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TR_GRID - Traversing Grid (challenge)

Starting at the top left corner of an NxM grid and facing towards the right, you keep walking one square at a time in the direction you are facing. If you reach the boundary of the grid or if the next square you are about to visit has already been visited, you turn right. You stop when all the squares in the grid have been visited. What direction will you be facing when you stop?

For example: Consider the case with N=3, M=3. The path followed will be (0,0) -> (0,1) -> (0,2) -> (1,2) -> (2,2) -> (2,1) -> (2,0) -> (1,0) -> (1,1). At this point, all squares have been visited, and you are facing right.

Input

The first line contains T (T<10001) the number of test cases. Each of the next T lines contain two integers N and M (0<N,M<=10⁹), denoting the number of rows and columns respectively.

Output

Output T lines, one for each test case, containing the required direction you will be facing at the end. Output L for left, R for right, U for up, and D for down.

Eample

Input:
4
1 1
2 2
3 1
3 3

Output:
R
L
D
R

Author of this problem is Varun Jalan.

Submit solution!

Added by:	Piotr Kąkol
Date:	2010-04-17
Time limit:	3.263s
Source limit:	50000B
Memory limit:	1536MB
Cluster:	Cube (Intel G860)
Languages:	All except: NODEJS OBJC SCM qobi VB.NET
Resource:	Copy of Varun Jalan's task TRGRID with different scoring

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2013-12-03 13:00:37 Linghui Liu First time to be shortest by only one submission:) Last edit: 2013-12-03 13:01:10
2013-12-02 20:21:10 ওয়াসী (Wasi) ha ha ha! After submitting a 38B solution thought i finally managed the best score for AWK. But here is also same thing best is 37B in AWK(by both dominique and piotr) :D I guess i should start from scratch again :P
2010-04-18 15:34:51 Piotr KÄ…kol Done. :-)
2010-04-17 16:11:23 Piotr KÄ…kol I see I have always to copy file with tests and correct it by such a program: `#include "stdio.h" int main(void) { int t, x, y; scanf("%d",&t); printf("%d\n",t); while(t--) { scanf("%d %d",&x,&y); printf("%d %d\n",x,y); } return 0; }` // Edit: I'll look into it later (probably tomorrow). Sorry. Lack of time today. Last edit: 2010-04-17 16:20:28
2010-04-17 15:55:25 numerix Could you please check the data. I get AC at TRGRID, but RTE at TR_GRID. Edit: Now my AC Lua-Version for TRGRID and TR_GRID has changed to WA after some minutes ... Last edit: 2010-04-17 16:38:42

Shortening codes

TR_GRID - Traversing Grid (challenge)