C++ Program C(n,k) can be rewritten as n(n-1)(n-2)...(n-k+1)/k!. Implement a program that computes C(n,k) based on this formula, using ints. Hint: the numerator is obviously an iteration, but what is the iteration variable?). Repeat the questions from above. Use property (P2) (P2) C(n,k) = C(n,n-k)to make your solution to 3 more efficient (in some cases). The formula for C(n,k) can be expressed as the product (1+(n-k)/1) (1+(n-k)/2) (1+(n-k)/3) ... (1+(n-k)/k). Write a program to implement this. Note that the terms in the product may not be integers. You should be able to handle much larger values of n and k now. Warning: a naive implementation that ignores the type casting needed to convert between ints and intermediate data types will result in incorrect results - you can compare the results from previous tasks and this. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!There are better algorithms that require only integer arithmetic, though we do not have enough C knowledge yet to implement these. If you wish to learn more, you can look up dynamic programming algorithms (and arrays to implement them). !!!!!!!!!!!!!!!!!!!!!!!!!!!!!