Color game

Vasya plays an intricate game. In front of him are several circles with colored points, and each circle has the same number of points. Note that the circles themselves are arranged in a circle. All circles are numbered from $1$ to $N$, and the points on these circles are numbered from $1$ to $M$. Each point is colored in one of $30$ colors.

Initially, Vasya puts a token on the first point of the first circle. Then he moves the token $T$ times as follows:

1. Let the token be in circle $C$ at the point numbered $P$.

2. Let $S$ be the number of different colors among the points in the $K$-neighborhood of point $P$ on circle $C$, that is, on the segment [P-K, P+K]. Note that the segment wraps around the circle, so point $M$ is followed by point $1$. For example, if M = 6, P = 5, K = 2, then the segment [P-2, P+2] consists of points $[3,6]$ and $[1,1]$.

3. Move the token to circle (N-C+1)+S at point P+S. Note that the circles themselves are arranged in a circle, and after circle $N$ comes circle $1$.

Vasya wants to determine, after all these moves, on which circle and at which point the token will be.

Consider an example. Let N = 5, M = 4, K = 1. In this example, only two colors are used: black and white. The dotted lines in the picture show the neighborhoods of the points where the token was.

Initially, C = 1, P = 1. In the $1$-neighborhood there are both colors, that is S = 2. Hence, C' = (5-1+1)+2=2, P' = 1+2 = 3. At this new position, the $1$-neighborhood contains only white color, so S = 1. C''=(5-2+1)+1=5, P''=3+1=4. Finally, in the next-to-last position, the $1$-neighborhood contains both colors, S = 2, C'''=(5-5+1)+2=3, P'''=4+2=2.

Given a set of circles and the number $T$, find where the token will be after $T$ moves.

Note that the given circles have the following property: for i = 1, 2, \ldots, N-1, circle $i$ differs from circle i+1 in at most one point.