Dragon curve

$D_0$ is the string Fa. For $n \ge 1$, build $D_n$ by rewriting every character of $D_{n-1}$:

• a becomes aRbFR.
• b becomes LFaLb.
• F, L, and R stay as they are.

So $D_0$ is Fa, $D_1$ is FaRbFR, and $D_2$ is FaRbFRRLFaLbFR.

Read the string as drawing commands. F means move one unit forward along the current heading and draw the segment, L means turn 90 degrees left, and R means turn 90 degrees right. a and b do nothing. The cursor starts at $(0, 0)$ facing $(0, 1)$. The picture drawn by running all of $D_n$ is the dragon curve of order $n$, and the image above is $D_{10}$.

One F counts as one step. Run the commands of $D_N$ from the beginning and report where the cursor is once it has finished step $X$.

The input holds several test cases. Each line has two integers $X$ and $N$ separated by one space, and the input ends at end of file.

$0 \le X \le 10^{13}$ and $0 \le N \le 100$. $X$ never exceeds the number of F characters in $D_N$. If $X$ is 0, the cursor has not moved yet.

For each test case, print the $x$ coordinate and the $y$ coordinate of the cursor on one line, separated by one space.