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)

require 'pp'

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

flag = 0
count = 0
x_list = Array.new
y_list = Array.new
while v = s.shift
    if v == "F"
        count += 1
    else
        if flag == 0
            x_list << count
            flag = 1
        else
            y_list << count
            flag = 0
        end
        count = 0
    end
end
if count != 0
    if flag == 0
        x_list << count
    else
        y_list << count
    end
end

dp_x = Array.new
dp_y = Array.new

dp_x[0] = [0]
dp_y[0] = [0]

x_list.each_with_index do |val, i|
    dp_x[i+1] = Array.new(0)
    dp_x[i].each do |w|
        dp_x[i+1].push(w+val)
        dp_x[i+1].push(w-val)
    end
    dp_x[i+1].uniq!
end

y_list.each_with_index do |val, i|
    dp_y[i+1] = Array.new
    dp_y[i].each do |w|
        dp_y[i+1].push(w+val)
        dp_y[i+1].push(w-val)
    end
    dp_y[i+1].uniq!
end

if dp_x[x_list.size].include?(x) && dp_y[y_list.size].include?(y)
    puts "Yes"
else
    puts "No"
end