100823: [AtCoder]ABC082 D - FT Robot

Problem Statement

A robot is put at the origin in a two-dimensional plane. Initially, the robot is facing in the positive $x$-axis direction.

This robot will be given an instruction sequence $s$. $s$ consists of the following two kinds of letters, and will be executed in order from front to back.

• F : Move in the current direction by distance $1$.
• T : Turn $90$ degrees, either clockwise or counterclockwise.

The objective of the robot is to be at coordinates $(x, y)$ after all the instructions are executed. Determine whether this objective is achievable.

Constraints

• $s$ consists of F and T.
• $1 \leq |s| \leq 8$ $000$
• $x$ and $y$ are integers.
• $|x|, |y| \leq |s|$

Input

Input is given from Standard Input in the following format:

$s$
$x$ $y$

Output

If the objective is achievable, print Yes; if it is not, print No.

Sample Input 1

FTFFTFFF
4 2

Sample Output 1

Yes

The objective can be achieved by, for example, turning counterclockwise in the first T and turning clockwise in the second T.

Sample Input 2

FTFFTFFF
-2 -2

Sample Output 2

Yes

The objective can be achieved by, for example, turning clockwise in the first T and turning clockwise in the second T.

Sample Input 3

FF
1 0

Sample Output 3

No

Sample Input 4

TF
1 0

Sample Output 4

No

Sample Input 5

FFTTFF
0 0

Sample Output 5

Yes

The objective can be achieved by, for example, turning counterclockwise in the first T and turning counterclockwise in the second T.

Sample Input 6

TTTT
1 0

Sample Output 6

No