Doctor Ninja's House Problem Statement

In a network of 'N' cities with 'M' paths connecting them, Doctor Ninja aims to purchase a house in a city 'X' such that it is possible to reach every other city from city 'X'. Your task is to determine the city 'X'.

If there are multiple options for city 'X', select the city with the smallest number. If no such city exists, return -1.

Example:

Input:

T = 1
N = 8, M = 10
Paths:
0 1
0 2
1 3
2 3
2 4
3 5
4 5
4 6
5 7
6 7

Output:

0

Explanation:

In the given graph configuration, city 0 can reach all the other cities either directly or indirectly, making it the mother vertex. Thus, the output is 0.

Constraints:

• 1 <= T <= 10
• 1 <= N <= 10⁴
• 1 <= M <= 10⁵
• 0 <= X < N
• Time Limit: 1 sec.

Note:

You are not responsible for printing anything, as this is handled externally. Your task is to implement the function to find the solution.