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)

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

first = 0
while ss[0] == 'F' do
    first += 1
    ss.shift
end

verts = []
vi = 0
horis = []
hi = 0
hori_now = true

while ss.length > 0 do
    s = ss.shift
    if s == 'F'
        if hori_now
            horis[hi] ||= 0
            horis[hi] += 1
        else
            verts[vi] ||= 0
            verts[vi] += 1
        end
    else
        if hori_now
            hori_now = false
            hi += 1
        else
            hori_now = true
            vi += 1
        end
    end
end

verts.compact!
horis.compact!

def check(arr, target)
    n = arr.length

    if n == 0
        return target == 0
    end
    
    sum = arr.inject(:+)

    if (target + sum) % 2 == 1
        return false
    end
    target = (target + sum) / 2
    dp = Array.new(n + 1){Array.new(sum + 1, false)}
    dp[0][0] = true
    arr.each do |a|
        dp[0][a] = true
    end

    (1...n).each do |i|
        (0..sum).each do |j|
            dp[i][j] = dp[i - 1][j]
            dp[i][j] ||= dp[i - 1][j - arr[i]] if j - arr[i] >= 0
        end
    end
    return dp[n - 1][sum]
end

if check(verts, y) && check(horis, x - first)
    print 'Yes'
else
    print 'No'
end