Steps in Euclid's algorithm (noch nicht übersetzt)

Problem 433

Let E(x0, y0) be the number of steps it takes to determine the greatest common divisor of x0 and y0 with Euclid's algorithm. More formally:
x1 = y0, y1 = x0 mod y0
xn = yn-1, yn = xn-1 mod yn-1
E(x0, y0) is the smallest n such that yn = 0.

We have E(1,1) = 1, E(10,6) = 3 and E(6,10) = 4.

Define S(N) as the sum of E(x,y) for 1 ≤ x,y ≤ N.
We have S(1) = 1, S(10) = 221 and S(100) = 39826.

Find S(5·106).