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: Time Limit Exceeded)

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

while s[0] == 'F'
    x -= 1
    s.shift
end

moves_x = []
moves_y = []
move_x = true
while s.length > 0 do
    if s[0] == 'T'
        move_x = !move_x
        s.shift
    else
        m = 0
        while s[0] == 'F' do
            s.shift
            m += 1
        end
        if move_x
            moves_x.push(m)
        else
            moves_y.push(m)
        end
    end
end

def check(moves, target)
    len = moves.length
    if len == 0
        return target == 0
    end
    total = moves.inject(:+)
    return false if (total + target) % 2 == 1
    return false if total < target.abs
    target = (total + target) / 2

    dp = Array.new(len){Array.new(target+1)}
    dp[0][0] = true
    dp[0][moves[0]] = true
    (1...len).each do |i|
        (0..target).each do |j|
            dp[i][j] = dp[i - 1][j]
            dp[i][j] ||= dp[i - 1][j - moves[i]] if j - moves[i] >= 0
        end
    end
    return dp[len - 1][target]
end

if check(moves_x, x) && check(moves_y, y)
    puts 'Yes'
else
    puts 'No'
end