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: Time Limit Exceeded)

{-# OPTIONS_GHC -O2 -funbox-strict-fields #-}
import           Data.Array.Unboxed
import qualified Data.ByteString.Char8 as BC
import           Data.List             (foldl')
import           Data.Maybe            (fromJust)

main :: IO ()
main = do
  s <- getLine
  [x, y] <- readInts
  putStrLn . showResult $ solve s x y

readInts :: IO [Int]
readInts = map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine

showResult True  = "Yes"
showResult False = "No"

solve :: String -> Int -> Int -> Bool
solve s x y = check dxs x && check (0:dys) y where
  (dxs, dys) = divide2 . map length $ splitOnT s

divide2 xs = (evens, odds) where
  xis   = xs `zip` [0 .. ]
  evens = [x | (x, i) <- xis, i `mod` 2 == 0]
  odds  = [x | (x, i) <- xis, i `mod` 2 == 1]

splitOnT :: String -> [String]
splitOnT = reverse . go [] [] where
  go acc1 acc2 []       = acc2 : acc1
  go acc1 acc2 ('T':xs) = go (acc2 : acc1) [] xs
  go acc1 acc2 (x:xs)   = go acc1 (x : acc2) xs

check :: [Int] -> Int -> Bool
check [] x = x == 0
check (d:ds) x = dp ! x where
  dp = foldl' folder dp0 ds
  dp0 = array (-s, s) $ (d, True) : [(i, False) | i <- [-s .. s], i /= d] :: UArray Int Bool

folder :: UArray Int Bool -> Int -> UArray Int Bool
folder bs d = array (-s, s) [(i, bs `at` (i - d) || bs `at` (i + d)) | i <- [-s .. s]]

s = 8001

at :: UArray Int Bool -> Int -> Bool
at bs i
  | i < -s = False
  | i > s  = False
  | otherwise = bs ! i