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: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Reflection.Emit;
using System.Security.Cryptography;
using System.Text;
namespace Program{
    class MainClass{
        ////////////////////////////////////////////////////////////
        private string s;
        private int x, y;
        private const int size = 8000;
        private const int offs = size / 2;
        void Solve(){
            var xDP = new bool[size, size*2];
            var yDP = new bool[size, size*2];
            io.i(out s, out x, out y);
            var f = s.Split('T').Select(v => v.Length).ToArray();
            var fx = f.Where((v, i) => !i.Odd()).ToArray();            
            var fy = new int[]{0}.Concat(f.Where((v, i) => i.Odd())).ToArray();
            //fy[0]は初期y座標
            
            //x軸検証
            xDP[0, fx[0] + offs] = true;
            for(int i = 1; i < fx.Length; ++i){
                size.REP(j =>{
                    if(0 <= j - fx[i] && j + fx[i] < size) 
                        xDP[i, j] = xDP[i - 1, j - fx[i]] || xDP[i - 1, j + fx[i]];
                });
            }
            //y軸検証
            yDP[0, fy[0] + offs] = true;
            for(int i = 1; i < fy.Length; ++i){
                size.REP(j =>{
                    if(0 <= j - fy[i] && j + fy[i] < size) 
                        yDP[i, j] = yDP[i - 1, j - fy[i]] || yDP[i - 1, j + fy[i]];
                });
            }
            io.Yn(xDP[fx.Length-1,x+offs]&&yDP[fy.Length-1,y+offs]);           
        }

        ////////////////////////////////////////////////////////////
        public static void Main() { new MainClass().Stream(); }
        IO io = new IO();
        Mat mat = new Mat();
        void Stream(){
            Solve();
            io.writeFlush();
        }
        //void Stream() { Test(); io.writeFlush(); }
        void Test() { }
        #region MockMacro
        //cannot use break,continue,goto
        void FOR(int a, int b, Action<int> act){
            for(int i = a; i < b; ++i) act(i);
        }
        void FORR(int a, int b, Action<int> act){
            for(int i = a - 1; i >= b; --i) act(i);
        }
        #endregion
        ////////////////////////////////////////////////////////////
    }
    #region default
    class IO{
        string[] nextBuffer;
        int BufferCnt;
        char[] cs = new char[]{' '};
        StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
        public IO(){
            nextBuffer = new string[0];
            BufferCnt = 0;
            Console.SetOut(sw);
        }
        public string Next(){
            if(BufferCnt < nextBuffer.Length) return nextBuffer[BufferCnt++];
            string st = Console.ReadLine();
            while(st == "") st = Console.ReadLine();
            nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            BufferCnt = 0;
            return nextBuffer[BufferCnt++];
        }
        public string String => Next();
        public char Char => char.Parse(String);
        //public int Int => int.Parse(String);
        public int Int => String.toInt();
        public long Long => String.toLong();
        public double Double => double.Parse(String);
        public string[] arr => Console.ReadLine().Split(' ');
        public char[] arrChar => Array.ConvertAll(arr, char.Parse);
        //public int[] arrInt => Array.ConvertAll(arr, int.Parse);
        public int[] arrInt => arr.Select(v => v.toInt()).ToArray();
        //public long[] arrLong => Array.ConvertAll(arr, long.Parse);
        public long[] arrLong => arr.Select(v => v.toLong()).ToArray();
        public double[] arrDouble => Array.ConvertAll(arr, double.Parse);
        public T i<T>() { return suitType<T>(String); }
        public void i<T>(out T v) { v = suitType<T>(String); }
        public void i<T, U>(out T v1, out U v2){
            i(out v1);
            i(out v2);
        }
        public void i<T, U, V>(out T v1, out U v2, out V v3){
            i(out v1);
