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 LuaJIT (2.0.4) (judge verdict: Accepted)

local str = io.read()
local n = #str
local startx = 0
local curlen = 0
local curIsY = false
local xlist = {}
local ylist = {}
local isfirst = true
for i = 1, n do
  if str:sub(i, i) == "F" then
    curlen = curlen + 1
  else
    if curIsY then
      table.insert(ylist, curlen)
    else
      if isfirst then
        startx = curlen
        isfirst = false
      else
        table.insert(xlist, curlen)
      end
    end
    curIsY = not curIsY
    curlen = 0
  end
end
if isfirst then
  startx = startx + curlen
else
  if curIsY then table.insert(ylist, curlen)
  else table.insert(xlist, curlen)
  end
end
local xdst, ydst = io.read("*n", "*n")
xdst = xdst - startx
local xsum, ysum = 0, 0
for i = 1, #xlist do xdst = xdst + xlist[i] end
for i = 1, #ylist do ydst = ydst + ylist[i] end

local function check(list, dst)
  if dst == 0 then return true end
  local t = {}
  local ln = #list
  for i = 1, dst do t[i] = false end
  local curmax = 0
  for i = 1, ln do
    for j = curmax, 1, -1 do
      if t[j] then
        if (j + list[i] * 2) == dst then
          return true
        elseif (j + list[i] * 2) < dst then
          t[j + list[i] * 2] = true
        end
      end
    end
    curmax = curmax + list[i] * 2
    t[list[i] * 2] = true
    if (list[i] * 2) == dst then return true end
  end
  return false
end
print(check(xlist, xdst) and check(ylist, ydst) and "Yes" or "No")