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 Oy axe, 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 plain. 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 it. When N commands have been executed, Watson was drawn away 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.
Input
The first line contains coordinates x and y, not exceeding 10^9 by absolute value.
The second line contains numbers describing required (a, b, c)-orientation (0 ≤ a, b, c < 6).
The third line contains integers N and K – number of executed and planned commands (0 ≤ N ≤ 10^9, 1 ≤ K ≤ 1000).
Output
You need to print "-1" (without quotes), if final state is not reachable, otherwise print sequence of K characters {L, R, U,D or –}.
Character "-" means that it is not necessary to move (final state has been reached).