            i(out v2);
            i(out v3);
        }
        public void i<T, U, V, W>(out T v1, out U v2, out V v3, out W v4){
            i(out v1);
            i(out v2);
            i(out v3);
            i(out v4);
        }
        public void i<T, U, V, W, X>(out T v1, out U v2, out V v3, out W v4, out X v5){
            i(out v1);
            i(out v2);
            i(out v3);
            i(out v4);
            i(out v5);
        }
        public void ini<T>(out T[] a, int n){
            a = new T[n];
            for(int i = 0; i < n; ++i) a[i] = suitType<T>(String);
        }
        public void ini<T, U>(out T[] a, out U[] b, int n){
            a = new T[n];
            b = new U[n];
            for(int i = 0; i < n; ++i){
                a[i] = i<T>();
                b[i] = i<U>();
            }
        }
        public void ini<T, U, V>(out T[] a, out U[] b, out V[] c, int n){
            a = new T[n];
            b = new U[n];
            c = new V[n];
            for(int i = 0; i < n; ++i){
                a[i] = i<T>();
                b[i] = i<U>();
                c[i] = i<V>();
            }
        }
        public void ini<T, U>(out Tuple<T, U>[] t, int n){
            t = new Tuple<T, U>[n];
            for(int j = 0; j < n; ++j){
                T i1;
                U i2;
                i(out i1);
                i(out i2);
                t[j] = Tuple.Create(i1, i2);
            }
        }
        public void ini<T, U, V>(out Tuple<T, U, V>[] t, int n){
            t = new Tuple<T, U, V>[n];
            for(int j = 0; j < n; ++j){
                T i1;
                U i2;
                V i3;
                i(out i1);
                i(out i2);
                i(out i3);
                t[j] = Tuple.Create(i1, i2, i3);
            }
        }
        public void ini<T>(out T[,] a, int h, int w){
            a = new T[h, w];
            for(int i = 0; i < h; ++i) for(int j = 0; j < w; ++j) a[i, j] = i<T>();
        }
        public void o<T>(T v) { Console.WriteLine(v); }
        public void o<T>(params T[] a) { Array.ForEach(a, n => o(n)); }
        public void o<T>(T[,] a){
            int a0 = a.GetLength(0), a1 = a.GetLength(1);
            for(int i = 0; i < a0; ++i){
                for(int j = 0; j < a1 - 1; ++j) Console.Write(a[i, j] + " ");
                Console.WriteLine(a[i, a1 - 1]);
            }
        }
        public void YN(bool f) { o(f ? "YES" : "NO"); }
        public void Yn(bool f) { o(f ? "Yes" : "No"); }
        public void yn(bool f) { o(f ? "yes" : "no"); }
        public void ol<T>(params T[] a) { o(connect<T>(a)); }
        public void or<T>(T a) { Console.Write(a); }
        public void br() { o(""); }
        public void writeFlush() { Console.Out.Flush(); }
        private string connect<T>(params T[] s) { return string.Join(" ", s); }
        private bool typeEQ<T, U>() { return typeof(T).Equals(typeof(U)); }
        private T convertType<T, U>(U v) { return (T) Convert.ChangeType(v, typeof(T)); }
        private T suitType<T>(string s){
            if(typeEQ<T, int>()) return convertType<T, int>(int.Parse(s));
            if(typeEQ<T, long>()) return convertType<T, long>(long.Parse(s));
            if(typeEQ<T, double>()) return convertType<T, double>(double.Parse(s));
            if(typeEQ<T, char>()) return convertType<T, char>(char.Parse(s));
            return convertType<T, string>(s);
        }
    }
    class PQueue<T> where T : struct, IComparable<T>{
        public List<T> heap;
        private Comparison<T> comp;
        private IComparer<T> comparer;
        private int size;
        private int type;//type=0->min
        public PQueue(int type = 0) : this(Comparer<T>.Default) { this.type = type; }
        public PQueue(IComparer<T> comparer) : this(16, comparer.Compare) { this.comparer = comparer; }
        public PQueue(Comparison<T> comparison) : this(16, comparison) { }
        public PQueue(int capacity, Comparison<T> comparison){
