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 Yorukatsu050.Questions;
using Yorukatsu050.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Yorukatsu050.Questions
{
    /// <summary>
    /// https://atcoder.jp/contests/abc082/tasks/arc087_b
    /// </summary>
    public class QuestionE : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var s = inputStream.ReadLine();
            var xy = inputStream.ReadIntArray();
            var x = xy[0];
            var y = xy[1];

            List<int> xOrders, yOrders;
            Decode(s, out xOrders, out yOrders);

            var initialX = s.TakeWhile(c => c == 'F').Count();
            if (CheckReachable(initialX, x, xOrders) && CheckReachable(0, y, yOrders))
            {
                yield return "Yes";
            }
            else
            {
                yield return "No";
            }
        }

        private static void Decode(string s, out List<int> xOrders, out List<int> yOrders)
        {
            xOrders = new List<int>();
            yOrders = new List<int>();
            var currentDirection = Direction.X;
            var currentDistance = 0;
            foreach (var c in s.SkipWhile(c => c == 'F'))
            {
                if (c == 'T')
                {
                    currentDirection = AddOrderAndTurn(xOrders, yOrders, currentDirection, currentDistance);
                    currentDistance = 0;
                }
                else
                {
                    currentDistance++;
                }
            }
            AddOrderAndTurn(xOrders, yOrders, currentDirection, currentDistance);
        }

        private static Direction AddOrderAndTurn(List<int> xOrders, List<int> yOrders, Direction currentDirection, int currentDistance)
        {
            switch (currentDirection)
            {
                case Direction.X:
                    xOrders.Add(currentDistance);
                    currentDirection = Direction.Y;
                    break;
                case Direction.Y:
                    yOrders.Add(currentDistance);
                    currentDirection = Direction.X;
                    break;
            }

            return currentDirection;
        }

        bool CheckReachable(int start, int goal, IList<int> orders)
        {
            const int loop = 20000;
            var reachable = new bool[orders.Count + 1, loop];
            reachable[0, start] = true;

            for (int orderIndex = 0; orderIndex < orders.Count; orderIndex++)
            {
                for (int coordinate = 0; coordinate < reachable.GetLength(1); coordinate++)
                {
                    if (reachable[orderIndex, coordinate])
                    {
                        var order = orders[orderIndex];
                        reachable[orderIndex + 1, (coordinate + order) % loop] = true;
                        reachable[orderIndex + 1, (coordinate - order + loop) % loop] = true;
                    }
                }
            }

            return reachable[orders.Count, (goal + loop) % loop];
        }

        enum Direction
        {
            X,
            Y
        }
    }
}


namespace Yorukatsu050
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionE();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Yorukatsu050.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Yorukatsu050.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion