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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
    }
    static void Solve()
    {
        var S = sc.ReadStr();
        X = sc.ReadInt();
        Y = sc.ReadInt();
        R = RLE(S).ToArray();
        dir = new Tuple<int, int>[4];
        dir[0] = Tuple.Create(1, 0);
        dir[1] = Tuple.Create(0, -1);
        dir[2] = Tuple.Create(-1, 0);
        dir[3] = Tuple.Create(0, 1);
        var totF = R.Where(r => r.Item1 == 'F').Sum(r => r.Item2);
        if (Rec(0, 0, 0, 0, totF))
        {
            Console.WriteLine("Yes");
        }
        else
        {
            Console.WriteLine("No");
        }
    }
    static int X, Y;
    static bool Rec(int index, int x, int y, int d, int remF)
    {
        if (index == R.Length)
        {
            return x == X && y == Y;
        }
        if (NG.Contains(Tuple.Create(index, x, y, d))) return false;

        var dist = Math.Abs(X - x) + Math.Abs(Y - y);
        if (dist > remF) return false;

        var t = R[index];
        var count = t.Item2;
        var ok = false;
        if (t.Item1 == 'F')
        {
            var nd = d;
            var nx = x + dir[nd].Item1 * count;
            var ny = y + dir[nd].Item2 * count;
            ok |= Rec(index + 1, nx, ny, nd, remF - count);
            if (ok) return true;
        }
        else
        {
            for (int i = 0; i < 2; i++)
            {
                var nd = d;
                if (count % 2 == 0)
                {
                    if (i == 1)
                    {
                        nd += 2;
                        nd %= 4;
                    }
                }
                else
                {
                    if (i == 0) nd += 1;
                    else nd -= 1;
                    if (nd < 0) nd += 4;
                    else nd %= 4;
                }
                var nx = x;
                var ny = y;
                ok |= Rec(index + 1, nx, ny, nd, remF);
                if (ok) return true;
            }
        }
        NG.Add(Tuple.Create(index, x, y, d));
        return false;
    }
    static HashSet<Tuple<int, int, int, int>> NG = new HashSet<Tuple<int, int, int, int>>();
    static Tuple<int, int>[] dir;

    static Tuple<char, int>[] R;
    static IEnumerable<Tuple<char, int>> RLE(string s)
    {
        var count = 1;
        var c = s[0];
        for (int i = 1; i < s.Length; i++)
        {
            if (c == s[i])
            {
                count++;
            }
            else
            {
                yield return Tuple.Create(c, count);
                count = 1;
            }
            c = s[i];
        }
        yield return Tuple.Create(c, count);
    }
    static Scanner sc = new Scanner();
}
class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public Tuple<int, int> ReadTup(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<long, long> ReadTupLong(int add = 0)
    {
        return Tuple.Create(this.ReadLong() + add, this.ReadLong() + add);
    }
    public Tuple<int, int, int> ReadTup3(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<int, int, int, int> ReadTup4(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
    public Tuple<long, long>[] ReadTupLongArray(int n, int add = 0)
    {
        var array = new Tuple<long, long>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTupLong(add);
        }
        return array;
    }
    public Tuple<int, int>[] ReadTupArray(int n, int add = 0)
    {
        var array = new Tuple<int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup(add);
        }
        return array;
    }
    public Tuple<int, int, int>[] ReadTup3Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup3(add);
        }
        return array;
    }
    public Tuple<int, int, int, int>[] ReadTup4Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup4(add);
        }
        return array;
    }
}