405958: GYM102191 I Project Presentation

You are given a tree that represents a hierarchy in a company, where the parent of node u is their direct manager.

Each employee is assigned a project, and multiple employees can be assigned to the same project. When it is time for the presentation of the i^th project, all employees u that are assigned that project and their direct and indirect managers must attend the presentation (u and their manager and their manager's manager and so on until the CEO).

Find for each project the number of people attending its presentation.

The first line of input is n and m (1 ≤ m ≤ n ≤ 10⁶), the number of employees and the number of projects, respectively.

The second line of input contains n integers a_i (1 ≤ a_i ≤ m), where a_i is the project assigned to the i^th employee. It is guaranteed that each project has at least one employee assigned to it.

The third line of input contains n integers p_i (0 ≤ p_i ≤ n), where p_i is the direct manager of the i^th employee. If p_i = 0, then the i^th employee is the CEO and does not have a manager. It is guaranteed that there is only one CEO, and this CEO is a direct or indirect manager of all other employees.

Output m integers, where the i^th integer is the number of people attending the presentation of the i^th project.

6 4
1 2 4 3 2 4
0 1 1 3 3 2

1 4 3 4