Problem Statement

A robot is at the origin of a coordinate plane where the positive x-axis points to the right and the positive y-axis points upwards. Initially, the robot is facing the positive x-direction.
You will perform the following operation for $i=1,\ldots,N$ in this order.

• Rotate the robot 90 degrees clockwise or counterclockwise. Then, the robot moves forward A_i units in the direction it is facing.

Can the direction of rotation be chosen so that the robot will be at the coordinates (X,Y) after the N operations?
If it is possible, determine which direction, clockwise or counterclockwise, should be chosen for each operation.

Input

The input is given from Standard Input in the following format:
N X Y
$A_1 \ldots A_N$

Output

If the robot cannot be at the coordinates (X,Y) after the N operations, print No.
If the robot can be at the coordinates (X,Y) after the N operations, the first line should contain Yes, and the second line should contain a string S of length N that satisfies the following condition.
Condition: S consists of L and R, and the following choices can put the robot at the coordinates (X,Y) after the N operations: in the i-th operation, rotate the robot counterclockwise if the i-th character of S is L, and rotate it clockwise if it is R.
If there are multiple solutions, you may print any of them.

Constraints

• $1 \leq N \leq 80$
• $1 \leq A_i \leq 10^7$
• -$10^9\leq X,Y \leq 10^9$
• All input values are integers.

Sample Input 1

3 -2 4
3 2 1

Sample Output 1

Yes
LLR

Initially, the robot is at (0,0) and facing the positive x-direction. The following choices can put the robot at the coordinates (X,Y) after the N operations.

• First operation: Rotate the robot 90 degrees counterclockwise to face the positive y-direction. The robot moves forward A_1=3 units in the direction it is facing, and moves to (0,3).
• Second operation: Rotate the robot 90 degrees counterclockwise to face the negative x-direction. The robot moves forward A_2=2 units in the direction it is facing, and moves to (-2,3).
• Third operation: Rotate the robot 90 degrees clockwise to face the positive y-direction. The robot moves forward A_3=1 unit in the direction it is facing, and moves to (-2,4).

Sample Input 2

1 0 0
1

Sample Output 2

No

Sample Input 3

4 0 0
1 1 1 1

Sample Output 3

Yes
LRRR

Outputs such as LLLL and RRRR are also accepted.

Sample Input 4

14 2543269 -1705099
3 14 159 2653 58979 323846 2643383 2795028 841971 69399 37510 58 20 9

Sample Output 4

Yes
LLLLLLLLLRLRRR

见题面 Input 部分

见题面 Output 部分