Path count II

Construct a directed acyclic graph with the nodes 1,2,\dots,100. The graph should have exactly x different paths from the node 1 to the node 100. The graph can have at most 1000 edges, and each edge must be unique.

In a file paths2.py, implement the function create_edges the returns the graph as a list of the edges. For example, the list [(1, 2), (4, 5)] represents a graph with the two edges 1 \rightarrow 2 and 4 \rightarrow 5.

You can assume that x is in the range 0 \dots 10^9 in all tests.

You can test your function using the class CountPaths in the course material. In the code template below, the method count_paths should return 123456789, when the graph is correctly constructed.

class CountPaths:
    # you can copy this class from the course material

def create_edges(x):
    # TODO

if __name__ == "__main__":
    edges = create_edges(123456789)

    counter = CountPaths(range(1, 100 + 1))
    for edge in edges:
        counter.add_edge(edge[0], edge[1])
    print(counter.count_paths(1, 100)) # 123456789