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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;
using static _20200218.Cin;
using static _20200218.Util;
using Pair = _20200218.VTuple<long, long>;
using Graph = System.Collections.Generic.List<System.Collections.Generic.List<long>>;
using System.Text;

namespace _20200218
{
    public class Program
    {
        public static void Main(string[] args)
        {
            // A(); 15m
            // B(); 21m
            // C(); 32m
            // D(); 43m
            // E(); 67m
            // F(); 92m
            // G(); 110m

            // ABC057_C();11m
            // ABC142_D(); // 60m
            ARC087_D();
        }

        public static void ARC087_D()
        {
            const long MC = 8001;
            string s = rs;
            long x = rl;
            long y = rl;
            bool[][] dp = new bool[2][];
            dp[0] = new bool[MC];
            dp[1] = new bool[MC];
            dp[0][0] = true;
            dp[1][0] = true;

            s += "T";
            int i = 0;
            while (i < s.Length && s[i] == 'F')
                i++;
            x -= i;
            if (Abs(x) + i >= MC)
            {
                Console.WriteLine("No");
                return;
            }

            int turn = 0;
            long cnt = 0;
            for (; i < s.Length; i++)
            {
                if(s[i] == 'F')
                {
                    cnt++;
                }
                else
                {
                    bool[] nxt = new bool[MC];
                    for (int j = 0; j < i; j++)
                    {
                        if (!dp[turn][j]) continue;
                        nxt[j + cnt] = nxt[Abs(j - cnt)] = true;
                    }

                    dp[turn] = nxt;
                    cnt = 0;
                    turn ^= 1;
                }
            }

            string ans = dp[0][Abs(x)] && dp[1][Abs(y)] ? "Yes" : "No";
            Console.WriteLine(ans);
        }

        public static void ABC142_D()
        {
            long A = rl;
            long B = rl;

            List<long> primes = new List<long>();
            primes.Add(1);
            if (A % 2 == 0)
            {
                primes.Add(2);
                while (A % 2 == 0)
                    A /= 2;
            }
            for (long i = 3; i * i <= A; i+=2)
            {
                if (A % i == 0)
                {
                    primes.Add(i);
                    while (A % i == 0)
                        A /= i;                        
                }
            }
            if (A != 1)
                primes.Add(A);

            long ans = 0;
            foreach(var p in primes)
            {
                if (B % p == 0)
                    ans++;
            }

            Console.WriteLine(ans);
        }

        public static void ABC057_C()
        {
            long N = rl;
            long root = (long)Sqrt(N);
            long A = 1;
            for (int i = 2; i <= root; i++)
            {
                if(N % i == 0)
                {
                    A = i;
                }
            }

            long B = N / A;
            long ans = 0;
            while (B != 0)
            {
                B /= 10;
                ans++;
            }

            Console.WriteLine(ans);
        }

        public static void G()
        {
            long N = rl;
            long M = rl;
            Graph G = new Graph();
            for (int i = 0; i < N; i++)
            {
                G.Add(new List<long>());
            }
            for (int i = 0; i < M; i++)
            {
                int x = (int)rl-1;
                int y = (int)rl-1;
                G[x].Add(y);
            }

            int[] memo = new int[N + 1];
            FillArray(memo, -1);
            Func<int, int> rec = null;
            rec = (v) =>
            {
                if (memo[v] != -1) return memo[v];

                if (!G[v].Any())
                {
                    return memo[v] = 0;
                }

                long res = 0;
                foreach(int nv in G[v])
                {
                    ChMax(ref res, rec(nv) + 1);
                };
                                
                return memo[v] = (int)res;
            };

            long ans = -1;
            for (int i = 0; i < N; i++)
            {
                ChMax(ref ans, rec(i));
            }

            Console.WriteLine(ans);
        }

        public static void F()
        {
            string s = rs;
            string t = rs;

            long[,] dp = new long[s.Length + 1, t.Length + 1];
            for (int i = 1; i <= s.Length; i++)
            {
                for (int j = 1; j <= t.Length; j++)
                {
                    if (s[i - 1] == t[j - 1])
                    {
                        dp[i, j] = dp[i - 1, j - 1] + 1;
                    }
                    else
                    {
                        dp[i, j] = Max(dp[i - 1, j], dp[i, j - 1]);
                    }
                }
            }

