Let A and B be two sequences of digits, each digit takes value from 0 to k-1. If a common subsequence between A and B has 1 digits, it can be treated as an l-digit number. The largest common subsequence is the one with the largest value. For example, with k = 10, A = {1,9,2}, B={9,1,2}, the longest common subsequences are {1, 2} and {9,2}, but the largest common subsequence is just {9,2}. (a) (6 points) Design a dynamic programming algorithm to find the largest common subsequence between two sequences of n and m digits respectively. Your algorithm should output the value of the largest common subsequence. What is the complexity of your algorithm? (b) (4 points) Apply your algorithm to find the largest common subsequence between {1, 2, 3, 9, 4, 6, 7,5} and {2,8,3,1,4,6,9,5), with k = 10. Show the intermediate results of your algorithm to get the final solution.