A call bell is ringing in room ~k~, but you are in the hospital's break room. You need to get to your patient, stat!

The hospital has ~n~ rooms, numbered ~1~ to ~n~, joined by ~n-1~ one-way hallways. Every room except room ~1~ has exactly one hallway leading into it, and every room can be reached from room ~1~. You start in room ~1~ and need to get to room ~k~. More formally, it is a unidirectional tree rooted at node ~1~.

We'll say that room ~b~ is ~d~ hallways deeper than room ~a~ if the route from ~a~ to ~b~ passes through exactly ~d~ hallways.

To move between rooms, the hospital is trialling an inter-dimensional remote. If you are standing in some room ~v~, you can pick an integer ~d~ with ~1 \le d \le m~ and teleport to any room ~d~ hallways deeper than ~v~. More formally, you can pick an integer ~d~ with ~1 \le d \le m~ and teleport to any node in ~v~'s subtree that is ~d~ hallways deeper than ~v~.

However, teleporting is very loud! Each time you use the remote, you must first warn every room that is ~d~ hallways deeper than ~v~, including the one you are traveling to. Warnings take ~1~ second per room.

Moving optimally, what is the minimum total time required to get from room ~1~ to room ~k~?

Input

The first line contains three integers ~n~, ~k~, and ~m~ (~2 \le n \le 10^5~, ~2 \le k \le n~, ~1 \le m \le n~), the number of rooms in the hospital, the room you need to travel to, and the greatest depth you can travel with a single use of the remote.

The second line contains ~n-1~ integers ~p_2, p_3, \dots, p_n~ (~1 \le p_i \le n~), where ~p_i~ is the room that the hallway leading into room ~i~.

It is guaranteed that ~n \times m \leq 10^6~.

Output

Output a single integer, the minimum total time to reach room ~k~, in seconds.

Example

Input 1

12 12 2
1 1 2 2 2 2 2 3 7 7 11

Output 1

5

The optimal route is:

• Teleport from room ~1~ to room ~2~, which is ~1~ hallway deeper. There are ~2~ rooms exactly ~1~ hallway deeper than room ~1~, so you spend ~2~ seconds warning them.
• Teleport from room ~2~ to room ~11~, which is ~2~ hallways deeper. There are ~2~ rooms exactly ~2~ hallways deeper than room ~2~, so you spend ~2~ seconds warning them.
• Teleport from room ~11~ to room ~12~, which is ~1~ hallway deeper. There is only ~1~ room exactly ~1~ hallway deeper than room ~11~, so you spend ~1~ second warning it.

This gives a total of ~5~ seconds.

Input 2

17 14 2
1 6 1 1 2 4 7 14 17 17 17 17 10 1 11 6

Output 2

6

Input 3

20 20 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Output 3

3