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 V_i leagues per hour; V_i < V_j 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 V_i  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 V_i (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.