Marbles in a Circle

Colored marbles sit in a circle. Each marble is red, white, or green. Every second all marbles change color at the same time, and a marble's new color depends only on its own color and the color of the marble to its right.

The rules for changing color are:

• if the marble is white, its new color is the current color of the marble to its right.
• otherwise, if the marble to its right is white, the marble keeps its color.
• otherwise, if the marble to its right has a different color, the marble becomes white.
• otherwise the marble has the same color as the one to its right, and it flips: red becomes green, green becomes red.

You are given a string $S$ and an integer $N$. Read $S$ as an array of characters of length $L$, so the circle holds $L$ marbles. The character W is a white marble, R is red, and G is green. Marble $i+1$ is to the right of marble $i$, and marble $0$ is to the right of marble $L-1$. Determine the state of the circle after $N$ seconds.

The first line contains $T$ ($T \le 20$), the number of test cases.

Each of the next $T$ lines contains a string $S$ ($1 \le |S| \le 20000$) and an integer $N$ ($1 \le N \le 10^{18}$) separated by a single space. $S$ consists only of the characters W, R, and G.

For each test case, print one line in the form Case #X: W R G, where $X$ is the test case number starting from 1, $W$ is the number of white marbles, $R$ is the number of red marbles, and $G$ is the number of green marbles after $N$ seconds. Separate the four values with a single space.