Finding prefix sums is a generalization of global sum. rather than simply finding the sum of n values the prefix sums are the n partial sums a. devise a serial algorithm for computing the n prefix sums of an array with b. parallelize your serial algorithm for a system with n processes, each of c. suppose n- 2* for some positive integer k. can you devise a serial algo- n elements. which is storing one of the x_is. rithm and a parallelization of the serial algorithm so that the parallel algorithm requires only k communication phases? d. mpi provides a collective communication function, mpi. scan, that can be used to compute prefix sums: int mpi. scan( void void sendbuf p in */. recvbuf-p out/. count / in mpi datatype datatypein */, mp iop mp icomm / in comm it operates on arrays with count elements; both sendbuf. p and recvbufp should refer to blocks of count elements of type datatype. the op argu- ment is the same as op for mpi-reduce. write an mpi program that generates a random array of count elements on each mpi process, finds the prefix sums, and prints the results.