Print All Paths Problem Statement

In this problem, you are provided with a graph consisting of 'N' nodes and 'M' unidirectional edges. Additionally, two integers 'S' and 'D' are given, representing the source and destination respectively. Your task is to identify all unique paths from the source node 'S' to the destination node 'D'.

Note:

For a path to be considered valid, all nodes in the ordered set { S, u1, u2,..., un, D} must be unique.

Example:

Input:

N = 4,
M = 4,
S = 0,
D = 3

Explanation:

Consider the following paths:

• The path 0 -> 1 -> 3 is valid as all nodes are unique.
• The path 0 -> 1 -> 2 -> 1 -> 3 is invalid because node 1 is repeated.

Constraints:

• 1 ≤ T ≤ 5
• 1 ≤ N ≤ 5
• 1 ≤ M ≤ 10
• 0 ≤ u, v, S, D ≤ N-1
• Time Limit: 1 sec.

Input:

The first line consists of a single integer 'T', indicating the number of test cases. Each test case follows the format:

The first line contains two integers 'N' and 'M', representing the number of nodes and edges, respectively.
The subsequent 'M' lines contain two integers 'u' and 'v', depicting a directed edge from 'u' to 'v'.
The last line contains two integers 'S' and 'D', denoting the source and destination nodes.

Output:

For each test case, output consists of:
An integer 'N', representing the total number of valid paths from 'S' to 'D'.
The following 'N' lines list all nodes from 'S' to 'D' in the 'i-th' valid path (1 ≤ i ≤ N).
If multiple paths exist, they should be sorted in lexicographical order.

Note:

You are not required to print anything. Implement the function as specified.