Aragorn, Legolas, and Gimli chase a squadron of Uruks sent by Saruman. The friends have already went *K* leagues (*K* < 20). On the *i*th 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.

### Input

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

### Output

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.

### Sample

**Problem Author: **Alexander Ipatov

**Problem Source: **VIII USU Open Personal Contest (March 3, 2007)