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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

// package arc.arc087;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        char[] s = in.nextToken().toCharArray();
        int x = in.nextInt();
        int y = in.nextInt();


        int n = s.length;
        List<Integer> xs = new ArrayList<>();
        List<Integer> ys = new ArrayList<>();

        int ti = 0;
        while (ti < n && s[ti] == 'F') {
            ti++;
        }
        x -= ti;


        boolean flg = true;
        for (int i = ti; i < n ; ) {
            if (s[i] == 'T') {
                flg = !flg;
                i++;
                continue;
            }

            int j = i;
            while (j < n && s[j] == 'F') {
                j++;
            }
            if (flg) {
                xs.add(j-i);
            } else {
                ys.add(j-i);
            }
            i = j;
        }

        out.println(solve(x, xs) && solve(y, ys) ? "Yes" : "No");
        out.flush();
    }

    private static boolean solve(int L, List<Integer> xs) {
        int n = xs.size();

        Collections.sort(xs);

        int s = 0;
        for (int xi : xs) {
            s += xi;
        }
        int GETA = (s+10);
        int MAX = GETA*2;

        int[][] dp = new int[2][MAX];
        dp[0][GETA] = 1;
        for (int i = 0; i < n ; i++) {
            int fr = i % 2;
            int to = 1 - fr;
            int d = xs.get(i);
            Arrays.fill(dp[to], 0);
            for (int j = 0; j < MAX ; j++) {
                if (dp[fr][j] == 1) {
                    if (j - d >= 0) {
                        dp[to][j-d] = 1;
                    }
                    if (j + d < MAX) {
                        dp[to][j+d] = 1;
                    }
                }
            }
        }
        return GETA+L >= 0 && GETA+L < MAX && dp[n%2][GETA+L] == 1;
    }

    public static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    public static class InputReader {
        private static final int BUFFER_LENGTH = 1 << 12;
        private InputStream stream;
        private byte[] buf = new byte[BUFFER_LENGTH];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int next() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            return (char) skipWhileSpace();
        }

        public String nextToken() {
            int c = skipWhileSpace();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public long nextLong() {
            int c = skipWhileSpace();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        int skipWhileSpace() {
            int c = next();
            while (isSpaceChar(c)) {
                c = next();
            }
            return c;
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}