;z--)
				{
					chkmin(f[now][j+z][0],f[now][j][0]+f[to][z][0]+vl+vl);
					chkmin(f[now][j+z][1],f[now][j][0]+f[to][z][1]+vl);
					chkmin(f[now][j+z][1],f[now][j][1]+f[to][z][0]+vl+vl);
					chkmin(f[now][j+z][2],f[now][j][2]+f[to][z][0]+vl+vl);
					chkmin(f[now][j+z][2],f[now][j][0]+f[to][z][2]+vl+vl);
					chkmin(f[now][j+z][2],f[now][j][1]+f[to][z][1]+vl);
				}
			siz[now]+=siz[to];
		}
	ans=min(ans,f[now][k][2]);
	return;
}
int main()
{
	n=read(),k=read();
	for(int i=1,x,y,z;i<n;i++)
		x=read(),y=read(),z=read(),
		add(x,y,z),add(y,x,z);
	memset(f,0x7f/2,sizeof(f));
	dfs(1,0);
	cout<<ans<<'\n';
	fwrite(PUF,1,Pout-PUF,stdout);
	return 0;
}