            this.heap = new List<T>(capacity);
            this.comp = comparison;
        }
        public void Enqueue(T item){
            this.heap.Add(item);
            var i = size++;
            while(i > 0){
                var p = (i - 1) >> 1;
                if(Compare(this.heap[p], item) <= 0) break;
                this.heap[i] = heap[p];
                i = p;
            }
            this.heap[i] = item;
        }
        public T Dequeue(){
            var ret = this.heap[0];
            var x = this.heap[--size];
            var i = 0;
            while((i << 1) + 1 < size){
                var a = (i << 1) + 1;
                var b = (i << 1) + 2;
                if(b < size && Compare(heap[b], heap[a]) < 0) a = b;
                if(Compare(heap[a], x) >= 0) break;
                heap[i] = heap[a];
                i = a;
            }
            heap[i] = x;
            heap.RemoveAt(size);
            return ret;
        }
        public T Peek() { return heap[0]; }
        public int Count { get { return size; } }
        public bool Any() { return size > 0; }
        public bool Empty() { return !Any(); }
        public bool Contains(T v) { return heap.Contains(v); }
        private int Compare(T x, T y) { return type == 0 ? x.CompareTo(y) : y.CompareTo(x); }
    }
    class AssociativeArray<T> : IEnumerable{
        public Dictionary<T, int> dic;
        public AssociativeArray() { dic = new Dictionary<T, int>(); }
        public AssociativeArray(params T[] a){
            dic = new Dictionary<T, int>();
            Add(a);
        }
        public void Add(T a){
            if(!conK(a)) dic[a] = 0;
            dic[a]++;
        }
        public void Add(params T[] a){
            a.Length.REP(i =>{
                if(!conK(a[i])) dic[a[i]] = 0;
                dic[a[i]]++;
            });
        }
        public void Set(T k, int v){
            if(!dic.ContainsKey(k)) dic[k] = 0;
            dic[k] = v;
        }
        public void Remove(params T[] a){
            a.Length.REP(i =>{
                if(conK(a[i])) dic.Remove(a[i]);
            });
        }
        public T[] Keys() { return dic.Keys.ToArray<T>(); }
        public int Val(T k) { return (dic.ContainsKey(k)) ? dic[k] : 0; }
        public int Val(params T[] k) { return k.Aggregate(0, (x, xs) => x + Val(xs)); }
        public int ValSum => dic.Values.Sum();
        public int KeyNum => dic.Keys.Count;
        public int MaxVal => dic.Values.Max();
        public int MinVal => dic.Values.Min();
        public T MaxKey => MaxK();
        public T MinKey => MinK();
        public T MaxK(){
            var maxV = MaxVal;
            return dic.First(d => d.Value == maxV).Key;
        }
        public T MinK(){
            var minV = MinVal;
            return dic.First(d => d.Value == minV).Key;
        }
        public T[] MaxKeys(){
            var maxV = MaxVal;
            return dic.Where(kp => kp.Value == maxV).ToDictionary(kp => kp.Key, kp => kp.Value).Keys.ToArray();
        }
        public T[] MinKeys(){
            var minV = MinVal;
            return dic.Where(kp => kp.Value == minV).ToDictionary(kp => kp.Key, kp => kp.Value).Keys.ToArray();
        }
        public bool conK(T k) { return dic.ContainsKey(k); }
        public bool anyK(params T[] k) { return k.Any(key => conK(key)); }
        public bool allK(params T[] k) { return k.All(key => conK(key)); }
        public void Show(){
            foreach(var v in dic) { Console.WriteLine(v.Key + " : " + v.Value); }
        }
        public T[] ValueSortedKey(bool inc = true) { return (inc ? (dic.OrderBy(kp => kp.Value)) : (dic.OrderByDescending(kp => kp.Value))).ThenBy(kp => kp.Key).ToDictionary(kp => kp.Key, kp => kp.Value).Keys.ToArray(); }
        public IEnumerator GetEnumerator(){
            foreach(var kp in dic) yield return kp;
        }
        //:sort->array
    }
    public struct edge : IComparable<edge>{
        public int to;
        public long cost;
        public edge(int to, long cost){
