Problem G. Gray, black and white squares

Author:Антон Карабанов   Time limit:1 sec
Input file:Standard input   Memory limit:256 Mb
Output file:Standard output  

Statement

Timofey has two semi-transparent films with a gray-and-white checkered pattern, each of size n × n. The first film has a cell size of 1 × 1, and the second film has a cell size of a × a. Both films start with a gray square in the top-left corner.

Today, Timofey placed the two films on top of each other. As a result:

Where gray squares from both films overlapped, the color turned black.

Where gray squares overlapped with white squares, the color remained gray.

Where white squares overlapped with white squares, the color remained white.

Your task is to determine how many single-unit squares of black, gray, and white color there are in total.

Input format

The input consists of two natural numbers, a and n.

Output format

The output should be three natural numbers — the number of black, gray, and white unit squares.

Constraints

2 ≤ a < n ≤ 109

Example explanation

See the diagram for an example of tiling.

Sample tests

No. Standard input Standard output
1
3
10
30
42
28

0.104s 0.043s 15