Problem:
Score : 500 points

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

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import qualified Data.Set as S
 
type Dir = Int
type Pos = (Int, Int)
type State = (Dir, Pos)
 
main :: IO ()
main = do
  s <- getLine
  [x, y] <- map read . words <$> getLine
  putStr $ solve (x, y) s
 
solve :: Pos -> String -> String
solve z = judge z . mkSet initialState
 
initialState :: State
initialState = (0, (0, 0))
 
judge :: Pos -> S.Set State -> String
judge z set
  | any (`S.member` set) [ (dir, z) | dir <- [0..3] ] = "Yes"
  | otherwise= "No"
 
mkSet :: State -> String -> S.Set State
mkSet sta [] = S.empty
mkSet sta (x:xs) =  bind (mkSet sta xs)  (run x)
 
bind :: S.Set State -> (State -> S.Set State) -> S.Set State
bind s f = joinS $ S.map f s
 
joinS :: S.Set (S.Set State) -> S.Set State
joinS = S.foldr S.union S.empty
 
run :: Char -> State -> S.Set State
run 'F' (0, (x, y)) = S.singleton (0, (x + 1, y))
run 'F' (1, (x, y)) = S.singleton (1, (x, y + 1))
run 'F' (2, (x, y)) = S.singleton (2, (x - 1, y))
run 'F' (3, (x, y)) = S.singleton (3, (x, y - 1))
run 'T' (0, z) = S.fromList [(3, z), (1, z)]
run 'T' (1, z) = S.fromList [(0, z), (2, z)]
run 'T' (2, z) = S.fromList [(1, z), (3, z)]
run 'T' (3, z) = S.fromList [(2, z), (0, z)]