            this.to = to;
            this.cost = cost;
        }
        public int CompareTo(edge e) { return cost.CompareTo(e.cost); }
    }
    public struct Indexed : IComparable<Indexed>{
        public long Value;
        public int Index;
        public Indexed(long value, int index){
            Value = value;
            Index = index;
        }
        public int CompareTo(Indexed i) { return Value.CompareTo(i.Value); }
    }
    class Mat{
        public long mod = 1000000007;//10^9+7
        public long Pow(long a, long b){
            if(b == 0) return 1;
            if(b % 2 == 1) return (a % mod * Pow(a % mod, b - 1) % mod) % mod;
            else return Pow(a * a % mod, b / 2) % mod;
        }
        public long Fact(long n){
            long ret = 1;
            for(long i = 1; i <= n; i++) ret = (ret * i) % mod;
            return ret;
        }
        public long ModC(long n, long r){
            if(r == 0 || n == r) return 1;
            if(n == 0) return 0;
            if(n < 0 || n < r) throw new ArgumentException("n,r invalid");
            else return (Fact(n) % mod * Pow((Fact(n - r) % mod * Fact(r) % mod) % mod, mod - 2) % mod) % mod;
        }
        public long[,] C(int N){
            long[,] Co = new long[N + 1, N + 1];
            (N + 1).REP(i => (i + 1).REP(j => Co[i, j] = (j == 0 || j == i) ? 1L : Co[i - 1, j - 1] + Co[i - 1, j]));
            return Co;
        }
        public long DupC(long n, long r) { return ModC(n + r - 1, r); }
        public long P(long n, long r) { return Fact(n) / (Fact(n - r)); }//test
        public bool isPrime(long n){
            if(n == 2) return true;
            if(n < 2 || n % 2 == 0) return false;
            for(long v = 3; v <= (long) Math.Sqrt(n); v += 2) if(n % v == 0) return false;
            return true;
        }
        public long LCM(long a, long b) { return a * (b / GCD(a, b)); }
        public long LCM(params long[] a) { return a.Aggregate((v, n) => LCM(v, n)); }
        public long GCD(long a, long b){
            if(a < b) Swap(ref a, ref b);
            return b == 0 ? a : GCD(b, a % b);
        }
        public long GCD(params long[] array) { return array.Aggregate((v, n) => GCD(v, n)); }
        public T Max<T>(params T[] a) { return a.Max(); }
        public T Min<T>(params T[] a) { return a.Min(); }
        public void Swap<T>(ref T a, ref T b){
            T tmp = a;
            a = b;
            b = tmp;
        }
        public double Dis(int x1, int y1, int x2, int y2) { return Math.Sqrt(Math.Pow((x2 - x1), 2) + Math.Pow((y2 - y1), 2)); }
        public int mDis(int x1, int y1, int x2, int y2) { return Math.Abs(x1 - x2) + Math.Abs(y1 - y2); }
        public int[] DigArr(int n){
            int[] ret = new int[Digit(n)];
            ret.Length.REP(i => ret[i] = DigVal(n, i + 1));
            return ret;
        }
        public long DigArr2Num(IEnumerable<int> enu) { return enu.Aggregate((v, n) => v * 10 + n); }
        public int Digit(long n) { return (n == 0) ? 1 : (int) Math.Log10(n) + 1; }
        public int DigVal(int n, int dig) { return (n % (int) Pow(10, dig)) / (int) Pow(10, dig - 1); }
        public long Tousa(long a, long d, long n) { return a + (n - 1) * d; }
        public long TousaSum(long a, long d, long n) { return n * (2 * a + (n - 1) * d) / 2; }
        public long[] EnuDivsor(long N){
            var ret = new SortedSet<long>();
            for(long i = 1; i * i <= N; i++)
                if(N % i == 0){
                    ret.Add(i);
                    ret.Add(N / i);
                }
            return ret.ToArray();
        }
        public Dictionary<long, long> PrimeFactor(long n){
            var ret = new Dictionary<long, long>();
            for(int i = 2; i * i <= n; ++i){
                if(!ret.ContainsKey(i)) ret[i] = 0;
                while(n % i == 0){
                    ++ret[i];
                    n /= i;
                }
            }
            return ret.Where(kp => kp.Value != 0).ToDictionary(kp => kp.Key, kp => kp.Value);
