Problem Statement

Consider an undirected tree with $N$ vertices. The vertices of this tree are numbered $1,2,\cdots,N$. For the $N-1$ edges, the endpoints of the $i$-th edge are vertex $a_i$ and vertex $b_i$.

Initially, $K$ coins are placed on vertex $1$.
From this state, you may perform the following operation any number of times: "choose one vertex with at least 1 coin on it, choose any number (at least 1) of the coins on that vertex, and move them to an adjacent vertex." The goal is to reach a state in which every vertex has at most 1 coin on it.

If it is possible to reach this state, find the minimum number of operations required.

Input

$N\ K$
$a_1$ $b_1$
$a_2$ $b_2$
$\vdots$
$a_{N-1}$ $b_{N-1}$

Constraints

• All inputs are integers.
• $2\le N\le 10^5$
• $1\le K\le 10^5$
• $1\le a_i,b_i \le N$
• If $i\ne j$, then $(a_i,b_i)\ne(a_j,b_j)$
• The graph given by the input is a tree.

Output

If the required state can be reached, output the minimum number of operations; otherwise, output '-1'. Print a newline at the end.

Sample

4 2
1 2
2 3
3 4

1

5 6
1 2
1 3
1 4
2 5

-1

5 3
1 2
2 3
2 4
1 5

2