Aragorn, Legolas, and Gimli chase a squadron of Uruks sent by Saruman. The friends have already went K leagues (K < 20). On the ith segment of length 1 league of their path
(1 ≤ i ≤ K),
their average velocity was Vi leagues per hour;
Vi < Vj for
i > j.
Gimli notes that M/N hours have passed since the start of the chase, and it's time to overtake the Uruks at last. Find K if it is known that all Vi are integers.
The first line contains coprime integers M and N,
1 ≤ M, N ≤ 50; M/N ≤ 3.
In the first line output the number K and in the second line output the numbers Vi (1 ≤ i ≤ K) separated with a space. Note that nobody in Middle-earth can move faster than 100000 leagues per hour. If there are many solutions, then output any of them. If there is no solution, then output −1.
Problem Author: Alexander Ipatov
Problem Source: VIII USU Open Personal Contest (March 3, 2007)