Cycle Detection in a Directed Graph

Determine if a given directed graph contains a cycle. Return true if at least one cycle is found, otherwise return false.

Input:

T
The first line consists of the integer T, representing the number of test cases.
For each test case, the first line contains two integers V and E.
V is the number of vertices, and E is the number of edges. 
The next E lines each comprise two space-separated integers A and B, indicating a directed edge from vertex A to vertex B.

Output:

For every test case, output "true" if a cycle exists in the graph, otherwise show "false".

Example:

Input:
1
4 4
0 1
1 2
2 3
3 1

Output:
true

Explanation: The graph depicted in the example above includes a cycle involving the vertices represented by the edges (1,2), (2,3), and (3,1).

Constraints:

• 1 <= T <= 10
• 1 <= V <= 10^3
• 0 <= E <= 10^3
• 0 <= A, B < V
• Time Limit: 1 sec