Description

You have a tree with $n$ vertices. You also have a starting vertex $s$ on this tree.

You need to start from vertex $s$ and take at most $k$ steps. At each step, you can move to any adjacent vertex. You want to know how many different vertices can you pass through at most. (Including the starting vertex $s$)

Input

First line has three integers, $n,s,k$.

Next, we have $n-1$ lines. Each line contains two intergers $u_i,v_i$, means there has an edge between vertex $u_i$ and $v_i$.

Output

One line with one integer, means the maximum number of different vertices that can be passed through.

Sample Input

5 1 4
1 2
1 3
1 4
4 5

Sample Output

4

Tips

The figure shows a feasible solution. Take $4$ steps, passed through $4$ different vertices.

数据范围

$1\leq s\leq n\leq 10^6$

$1\leq k\leq 2\times 10^6$