Cube

Watson has a cube, which is placed on an infinite plane. We will use Cartesian coordinate system on it. Center of cube's bottom face is located at point $(0,0)$, all its edges are either parallel or orthogonal to the coordinate axes. We will number its faces from $0$ to $5$, in the way that sum of numbers at opposite faces equals $5$, and if we look at the cube along the $Oy$ axis, we will see face $0$, while top and right faces will have numbers $1$ and $2$ correspondingly. We say that this orientation is (0, 1, 2)-orientation of the cube on the plane. Watson is to move the cube to coordinates $(x,y)$ and put it into (a, b, c)-orientation. Cube can be rolled left, right, forward or backward, giving control commands L, R, U, D:

L – roll left ($x$ coordinate is decreased by $1$),

R – roll right ($x$ coordinate is increased by $1$),

U – roll forward ($y$ coordinate is increased by $1$),

D – roll backward ($y$ coordinate is decreased by $1$).

Watson is going to do as little operations as possible, so he wants to build a sequence of control commands as short as possible. If several sequences are possible, he chooses lexicographically smallest one. Certainly, Rybka is assigned to move the cube. Watson started to transfer commands to Rybka, and she started executing them. When $N$ commands have been executed, Watson had to leave by important surgery. Still Rybka does not want to stop and plans to execute additional $K$ commands. Help Rybka to find out necessary sequence of commands.