        }
    }
    #endregion
    #region Ex
    static class StringEX{
        public static string Reversed(this string s) { return string.Join("", s.Reverse()); }
        public static string Repeat(this string s, int n) { return string.Concat(Enumerable.Repeat(s, n).ToArray()); }
        public static int toInt(this string s){
            int n;
            return (int.TryParse(s.TrimStart('0'), out n)) ? n : 0;
        }
        public static int toInt(this char c) { return toInt(c.ToString()); }
        public static int toInt(this char[] c) { return toInt(new string(c)); }
        public static long[] toLong(this int[] a) { return a.Select(v => (long) v).ToArray(); }
        public static long[,] toLong(this int[,] m){
            var h = m.GetLength(0);
            var w = m.GetLength(1);
            var ret = new long[h, w];
            for(int i = 0; i < h; ++i) for(int j = 0; j < w; ++j) ret[i, j] = (long) m[i, j];
            return ret;
        }
        public static long toLong(this string s){
            long n;
            return (long.TryParse(s.TrimStart('0'), out n)) ? n : (long) 0;
        }
        public static long toLong(this char c) { return toLong(c.ToString()); }
        public static long toLong(this char[] c) { return toLong(new string(c)); }
        public static string toString(this char[] c) { return new string(c); }
    }
    static class NumericEx{
        public static string pad0<T>(this T v, int n) { return v.ToString().PadLeft(n, '0'); }
        public static double RoundOff(this double v, int n) { return Math.Round(v, n - 1, MidpointRounding.AwayFromZero); }
        public static double RoundUp(this double v) { return Math.Ceiling(v); }
        public static double RoundDown(this double v) { return Math.Floor(v); }
        public static bool Odd(this int v) { return v % 2 != 0; }
        public static bool Odd(this long v) { return v % 2 != 0; }
        public static void REP(this int v, Action<int> act){
            for(int i = 0; i < v; ++i) act(i);
        }
        public static void REPR(this int v, Action<int> act){
            for(int i = v - 1; i >= 0; --i) act(i);
        }
    }
    static class ArrayEX{
        public static T[] Sort<T>(this T[] a){
            Array.Sort(a);
            return a;
        }
        public static T[] SortR<T>(this T[] a){
            Array.Sort(a);
            Array.Reverse(a);
            return a;
        }
        public static void Set<T>(this T[] a, T v) { a.Length.REP(i => a[i] = v); }
        public static void Set<T>(this T[,] a, T v) { a.GetLength(0).REP(i => a.GetLength(1).REP(j => a[i, j] = v)); }
        public static int[] toIntArr(this string a) { return a.Select(c => c.toInt()).ToArray(); }
        public static int[] toIntArr(this string[] a) { return Array.ConvertAll(a, int.Parse); }
        public static long[] toLongArr(this string a) { return a.Select(c => c.toLong()).ToArray(); }
        public static long[] toLongArr(this string[] a) { return Array.ConvertAll(a, long.Parse); }
        public static double[] toDoubleArr(this string[] a) { return Array.ConvertAll(a, double.Parse); }
        public static char[] toCharArr(this string[] a) { return Array.ConvertAll(a, char.Parse); }
        public static int LowerBound<T>(this T[] a, T x) where T : IComparable{
            Array.Sort(a);
            int lb = -1, ub = a.Length;
            while(ub - lb > 1){
                int mid = (ub + lb) / 2;
                if(a[mid].CompareTo(x) >= 0) ub = mid;
                else lb = mid;
            }
            return ub;
        }
        public static int UpperBound<T>(this T[] a, T x) where T : IComparable{
            Array.Sort(a);
            int lb = -1, ub = a.Length;
            while(ub - lb > 1){
                int mid = (ub + lb) / 2;
                if(a[mid].CompareTo(x) > 0) ub = mid;
                else lb = mid;
            }
            return ub;
        }
    }
    #endregion
}