#include<bits/stdc++.h>
using namespace std;
#define N 3050
#define INF 0x3f3f3f3f
#define F(i,l,r) for(int i=(l);i<=(r);++i)
#define D(i,r,l) for(int i=(r);i>=(l);--i)
#define MEM(x,a) memset(x,a,sizeof(x))
int I() {char c=getchar(); int x=0; int f=1; while(c<'0' or c>'9') f=(c=='-')?-1:1,c=getchar(); while(c>='0' and c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar(); return ((f==1)?x:-x);}

int n,k;
struct Graph
{
    int to[N<<1],nx[N<<1],w[N<<1],h[N],ec=-1; void cl(){MEM(h,-1);ec=-1;}
    void ad(int u,int v,int ww){++ec;to[ec]=v;nx[ec]=h[u];w[ec]=ww;h[u]=ec;} void a2(int u,int v,int w){ad(u,v,w),ad(v,u,w);}
}G;
#define T(G,i,u)for(int i=G.h[u],v;~i;i=G.nx[i])
int sz[N]; int f[3][N][N];
int tmp[3][N];
inline void up(int&a,int b){a=(b<a)?b:a;}
void fuck(int u,int v,int w)
{
    F(i,0,3)F(j,0,sz[u]+sz[v])tmp[i][j]=INF;
    F(i,0,sz[u])F(j,0,sz[v])
    {
        up(tmp[2][i+j],f[2][u][i]+f[2][v][j]+2*w);
        up(tmp[1][i+j],f[1][u][i]+f[2][v][j]+2*w); up(tmp[1][i+j],f[2][u][i]+f[1][v][j]+w);
        up(tmp[0][i+j],f[1][u][i]+f[1][v][j]+w);
        up(tmp[0][i+j],f[2][u][i]+f[0][v][j]+2*w); up(tmp[0][i+j],f[0][u][i]+f[2][v][j]+2*w);
    }
    F(i,0,2)F(j,0,sz[u]+sz[v])up(f[i][u][j],tmp[i][j]);
}
void d0(int u,int fa)
{
    sz[u]=1;
    F(i,0,2)f[i][u][0]=f[i][u][1]=0;
    T(G,i,u)if((v=G.to[i])!=fa)
    {
        d0(v,u);
        fuck(u,v,G.w[i]);
        sz[u]+=sz[v];
    }
}
void flandre()
{
    n=I(),k=I(); G.cl();
    F(i,1,n-1){int u=I(),v=I(),w=I(); G.a2(u,v,w);}
    MEM(f,0x3f); d0(1,1);
    printf("%d\n",f[0][1][k]);
}
int main()
{
    int t=1;
    while(t-->0){flandre();}
    return 0;
}