            // 復元
            int x = s.Length;
            int y = t.Length;
            StringBuilder sb = new StringBuilder();
            while (dp[x,y] != 0)
            {
                while (dp[x - 1, y] == dp[x, y])
                    x--;
                while (dp[x, y - 1] == dp[x, y])
                    y--;

                x--;
                y--;
                sb.Append(s[x]);
            }

            string ans = string.Concat(sb.ToString().Reverse());
            Console.WriteLine(ans);
        }

        public static void E()
        {
            long N = rl;
            long W = rl;
            long[] w, v;
            ReadCols(out w, out v, N);
            long MAX_V = 1000 * N;
            long[,] dp = new long[N + 1, MAX_V + 1];
            FillArray(dp, INF);
            dp[0, 0] = 0;
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j <= MAX_V; j++)
                {
                    if(j - v[i] < 0)
                        dp[i + 1, j] = dp[i, j];
                    else
                    {
                        dp[i + 1, j] = Min(dp[i, j], dp[i, j - v[i]] + w[i]);
                    }
                }
            }

            long ans = 0;
            for (long i = 0; i <= MAX_V; i++)
            {
                if (dp[N, i] <= W)
                {
                    ans = i;
                }
            }

            Console.WriteLine(ans);
        }

        public static void D()
        {
            long N = rl;
            long W = rl;
            long[] w, v;
            ReadCols(out w, out v, N);
            long[,] dp = new long[N + 1, W + 1];
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j <= W; j++)
                {
                    if (j - w[i] < 0)
                    {
                        dp[i + 1, j] = dp[i, j];
                    }
                    else
                    {
                        dp[i + 1, j] = Max(dp[i, j], dp[i, j - w[i]] + v[i]);
                    }
                }                
            }
            Console.WriteLine(dp[N, W]);
        }

        public static void C()
        {
            long N = rl;
            long[] a, b, c;
            ReadCols(out a, out b, out c, N);

            long[,] dp = new long[N+1, 3];
            for (int i = 0; i < N; i++)
            {
                dp[i + 1, 0] = Max(dp[i, 1], dp[i, 2]) + a[i];
                dp[i + 1, 1] = Max(dp[i, 0], dp[i, 2]) + b[i];
                dp[i + 1, 2] = Max(dp[i, 0], dp[i, 1]) + c[i];
            }

            long ans = Max(dp[N, 0], Max(dp[N, 1], dp[N, 2]));
            Console.WriteLine(ans);
        }

        public static void B()
        {
            long N = rl;
            long K = rl;
            long[] A = rla;
            long[] dp = new long[N];
            FillArray(dp, INF);
            dp[0] = 0;
            for (int i = 0; i < N - 1; i++)
            {
                for (int j = 1; j <= K && i + j < N; j++)
                {
                    dp[i + j] = Min(dp[i + j], dp[i] + Abs(A[i + j] - A[i]));
                }
            }

            Console.WriteLine(dp[N-1]);
        }

        public static void A()
        {
            long N = rl;
            long[] A = rla;

            long[] dp = new long[N];
            FillArray(dp, INF);
            dp[0] = 0;
            for (int i = 0; i < N - 1; i++)
            {
                dp[i + 1] = Min(dp[i + 1], dp[i] + Abs(A[i + 1] - A[i]));
                if (i + 2 < N)
                    dp[i + 2] = dp[i] + Abs(A[i + 2] - A[i]);
            }

