Artifact Chain Assembler

You are given N fragments of an ancient artifact. Each fragment has a left connector value and a right connector value (integers). You need to find a sequence of exactly K distinct fragments such that each fragment's right connector matches the next fragment's left connector. Additionally, the sequence must form a loop: the right connector of the last fragment must match the left connector of the first fragment. Print the space-separated indices of the fragments (using their 0-indexed order in the input) that form the lexicographically smallest sequence of indices. If no such loop exists, print 'None'. Example: Input: 3 4 1 2 2 3 3 1 1 3 Output: 0 1 2 (Explanation: Fragment 0 (1,2), 1 (2,3), and 2 (3,1) form a chain 1-2-3-1 of length 3.)