Description

Winy is the owner of a bar. His bar offers two volumes of beer, $a$ ml and $b$ ml, served in cups with capacities $a$ ml and $b$ ml respectively.

Business is not good. Winy finds that the drunks are very poor. Sometimes they have to leave because they cannot afford $a$ ml or $b$ ml of beer. Therefore, Winy decides to sell a third volume of beer (a smaller volume).

Winy has only two cups with capacities $a$ ml and $b$ ml, and the cups have no markings. He can only obtain new volumes by pouring between the two cups and the barrel.

To simplify the pouring steps, Winy stipulates:

1. $a≥b$.
2. The barrel has infinite capacity, and the amount of beer in the barrel is also infinite (but much smaller than the barrel’s capacity).
3. Only three pouring operations are allowed:
   1. Pour beer from the barrel into the cup of capacity $b$ ml.
   2. Pour the beer from the cup of capacity $a$ ml into the barrel.
   3. Pour the beer from the cup of capacity $b$ ml into the cup of capacity $a$ ml.
4. Each pour must either fill the receiving cup to full or empty the source cup completely.

Winy hopes that after several pours, the remaining volume of beer in the $a$ ml cup is as small as possible. He asks you to help design a pouring plan.

Input Format

A single line with two integers $a$ and $b$, satisfying $0<b≤a≤10^9$.

Output Format

The first line contains an integer $c$, representing the minimal volume that can be obtained.

The second line contains two integers $P_a$ and $P_b$ (separated by a space), representing respectively the number of times pouring from the $a$ ml cup into the barrel and the number of times pouring into the $b$ ml cup from the barrel.

If multiple pairs $P_a,P_b$ satisfy the requirement, output the one with the smallest $P_a$. If there are still multiple choices under the smallest $P_a$, output the one with the smallest $P_b$.

5 3

1
1 2

Hint

Sample explanation:

The pouring plan is:

1. Barrel -> cup B.
2. Cup B -> cup A.
3. Barrel -> cup B.
4. Cup B -> cup A.
5. Cup A -> barrel.
6. Cup B -> cup A.

Translated by ChatGPT 5