## Paint Mix

You are given two large pails. One of them (known as the black pail) contains B gallons of black paint. The

other one (known as the white pail) contains W gallons of white paint. You will go through a number of

iterations of pouring paint first from the black pail into the white pail, then from the white pail into the black

pail. More specifically, in each iteration you first pour C cups of paint from the black pail into the white pail

(and thoroughly mix the paint in the white pail), then pour C cups of paint from the white pail back into the

black pail (and thoroughly mix the paint in the black pail). B, W, and C are positive integers; each of B and W

is less than or equal to 50, and C < 16 * B (recall that 1 gallon equals 16 cups). The white pail's capacity is at

least B+W.

As you perform many successive iterations, the ratio of black paint to white paint in each pail will approach

B/W. Although these ratios will never actually be equal to B/W one can ask: how many iterations are needed to

make sure that the black−to−white paint ratio in each of the two pails differs from B/W by less than a certain

tolerance. We define the tolerance to be 0.00001.

The input consists of a number of lines. Each line contains input for one instance of the problem: three
positive integers representing the values for B, W, and C, as described above. The input is terminated with a
line where B = W = C = 0.

Print one line of output for each instance. Each line of output will contain one positive integer: the smallest
number of iterations required such that the black&#8722;to&#8722;white paint ratio in each of the two pails differs from
B/W by less than the tolerance value.

2 1 1
2 1 4
3 20 7
0 0 0

145
38
66