#codingexercise
Implement a virtual pottery wheel method that conserves mass but shapes it according to external factor
List<int> ShapeOnPotteryWheel(List<int> diameters, List<int> touches)
{
assert(diameters.count == touches.count); // height of clay
Assert(touches.All( x => x >= 0));
double volume = 0;
for (int i = 0; i < touches.count; i++)
{
    var old = diameters[i];
    diameters[i] -= 2 × touches[i];
    var new = diameters[i];
    Assert(new > 0);
    volume += (PI/4) x (old^2 - new^2);
}
assert(volume >= 0);
// volume adds up the top
var last = diameters.Last();
int count = volume/((PI/4)×(last^2));
if (count > 0)
     diameters.AddRange(Enumerable.Repeat(last, count));
return diameters;
}