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)

s = gets.chomp
x, y = gets.split.map(&:to_i)
split = s.split("T")

first_step = !split.empty? && split.first.size > 0 ? true : false
horizontal = split.select.with_index { |c, i| i.even? && c.size > 0 }
horizontal_count = horizontal.size
horizontal_max = horizontal.join.size
horizontal_length = horizontal_max * 2 + 1
horizontal_dp = Array.new(horizontal_count + 1) { Array.new(horizontal_length) }
horizontal_dp[0][0] = true
horizontal_count.times do |from|
  dp_next = horizontal_dp[from + 1]
  step = horizontal[from].size
  horizontal_dp[from].each_with_index do |bool, index|
    next unless bool
    dp_next[(index + step) % horizontal_length] = true
    next if from == 0 && first_step
    dp_next[(index - step) % horizontal_length] = true
  end
end

vertical = split.select.with_index { |c, i| i.odd? && c.size > 0 }
vertical_count = vertical.size
vertical_max = vertical.join.size
vertical_length = vertical_max * 2 + 1
vertical_dp = Array.new(vertical_count + 1) { Array.new (vertical_length) }
vertical_dp[0][0] = true
vertical_count.times do |from|
  dp_next = vertical_dp[from + 1]
  step = vertical[from].size
  vertical_dp[from].each_with_index do |bool, index|
    next unless bool
    dp_next[(index + step) %  vertical_length] = true
    dp_next[(index - step) %  vertical_length] = true
  end
end

if x.abs <= horizontal_max && y.abs <= vertical_max && horizontal_dp.last[x] && vertical_dp.last[y]
  puts "Yes"
else
  puts "No"
end