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 (Lua 5.3.5) (judge verdict: Wrong Answer)

local str = io.read("*l")
local finalA = io.read("*n")
local finalB = io.read("*n")


local tb = {}
for i = 1, string.len(str) do
    table.insert(tb,string.sub(str,i,i))
end

local dirTb = {
    {0,1},
    {0,-1},
    {-1,0},
    {1,0}
}

local turnTb = {
    {3,4},
    {3,4},
    {1,2},
    {1,2}
}
local function digui( a,b,idx,curDir )
    print(a.." "..b)
    if a == finalA and b == finalB and idx == #tb + 1 then
        return true
    end

    if idx > #tb then
        return false
    end

    if math.abs(a) > #tb or math.abs(b) > #tb then
        return false
    end

    if tb[idx] == 'F' then
        return digui(a+dirTb[curDir][1],b+dirTb[curDir][2],idx+1,curDir)
    else
        return digui(a,b,idx+1,turnTb[curDir][1]) or digui(a,b,idx+1,turnTb[curDir][2]) 
    end

end

local f = digui(0,0,1,1) or digui(0,0,1,2) or digui(0,0,1,3) or digui(0,0,1,4)
print(f and "yes" or "no")