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 Python (3.4.3) (judge verdict: Accepted)

S = input()
X,Y = map(int,input().split())

# [文字,その文字が連続する数]
from collections import deque
sumS = deque()
import itertools
for key,g in itertools.groupby(S):
  sumS.append([key,len(list(g))])
  
startx = 0 # Fで始まる場合はX軸の正の方向にあらかじめ進めて置く
# 最初のTが出るまではX軸正の方向に進む
if sumS[0][0] == "F":
  startx = sumS[0][1]
  sumS.popleft()

xdir = True # X軸方向を向いている
dpXcur = set()
dpXcur.add(startx)
dpYcur = set()
dpYcur.add(0) # Y軸は必ず0から始まる
dpXnex = set()
dpYnex = set()
for i in range(len(sumS)):
  if sumS[i][0] == "F":
    steps = sumS[i][1] # 進む数
    if xdir: # X軸方向を向いている場合
      for x in dpXcur:
        dpXnex.add(x + steps)
        dpXnex.add(x - steps)
      dpXcur = dpXnex
      dpXnex = set()
    else:
      for y in dpYcur:
        dpYnex.add(y + steps)
        dpYnex.add(y - steps)
      dpYcur = dpYnex
      dpYnex = set()
  elif sumS[i][0] == "T":
    turns = sumS[i][1] # 方向転換する数
    if turns % 2 == 1:
      # 奇数回の場合はX/Y軸の切り替え (偶数回の場合は何も起こらない)
      xdir ^= True
      
if X in dpXcur and Y in dpYcur:
  print("Yes")
else:
  print("No")