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? }

xdp = Array.new(s_size * 2 + 1)
xdp[s_size] = true
x_min = s_size
x_max = s_size
x_counts.each do |c|
  next if c == 0
  (x_min..x_max).each do |i|
    next unless xdp[i]
    xdp[i - c] = true
    xdp[i + c] = true
    x_min = i - c if i - c < x_min
    x_max = i + c if i + c > x_max
  end
end

ydp = Array.new(s_size * 2 + 1)
ydp[s_size] = true
y_min = s_size
y_max = s_size
y_counts.each do |c|
  next if c == 0
  (y_min..y_max).each do |i|
    next unless ydp[i]
    ydp[i - c] = true
    ydp[i + c] = true
    y_min = i - c if i - c < y_min
    y_max = i + c if i + c > y_max
  end
end

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')