Could you please give a dp solution to the problem, provide the clear pseudocode and give the detailed explain and also the running time?

Thank you very much.

Counting heads. Given integers n and k, along with p,... ,Pn [0,1], you want to determine the probability of obtaining exactly k heads when n biased coins are tossed independently at random, where p is the probability that the ith coin comes up heads. Give an O(n2) algorithm for this task.2 Assume you can multiply and add two numbers in [0, 1] in O(1) time