Given a set of natural numbers B=[b1,b2,,bn] and a natural number k>0, design a dynamic programming algorithm to count the number of distinct subsets of elements that sum up to exactly k Example: B=[1,2,3,4,5] and k=5, your algorithm should output 3 since there are three subsets that add up to exactly five: {1,4};{2,3};{5}. Please answer the following parts: 1. Define the entries of your table in words. E.g. T(i) or T(i,j) is ... 2. State a recurrence for the entries of your table in terms of smaller subproblems. Don't forget your base case(s). 3. Write pseudocode for your algorithm to solve this problem. 4. State and analyze the running time of your algorithm. Faster (and correct) solutions are worth more credit