            Console.WriteLine(dp[N-1]);
        }
    }

    public class HashMap<K,V>:Dictionary<K,V>{V i;static Func<V>j=System.Linq.Expressions.Expression.Lambda<Func<V>>(System.Linq.Expressions.Expression.New(typeof(V))).Compile();public HashMap(){}public HashMap(V a){i=a;}new public V this[K a]{get{V b;if(TryGetValue(a,out b))return b;else return base[a]=i!=null?i:j();}set{base[a]=value;}}}public static class Util{public static readonly long INF=(long)1e17;public readonly static long MOD=(long)1e9+7;public static void DontAutoFlush(){var a=new System.IO.StreamWriter(Console.OpenStandardOutput()){AutoFlush=false};Console.SetOut(a);}public static void Flush(){Console.Out.Flush();}public static T[]Sort<T>(T[]a){Array.Sort<T>(a);return a;}public static T[]SortDecend<T>(T[]a){Array.Sort<T>(a);Array.Reverse(a);return a;}public static void Swap<T>(ref T a,ref T b){T c=a;a=b;b=c;}public static int GCD(int a,int b){return(b==0)?a:GCD(b,a%b);}public static void ChMax(ref long a,long b){if(a<b)a=b;}public static void ChMin(ref long a,long b){if(a>b)a=b;}public static long ModAdd(long a,long b){long c=a+b;if(c>=MOD)return c%MOD;return c;}public static long ModMul(long a,long b){long c=a*b;if(c>=MOD)return c%MOD;return c;}public static void ChModAdd(ref long a,long b){a+=b;if(a>=MOD)a%=MOD;}public static void ChModMul(ref long a,long b){a*=b;if(a>=MOD)a%=MOD;}public static void FillArray<T>(T[]a,T b){int c=a.Length;for(int d=0;d<c;d++)a[d]=b;}public static void FillArray<T>(T[,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);for(int e=0;e<c;e++)for(int f=0;f<d;f++){a[e,f]=b;}}public static void FillArray<T>(T[,,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);int e=a.GetLength(2);for(int f=0;f<c;f++)for(int g=0;g<d;g++){for(int h=0;h<e;h++){a[f,g,h]=b;}}}public static long[]Accumulate(long[]a){long[]b=new long[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}public static double[]Accumulate(double[]a){double[]b=new double[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}}public static class Cin{public static long rl{get{return ReadLong();}}public static long[]rla{get{return ReadLongArray();}}public static double rd{get{return ReadDouble();}}public static double[]rda{get{return ReadDoubleArray();}}public static string rs{get{return ReadString();}}public static int ReadInt(){return int.Parse(k());}public static long ReadLong(){return long.Parse(k());}public static double ReadDouble(){return double.Parse(k());}public static string ReadString(){return k();}public static int[]ReadIntArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);}public static long[]ReadLongArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);}public static double[]ReadDoubleArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),double.Parse);}public static void ReadCols(out long[]a,out long[]b,long c){a=new long[c];b=new long[c];for(int d=0;d<c;d++){a[d]=ReadLong();b[d]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,out long[]c,long d){a=new long[d];b=new long[d];c=new long[d];for(int e=0;e<d;e++){a[e]=ReadLong();b[e]=ReadLong();c[e]=ReadLong();}}public static int[][]ReadIntTable(int a){i=null;int[][]b=new int[a][];for(int c=0;c<a;c++)b[c]=ReadIntArray();return b;}public static long[][]ReadLongTable(long a){i=null;long[][]b=new long[a][];for(long c=0;c<a;c++)b[c]=ReadLongArray();return b;}static string[]i{get;set;}static int j{get;set;}static string k(){if(i==null||i.Length<=j){i=Console.ReadLine().Split(' ');j=0;}return i[j++];}}public struct VTuple<T1,T2>:IComparable<VTuple<T1,T2>>,IEquatable<VTuple<T1,T2>>{public T1 First;public T2 Second;public VTuple(T1 a,T2 b){First=a;Second=b;}public int CompareTo(VTuple<T1,T2>a){int b=Comparer<T1>.Default.Compare(First,a.First);if(b!=0)return b;return Comparer<T2>.Default.Compare(Second,a.Second);}public override bool Equals(object a){return a is VTuple<T1,T2>&&Equals((VTuple<T1,T2>)a);}public bool Equals(VTuple<T1,T2>a){return EqualityComparer<T1>.Default.Equals(First,a.First)&&EqualityComparer<T2>.Default.Equals(Second,a.Second);}public override int GetHashCode(){int a=First!=null?First.GetHashCode():0;int b=Second!=null?Second.GetHashCode():0;uint c=((uint)a<<5)|((uint)a>>27);return((int)c+a)^b;}}
}