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## J. Chase

Time limit: 1.0 second
Memory limit: 64 MB
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.

### Input

The first line contains coprime integers M and N, 1 ≤ MN ≤ 50; M/N ≤ 3.

### Output

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.

### Sample

inputoutput
```2 3
```
```2
6 2
```
Problem Author: Alexander Ipatov
Problem Source: VIII USU Open Personal Contest (March 3, 2007)
To submit the solution for this problem go to the Problem set: 1541. Chase