Write an MPI program mpi-ring.c which implements a ring communication between the processes. In details, let \(P\) be the number of MPI processes (to be specified with the
mpirun command); then, the program should behave according to the following specification:
The program receives an integer \(K\) from the command line. \(K\) represents the number of "turns" of the ring that (\(K \geq 1\)). Remember that all MPI processes have access to the command line, so that each one knows the value \(K\) without the need to communicate.
Process 0 (the master) sends process 1 an integer, whose initial value is 1.
Every process \(p\) (including the master) receives a value \(v\) from the predecessor \(p-1\), and sends \((v + 1)\) to the successor \(p+1\). The processes are considered to be organized as a ring, so that the predecessor of 0 is \((P - 1)\), and the successor of \((P - 1)\) is 0.
The master prints the value received after the \(K\)-th iteration and the program terminates. Given the number \(P\) of processes and the value of \(K\), what value should be printed at the end by the master?
For example, if \(K = 2\) and there are \(P = 4\) processes, the communication should be as shown in Figure 1 (circles are MPI processes; arrows are messages whose content is the number shown above). There are \(K = 2\) "turns" of the ring; at the end, process 0 receives and prints the value 8.
mpicc -std=c99 -Wall -Wpedantic mpi-ring.c -o mpi-ring
mpirun -n 4 ./mpi-ring