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: Wrong Answer)

s = gets.chomp
x, y = gets.split.map(&:to_i)
s_size = s.size

f_counts = s.split('T').map(&:size)
x_counts = f_counts.select.with_index { |size, i| i.even? }
y_counts = f_counts.select.with_index { |size, i| i.odd? }

def exec_dp(s_size, pos, counts)
  dp = {}
  dp[pos + s_size] = true
  min = s_size
  max = s_size
  counts.each do |c|
    next if c == 0
    new_dp = {}
    new_min = min
    new_max = max
    dp.each do |i, _|
      new_dp[i - c] = true
      new_dp[i + c] = true
    end
    dp = new_dp
  end
  dp
end

xdp = if x_counts.size == 0
  {}
else
  exec_dp(s_size, x_counts[0], x_counts[1..-1])
end
ydp = exec_dp(s_size, 0, y_counts)
xi = x < 0 ? s_size - x.abs : x + s_size
yi = x < 0 ? s_size - y.abs : y + s_size
is_ok = xdp[xi] && ydp[yi]
puts(is_ok ? 'Yes' : 'No')