Programming Problem #4
"Water Measuring"

You are given two plain glass jars A and B with capacities of a and b liters, respectively, and your job is to use A and B to measure exactly c liters of water. The quantities a, b and c are all positive integers. The only operations you are allowed to perform are: 
fill A                 fill B
empty A                empty B
pour A into B          pour B into A
Assuming that A and B are initially empty and that you have an unlimited supply of water, compute a sequence of operations that will leave c liters of water in either A or B. Note that the operation pour A into B only pours water from A into B until A is empty or B is full, whichever comes first; no water is wasted. The operation pour B into A works similarly.

The input consists of one or more lines, each containing three positive integers a, b and c, separated by spaces. All numbers will be less than 1000. For each line of input, output a sequence of operations that solves the problem as shown in the examples below, or output the word "impossible" if no solution exists. Note that spelling and punctuation must be exactly as shown. The problems are numbered consecutively beginning with #1.

Input must be read from the file "prob4.in", and output must be written to the file "prob4.out". All output to the screen will be ignored.

Example Input

<BOF>
7 4 1
2 8 5
3 1 3
<EOF>

Example Output

PROBLEM #1
fill B
pour B into A
fill B
pour B into A
B contains 1 liter of water
PROBLEM #2
impossible
PROBLEM #3
fill A
A contains 3 liters of water
Dr. Eric Shade