ProjectEuler 202

Three mirrors are arranged in the shape of an equilateral triangle, with their reflective surfaces pointing inwards. There is an infinitesimal gap at each vertex of the triangle through which a laser beam may pass.

Label the vertices A, B and C. There are 2 ways in which a laser beam may enter vertex C, bounce off 11 surfaces, then exit through the same vertex: one way is shown below; the other is the reverse of that. see the image here Image

There are 80840 ways in which a laser beam may enter vertex C, bounce off 1000001 surfaces, then exit through the same vertex.

In how many ways can a laser beam enter at vertex C, bounce off 12017639147 surfaces, then exit through the same vertex?

  
     import fractions
     surf = 12017639147
     row = (surf + 3)/2
     offset = 3 - (row %3)
     col = offset
     row -= offset
     total = 0
     while row > col:
       if fractions.gcd(row,col) == 1:
          total += 1
       row -= 3
       col += 3
       if row %1000000 == 0:
         print (total)
     print (total * 2)
  

This solution is taking a long time.How to do it in lesser time?