Problem Statement

Consider an infinite two-dimensional coordinate plane.
Takahashi, who is initially standing at (0,0), will do N jumps in one of the four directions he chooses every time: up, down, left, or right.
The length of each jump is fixed. Specifically, the i-th jump should cover the distance of D_i.
Determine whether it is possible to be exactly at (A, B) after N jumps. If it is possible, show one way to do so.
Here, for each direction, a jump of length D from (X, Y) takes him to the following point:

• up: $(X,Y) \to$ (X,Y+D)
• down: $(X,Y) \to$ (X,Y-D)
• left: $(X,Y) \to$ (X-D,Y)
• right: $(X,Y) \to$ (X+D,Y).

Input

Input is given from Standard Input in the following format:
N A B
$D_1 D_2 \ldots D_N$

Output

In the first line, print Yes if there is a desired sequence of jumps, and No otherwise.
In the case of Yes, print in the second line a desired sequence of jumps as a string S of length N consisting of U , D , L , R, as follows:

• if the i-th jump is upward, the i-th character should be U;
• if the i-th jump is downward, the i-th character should be D;
• if the i-th jump is to the left, the i-th character should be L;
• if the i-th jump is to the right, the i-th character should be R.

Constraints

• $1 \leq N \leq 2000$
• $\lvert A\rvert, \lvert B\rvert \leq 3.6\times 10^6$
• $1 \leq D_i \leq 1800$
• All values in input are integers.

Sample Input 1

3 2 -2
1 2 3

Sample Output 1

Yes
LDR

If he jumps left, down, right in this order, Takahashi moves $(0,0)\to(-1,0)\to(-1,-2)\to(2,-2)$ and ends up at (2, -2), which is desired.

Sample Input 2

2 1 0
1 6

Sample Output 2

No

It is impossible to be exactly at (1, 0) after the two jumps.

Sample Input 3

5 6 7
1 3 5 7 9

Sample Output 3

Yes
LRLUR

见题面 Input 部分

见题面 Output 部分