To solve this problem, we need to reconstruct the hidden subcontract chain starting from a given main contractor ( M ). The chain consists of subcontractors where each subcontractor has at most one direct subcontractor, forming a linear path. The goal is to traverse this path starting from the primary subcontractor of ( M ) until we reach a subcontractor who does not have any further subcontractors.

1. Problem Analysis: The problem involves processing a list of pairs ((A, B)) where ( A ) is the main contractor of ( B ). The chain starts at ( M ) and follows each subcontractor in sequence until a subcontractor with no further subcontractors is encountered.
2. Intuition: We can model the subcontract relationships as a directed graph where each node (contractor) has at most one outgoing edge (to their subcontractor). The chain is a path starting from ( M ) and following these edges.
3. Algorithm Selection:
   • Mapping Construction: Create a dictionary to map each contractor to their immediate subcontractor.
   • Traversal: Starting from ( M ), traverse the chain by following the subcontractor mappings. Track visited nodes to detect cycles and avoid infinite loops.
   • Termination: The traversal stops when a contractor is not found in the mapping (indicating no further subcontractors) or when a cycle is detected.
4. Complexity Analysis:
   • Time Complexity: ( O(n) ) where ( n ) is the number of pairs. We process each pair once to build the mapping and traverse the chain in linear time.
   • Space Complexity: ( O(n) ) for storing the mapping and the visited set