Path Counting in Directed Graph

Given a directed graph with a specified number of vertices V and edges E, your task is to calculate the total number of distinct paths from a given source node S to all other nodes. A path is considered distinct if either the destination node or the set of edges used differs from others. The result should be provided modulo 10⁹ + 7, as the number of paths can be very large.

Explanation:

Include the source node as a valid destination itself, and note that the graph contains no cycles.

Input:

The first input line will contain three integers V, E, and S, separated by spaces.
 The following E lines will describe the directed edges in the graph.
 Each edge is defined with two space-separated integers A and B, indicating a directed edge going from vertex A to vertex B. 

Output:

Output a single integer representing the total number of distinct paths modulo 109 + 7.

Example:

Input:
4 5 1
1 2
2 3
3 4
1 3
2 4

Output:
5

Constraints:

• 1 <= S, V <= 10^5
• 0 <= E <= 2 * 10^5
• Time limit: 1 second