N,K = map(int,input().split())
E = [[] for _ in range(N)]
AB = []
L = []
for i in range(N-1):
    a,b,c = map(int,input().split())
    a -= 1
    b -= 1
    E[a].append((b,c,i))
    E[b].append((a,c,i))
    AB.append((a,b))

C = [[] for _ in range(N-1)] #子孫に葉が幾つあるか
def dfs(x,p= -1):
    f = True
    ret = 0
    for y,c,id in E[x]:
        if y != p:
            f = False
            a = dfs(y,x)
            C[id] = [a,c,id]
            ret += a
    if f:
        return 1
    return ret


dfs(0)
C.sort(key = lambda x:(-x[0],-x[1]))
ans = 0
for a,c,id in C:
    ans += a * c
    if K >= c:
        K -= c
        ans += a * c
print(ans)