Water Jug Problem $(50$ points$).$

You are given two jugs of capacity M liters and N liters. You have to use these two jugs to measure out P liters

of water. The general solution to the problem is as follows;

$1.$ Fill the A liter jug and empty it into B liter jug.

$2.$ Whenever the A liter jug becomes empty fill it$.$

$3.$ Whenever the B liter jug becomes full empty it$.$

$4.$ Repeat the steps till either B liter jug or the A liter jug contains P liters of water.

We can have two solutions depending on whether A is set to M and B is set to N or vice versa.

a$)$ Write an algorithm that implements the above steps. By settng A and B to the different values compute

which of the solutions is the fastest. Remember to include checks for whether the problem cannot be

solved for a particular combinaEon of $($M$,$N$,$ and K$)$ and whether your code is running into a infinite loop

$(10$ points$).$

b$)$ Solving the Diophantine equaEon Mx$+$Ny$=$K will provide a faster method to find the minimum number of

steps. Develop a code to compute the steps by solving the equation. $(10$ points$).$

I need help with part b