Detect Cycle in a Directed Graph

Determine if a given directed graph contains a cycle. Your function should return true if the graph contains at least one cycle, and false otherwise.

Input:

The first line of input contains an integer T, representing the number of test cases.

The first line of each test case consists of two integers, V and E. V represents the number of vertices, and E represents the number of edges in the graph.

The next E lines for each test case describe the edges of the graph, where each edge is given by two integers A and B, indicating a directed edge from vertex A to vertex B.

Output:

For each test case, print "true" if a cycle exists in the graph, otherwise print "false".

Example:

Input:

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

Output:

true
false

Constraints:

• 1 ≤ T ≤ 10
• 1 ≤ V ≤ 10^3
• 0 ≤ E ≤ 10^3
• 0 ≤ A, B < V

Time Limit: 1 sec