You have n processes forming a rooted tree structure. You are given two integer arrays pid and ppid, where pid[i] is the ID of the ith process and ppid[i] is the ID of the ith process's parent process.

Each process has only one parent process but may have multiple children processes. Only one process has ppid[i] = 0, which means this process has no parent process (the root of the tree).

When a process is killed, all of its children processes will also be killed.

Given an integer kill representing the ID of a process you want to kill, return a list of the IDs of the processes that will be killed. You may return the answer in any order.

 

Example 1:

Input: pid = [1,3,10,5], ppid = [3,0,5,3], kill = 5
Output: [5,10]
Explanation: The processes colored in red are the processes that should be killed.

Example 2:

Input: pid = [1], ppid = [0], kill = 1
Output: [1]

 

Constraints:

• n == pid.length
• n == ppid.length
• 1 <= n <= 5 * 104
• 1 <= pid[i] <= 5 * 104
• 0 <= ppid[i] <= 5 * 104
• Only one process has no parent.
• All the values of pid are unique.
• kill is guaranteed to be in pid.