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     #define RG register#define IL inline#define _ 500005#define INF 1e18#define ll long longusing namespace std;IL ll gi(){    RG ll data = 0 , m = 1; RG char ch = 0;    while(ch != '-' && (ch<'0' || ch > '9')) ch = getchar();    if(ch == '-'){m = 0; ch = getchar();}    while(ch>='0' && ch<='9'){data = (data<<1) + (data<<3) + ch - '0' ;  ch = getchar();}    return (m) ? data : -data ; }struct DP{    ll v , cnt ;     IL DP(){cnt = v = 0 ; }    IL DP(RG ll a , RG ll b){v = a ; cnt = b ; }    IL void mem(){cnt = v = 0 ; }    DP operator + (RG DP &B){return DP(v + B.v , cnt + B.cnt) ; }    DP operator + (RG ll &B){return DP(v + B , cnt) ; }    DP operator * (RG DP &B){return DP(v + B.v , cnt + B.cnt - 1) ; }}f[_][3],Ans[_],tmp; IL DP Max(RG DP A , RG DP B){    if(A.v ^ B.v) return (A.v < B.v) ? B : A ;     else return (A.cnt < B.cnt) ? B : A ;  }ll n,K,L,R,C,Ret,head[_]; struct Edge{ll to,next,w;}t[_<<2] ; ll oo ;  IL void add(RG ll u,RG ll v,RG ll w){    t[++oo] = (Edge){v , head[u] , w} ; head[u] = oo ;     t[++oo] = (Edge){u , head[v] , w} ; head[v] = oo ; }void dfs(RG ll u,RG ll From){    f[u][0] = (DP){0 , 0} ; Ans[u] = (DP){-INF , 0} ;     f[u][1] = (DP){-C , 1} ; f[u][2] = (DP){-INF , 0} ;      for(RG ll i = head[u] ; i ; i = t[i].next){        RG ll v = t[i].to ; if(v == From) continue ;         dfs(v , u) ;         f[u][2] = Max(f[u][2] , f[u][2] + Ans[v]) ;         f[u][2] = Max(f[u][2] , (f[u][1] * f[v][1]) + t[i].w + C) ;        tmp = f[u][0] + f[v][0]; C = -C ; tmp = tmp + t[i].w + C; C = -C ; tmp.cnt ++ ;         f[u][1] = Max(f[u][1] , f[u][1] + Ans[v]) ;         f[u][1] = Max(f[u][1] , Max(f[u][0] + f[v][1] + t[i].w , tmp)) ;         f[u][0] = Max(f[u][0] , f[u][0] + Ans[v]) ;    }     Ans[u] = Max(Max(f[u][0] , f[u][1]) , f[u][2]) ; return ; }int main(){    n = gi() ; K = gi() ;     for(RG ll i = 1,u,v,w; i < n; i ++)        u = gi() , v = gi() , w = gi() , add(u , v , w) , R = R + abs(w);    ++ K ;  L = -R ;     while(L <= R){        C = (L + R) >> 1 ;               dfs(1 , 0) ;         if(Ans[1].cnt <= K) Ret = C , R = C - 1 ;         else L = C + 1;             }    C = Ret ; dfs(1 , 0) ;      printf("%lld\n" , Ans[1].v + Ret * Ans[1].cnt) ; return 0 ;     }