Algorithm title: UVA 571 (number theory)

Jugs

In the movie ' Die Hard 3, Bruce Willis and Samuel L. Jackson were confronted with the following puzzle. They were given a 3-gallon jug and a 5-gallon jug and were asked to fill the 5-gallon jug with exactly 4. This is problem generalizes that puzzle.

You have two jugs, A and B, and A infinite supply of water. There are three types of actions that can be use: (1) can fill a jug, (2) can empty a jug, and (3) can pour F Rom one jug to the other. Pouring from one jug to the "other stops" when the "the" is empty or the second jug are full, whichever comes. For example, if A has 5 gallons and B has 6 gallons and A capacity of 8, then pouring from a to B leaves B full and 3 gall ONS in A.

A problem is given by a triple (ca,cb,n), where Ca and Cb are the capacities of the jugs A and B, respectively, and N are T He goal. A solution is a sequence of the steps that leaves exactly N gallons in jug B. The possible steps are

Fill A

Fill B

Empty A

Empty B

Pour A B

Pour B A

Success

where ' pour A B ' means ' pour the contents of jug A into jug B ', and ' success ' means that goal has been .

You may assume this input you are given does have a solution.

Input

Input to your program consists of the a series of input lines each defining one puzzle. Input for each puzzle are a single line of three positive INTEGERS:CA, Cb, and N. Ca and CB are the capacities of jugs a nd B, and Nis the goal. You can assume $ < Ca le cb$ and $N le Cb le 1000$ and that's A and B are relatively prime to one another.

Output

Output from your program would consist of a series of instructions from the list of the potential output lines which would r Esult in either of the jugs containing exactly N gallons of water. The last line of output for each puzzle should is the line ' success '. Output lines start in column 1 and there should is no empty lines nor any trailing.

Sample Input

3 5 4

5 7 3

Sample Output

Fill B

Pour B A

Empty A

Pour B A

Fill B

Pour B A

Success

Fill A

Pour A B

Fill A

Pour A B

Empty B

Pour A B

Success