Problem Description

A robot is placed at point \( (0,0) \) on the \( xy \)-plane. You can give this robot a string consisting of L, R, U, D as an instruction. When given the string, the robot will move according to the characters in the string, starting from the first character: L means moving \( -1 \) in the \( x \)-axis direction, R means moving \( +1 \) in the \( x \)-axis direction, U means moving \( +1 \) in the \( y \)-axis direction, and D means moving \( -1 \) in the \( y \)-axis direction, until the last character is processed.

You have a string \( S \) consisting of W, X, Y, Z. You are trying to replace these four types of characters with either L, R, U, or D to form a string to give to the robot. However, different characters in \( S \) cannot be assigned the same character in the instruction.

You are given a string \( S \) and integers \( g_x \), \( g_y \). Determine if it is possible, through appropriate character assignments, for the robot to pass through the coordinate \( (g_x, g_y) \) at any point from the start to the end of its movement (including the start and end points). If possible, output Yes; otherwise, output No.

Input Format

The input is given from the standard input in the following format:

\( S \) \( g_x \) \( g_y \)

Output Format

Output Yes if it is possible for the robot to pass through the coordinate \( (g_x, g_y) \) at any point from the start to the end of its movement (including the start and end points) through appropriate character assignments. Otherwise, output No.

Sample Input and Output

Sample Input #1

WWYWYWWW
3 0

Sample Output #1

Yes

Sample Input #2

YYYYW
-1 -3

Sample Output #2

No

Sample Input #3

WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
0 50

Sample Output #3

Yes

Notes/Hints

Constraints

• \( 1 \leq |S| \leq 10^5 \)
• \( S \) is a string consisting of W, X, Y, Z
• \( |g_x|, |g_y| \leq 10^5 \)
• \( g_x \), \( g_y \) are integers

Sample Explanation 1

For example, by assigning W to R, X to U, Y to L, and Z to D, it is possible to pass through \( (3,0) \).

见题面 Input 部分

见题面 Output 部分