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 Ruby (2.3.3) (judge verdict: Accepted)

def s()
  gets().chomp
end
def i()
  gets.to_i
end
def li()
  gets.split.map(&:to_i)
end
def ili()
  n = gets.to_i
  as = gets.split.map(&:to_i)
  [n, as]
end

def get_bits(num)
  res = []
  (2**num).times{|i|
    res << i.to_s(2).rjust(num, "0")
  }
  return res
end

def naive(s, x, y)
  rui = s.count("T")
  bits =  get_bits(rui)
  dir = [1, 0, -1, 0]
  bits.each{|bit|
    vec = 0
    t_pos = 0
    pos = [0,0]
    s.each_char{|c|
      if c == "F"
        pos[0] += dir[vec]
        pos[1] += dir[vec^1]
      else
        if bit[t_pos] == "0"
          vec += 1
        else
          vec -= 1
        end
        if vec == 4 || vec == -5
          vec = 0
        end
        t_pos += 1
      end
    }
    p pos

    if pos[0] == x && pos[1] == y
      # puts "Yes"
      #  exit
    end
  }
  puts "No"
end

def check(moves, target)
  len = moves.length
  if len == 0
    return target == 0
  end
  dp = Array.new(len){Hash.new()}
  dp[0][moves[0]] = true
  dp[0][-moves[0]] = true
  (1...len).each do |i|
    dp[i - 1].each do |key, _|
      dp[i][key+moves[i]] = true
      dp[i][key-moves[i]] = true
    end
  end
  return dp[len - 1][target]
end


s = s()
x, y = li()
t_cnt = s.count("T")

moveCount = [Array.new(t_cnt/2+1, 0),Array.new(t_cnt/2+1, 0)]

currentVec = 0
j = 0
s.each_char{|c|
  if c=="F"
    moveCount[currentVec][j] += 1
  else
    if currentVec == 1
      j+=1
    end
    currentVec ^= 1
  end
}

if t_cnt == s.length
  if x==0 && y==0
    puts  "Yes"
  else
    puts "No"
  end
  exit
end

offset = moveCount[0].shift

if check(moveCount[0], x-offset)&&check(moveCount[1], y)
  puts "Yes"
else
  puts "No"
end