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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
//using System.Numerics;  //comment out if AOJ
using System.Text;

using Problem = Tmp.Problem;
using MyIO;

#pragma warning disable   //for AOJ

namespace Tmp
{
    class Problem : IDisposable
    {
        bool IsGCJ;
        int Repeat;
        Scanner sc;
        Printer pr;
        public Problem(bool isGCJ, Scanner scanner, Printer printer)
        {
            sc = scanner;
            pr = printer;
            IsGCJ = isGCJ;
            if (isGCJ) Repeat = sc.nextInt();
            else Read();
        }
        public Problem(bool isGCJ) : this(isGCJ, new Scanner(), new Printer()) { }
        public Problem(bool isGCJ, Scanner scanner) : this(isGCJ, scanner, new Printer()) { }
        public Problem(bool isGCJ, Printer printer) : this(isGCJ, new Scanner(), printer) { }
        public void Solve()
        {
            if (IsGCJ) for (var i = 0; i < Repeat; i++) { Read(); pr.Write("Case #" + (i + 1) + ": "); SolveOne(); }
            else SolveOne();
        }
        public void Dispose()
        {
            sc.Dispose();
            pr.Dispose();
        }
        public int Size { get { return 1; } }
        public const long Mod = 1000000007;

        // 使用する変数をここに書く
        // string S;
        // int a;
        int x, y;
        List<int> xls, yls;
        int xsum, ysum;
        bool xok, yok;
        /// <summary>
        /// 読み込み処理をここに書く
        /// </summary>
        void Read()
        {

        }
        /// <summary>
        /// メイン処理をここに書く
        /// </summary>
        void SolveOne()
        {
            string s = sc.next();
            x = sc.nextInt();
            y = sc.nextInt();
            xls = new List<int>();
            yls = new List<int>();
            xsum = 0;
            ysum = 0;
            xok = false;
            yok = false;
            bool xAxes = true;
            bool turned = false;

            int tmp = 0;
            for (int i = 0; i < s.Length; i++)
            {
                if(s[i] == 'F')
                {
                    tmp++;

                }
                if(s[i] =='T' || i == s.Length-1)
                {
                    if (turned)
                    {
                        if (tmp > 0)
                        {
                            if (xAxes)
                            {
                                xls.Add(tmp);
                                xsum += tmp;
                            }
                            else
                            {
                                yls.Add(tmp);
                                ysum += tmp;
                            }
                        }
                    }
                    else
                    {
                        x -= tmp;
                        turned = true;
                    }
                    xAxes = !xAxes;
                    tmp = 0;
                }
            }
            HashSet<int> xSet = new HashSet<int>();
            xSet.Add(0);
            if (xsum == x || -xsum == x) xok = true;
            for (int i = 0; i < xls.Count; i++)
            {
                List<int> lstmp = new List<int>();
                foreach (var v in xSet)
                {
                    lstmp.Add(v + xls[i]);
                }
                foreach (var v in lstmp)
                {
                    xSet.Add(v);
                    if (xsum - 2 * v == x || 2 * v - xsum == x)
                    {
                        xok = true;
                        break;
                    }
                }
                if (xok) break;
            }

            HashSet<int> ySet = new HashSet<int>();
            ySet.Add(0);
            if (ysum == y || -ysum == y) yok = true;

            for (int i = 0; i < yls.Count; i++)
            {
                List<int> lstmp = new List<int>();
                foreach (var v in ySet)
                {
                    lstmp.Add(v + yls[i]);
                }
                foreach (var v in lstmp)
                {
                    ySet.Add(v);
                    if (ysum - 2 * v == y || 2 * v - ysum == y)
                    {
                        yok = true;
                        break;
                    }
                }
                if (yok) break;
            }

            if (xok && yok) Console.WriteLine("Yes");
            else Console.WriteLine("No");
        }

    }
}
class Program
{
    //public static RandomSFMT rand = new RandomSFMT();
    public static bool IsJudgeMode = true;
    public static bool IsGCJMode = false;
    public static bool IsSolveCreated = true;
    static void Main()
    {
        if (IsJudgeMode)
            if (IsGCJMode) using (var problem = new Problem(true, new Scanner("C-large-practice.in.txt"), new Printer("output.txt"))) problem.Solve();
            else using (var problem = new Problem(false, new Printer())) problem.Solve();
        else
        {
            var num = 1;
            int size = 0;
            decimal time = 0;
            for (var tmp = 0; tmp < num; tmp++)
            {
                using (var P = IsSolveCreated ? new Problem(false, new Scanner("input.txt"), new Printer()) : new Problem(false))
                {
                    size = P.Size;
                    //time += Func.MeasureTime(() => P.Solve());
                }
            }
            Console.WriteLine("{0}, {1}ms", size, time / num);
        }
    }
}

/// <summary>
/// カスタマイズしたIO
/// </summary>
namespace MyIO
{
    class Printer : IDisposable
    {
        bool isConsole;
        TextWriter file;
        public Printer() { file = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; isConsole = true; }
        public Printer(string path) { file = new StreamWriter(path, false) { AutoFlush = false }; isConsole = false; }
        public void Write<T>(T value) { file.Write(value); }
        public void Write(bool b) { file.Write(b ? "YES" : "NO"); }
        public void Write(string str, params object[] args) { file.Write(str, args); }
        public void WriteLine() { file.WriteLine(); }
        public void WriteLine<T>(T value) { file.WriteLine(value); }
        public void WriteLine(bool b) { file.WriteLine(b ? "YES" : "NO"); }
        public void WriteLine<T>(IEnumerable<T> list) { foreach (var x in list) file.WriteLine(x); }
        public void WriteLine<T>(List<T> list) { foreach (var x in list) file.WriteLine(x); }
        public void WriteLine<T>(T[] list) { foreach (var x in list) file.WriteLine(x); }
        public void WriteLine(string str, params object[] args) { file.WriteLine(str, args); }
        public void Dispose() { file.Flush(); if (!isConsole) file.Dispose(); }
    }
    class Scanner : IDisposable
    {
        bool isConsole;
        TextReader file;
        public Scanner() { file = Console.In; }
        public Scanner(string path) { file = new StreamReader(path); isConsole = false; }
        public void Dispose() { if (!isConsole) file.Dispose(); }

        #region next読み込み
        string[] nextBuffer = new string[0];
        int BufferCnt = 0;

        char[] cs = new char[] { ' ' };

        public string next()
        {
            while (BufferCnt >= nextBuffer.Length)
            {
                string st = file.ReadLine();
                while (st == "") st = file.ReadLine();
                nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
                BufferCnt = 0;
            }
            return nextBuffer[BufferCnt++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }

        private T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public string[] next(int n) { return enumerate(n, next); }
        public double[] nextDouble(int n) { return enumerate(n, nextDouble); }
        public int[] nextInt(int n) { return enumerate(n, nextInt); }
        public long[] nextLong(int n) { return enumerate(n, nextLong); }
        #endregion
    }
}