You are maintaining a codebase containing n methods labeled from $0$ to n $- 1$.

You are given two integers n and k, and a $2$D integer array invocations, where invocations[i] $= [a_i, b_i]$ indicates that method $a_i$ invokes method $b_i$.

A group of methods is identified as suspicious:

• Method k is suspicious.

• Any method directly or indirectly invoked by a suspicious method is also suspicious.

You want to remove all suspicious methods from the codebase. However, they can only be removed if no non suspicious method invokes any suspicious method. If at least one non suspicious method invokes a suspicious method, no methods can be removed.

Return a list containing the indices of all remaining methods. If the suspicious methods cannot be removed, return all n method indices. The list may be returned in any order.

Constraints:

• $1 \leq$ n $\leq 10^5$

• $0 \leq$ k $\leq$ n $- 1$

• $0 \leq$ invocations.length $\leq 2 \times 10^5$

• invocations[i] $= [a_i, b_i]$

• $0 \leq a_i, b_i \leq$ n $- 1$

• $a_i \neq b_i$

• invocations[i] $\neq$ invocations[j]

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.