Color Change of Go Stones

A box holds plenty of black and white Go stones. Take $n$ stones out of the box. The $m$ stones taken out first are all white and the rest are all black. Lay all $n$ stones around a circle at even spacing, in the order they came out.

Next, look at the colors on that circle and take new stones from the box to build a new circle. Go around the circle once and place one new stone in each gap between two neighboring stones, by these rules.

• Between two white stones, place a black stone.
• Between a white stone and a black stone, place a white stone.
• Between two black stones, place a black stone.
• Between a black stone and a white stone, place a white stone.

There are $n$ gaps, so the new circle holds $n$ stones as well. Once every new stone is in place, remove all $n$ original stones. That is one repetition, and the circle that remains goes through the same process again.

Find how many white stones are on the circle after the $k$-th repetition.

The picture below shows the case $n = 8$, $m = 2$, $k = 2$. From the left: the starting circle, the circle after the first repetition, and the circle after the second repetition.

$n$ and $k$ are natural numbers with $0 < n < 129$ and $k < 10001$. $m$ satisfies $1 \le m \le n$.

Each line holds one group of data. A line has the natural numbers $n$, $m$, $k$ separated by single commas, with no spaces. The line after the last group holds -1, which marks the end of the input.

Print one line for each group of data. A line starts with the input data written back in the form n,m,k, then a colon and one space, then the number of white stones.