You are given a weighted tree that contains $N$ nodes and an integer $K$. You are required to remove some edges from the tree (the number of removed edges can also be zero). If you remove $M-1$ edges from the tree, then you can retrieve $M$ different trees from the original tree. You have to make sure that each diameter of the tree is less than or equal to $K$. Determine the minimum value of $M$.

Note: Diameter of a weighted tree is defined to be the maximum sum of weights on a path over all simple paths in the tree.    

Input format

• First line: Two space-separated integers $N$ and $K$
• Next $N-1$ lines: Three space-separated integers $u$, $v$, and $w$ denoting an edge of the length $w$, between $u$ and $v$. It is guaranteed that the given graph in the input is a tree.

Output format

Print a single integer denoting the minimum value of $M$ on a line.

Constraints

$2 \leq N \leq 500$
$1 \leq K \leq 500$
$1 \leq u, v \leq N$
$1 \leq w \leq 500$