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 Lua (5.3.2) (judge verdict: Time Limit Exceeded)


-- F
local sub = string.sub
local insert = table.insert
s = io.read("*l")
x, y = io.read("*n", "*n", "*l")

local t1 = {}
local ok1 = false
local function dfs1(i, val)
	if ok1 then
		return true
	end
	if i == 0 then
		if val == 0 then
			ok1 = true
			return true
		end
		return false
	end
	return dfs1(i-1, val-t1[i]) or dfs1(i-1, val+t1[i])
end
local t2 = {}
local ok2 = false
local function dfs2(i, val)
	if ok2 then
		return true
	end
	if i == 0 then
		if val == 0 then
			ok2 = true
			return true
		end
		return false
	end
	return dfs2(i-1, val-t2[i]) or dfs2(i-1, val+t2[i])
end

local function solve()
	local n = 0
	local dirchange = false
	local dir = true -- x zhou
	-- first
	local st = 1
	while sub(s, st, st) == "F" do
		st = st + 1
	end
	x = x - (st - 1)
	for i = st, #s do
		local c = sub(s, i, i)
		if c == "F" then
			n = n + 1
		else
			if n ~= 0 then
				if dir then
					insert(t1, n)
				else
					insert(t2, n)
				end
				n = 0
				dirchange = false
			end
			dirchange = true
			dir = not dir
		end
	end
	if n ~= 0 then
		if dir then
			insert(t1, n)
		else
			insert(t2, n)
		end
	end
	if  dfs1(#t1, x) and dfs2(#t2, y) then
		return "Yes"
	else
		return "No"
	end
end
print(solve())