Rectangle into Squares

The drawing below gives an idea of how to cut a given "true" rectangle into squares ("true" rectangle meaning that the two dimensions are different).

Can you translate this drawing into an algorithm?

You will be given two dimensions

1. a positive integer length (parameter named lng)
2. a positive integer width (parameter named wdth)

You will return an array or a string (depending on the language; Shell bash, PowerShell and Fortran return a string) with the size of each of the squares.

  sqInRect(5, 3) should return [3, 2, 1, 1]
  sqInRect(3, 5) should return [3, 2, 1, 1]
  or (Haskell)
  squaresInRect  5  3 `shouldBe` Just [3,2,1,1]
  squaresInRect  3  5 `shouldBe` Just [3,2,1,1]
  or (Fsharp)
  squaresInRect  5  3 should return Some [3,2,1,1]
  squaresInRect  3  5 should return Some [3,2,1,1]
  or (Swift)
  squaresInRect  5  3 should return [3,2,1,1] as optional
  squaresInRect  3  5 should return [3,2,1,1] as optional
  or (Cpp)
  sqInRect(5, 3) should return {3, 2, 1, 1}
  sqInRect(3, 5) should return {3, 2, 1, 1}
  (C)
  C returns a structure, see the "Solution" and "Examples" tabs.
  Your result and the reference test solution are compared by strings.

typedef struct Data Data;
struct Data {
     int *array;
     int sz;
};

Data* sqInRect(int lng, int wdth) {
  
  int tmplng = lng;
  int tmpwdth = wdth;
  Data* pData = (Data*)malloc(sizeof(Data));
  int i;
  int size = 0;
  int * pIntarr;
  
  while(tmplng != tmpwdth)
  {
    if(tmplng > tmpwdth)
    {
      tmplng = tmplng - tmpwdth;
    }
    else
    {
      tmpwdth = tmpwdth - tmplng;
    }
    size ++;
  }
  
  if(size != 0)
  { 
    size ++;
    tmplng = lng;
    tmpwdth = wdth;
    pIntarr = (int*)malloc(sizeof(int) * size);
    for(i=0; i<size-1; i++)
    {
      if(tmplng > tmpwdth)
      {
        tmplng = tmplng - tmpwdth;
        pIntarr[i] = tmpwdth;
      }
      else
      {
        tmpwdth = tmpwdth - tmplng;
        pIntarr[i] = tmplng;
      }
    }
    pIntarr[i] = pIntarr[i-1];
  }
  
  pData->sz = size;
  pData->array = pIntarr;
  return pData;
}