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)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashSet;
import java.util.NoSuchElementException;

public class Main {

	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);

		char[] s = sc.next().toCharArray();
		int x = sc.nextInt();
		int y = sc.nextInt();

		int i = 0;
		for (i = 0; i < s.length; i++) {
			if (s[i] != 'F') break;
			x--;
		}

		ArrayList<Integer> xs = new ArrayList<>(), ys = new ArrayList<>();
		int tmp = 0, dir = 0;
		for (; i < s.length; i++) {
			switch (s[i]) {
				case 'F':
					tmp++;
					break;
				case 'T':
					if (tmp > 0) {
						if (dir == 0) xs.add(tmp);
						else ys.add(tmp);
					}
					dir = (dir + 1) % 2;
					tmp = 0;
					break;
			}
		}
		if (dir == 0) xs.add(tmp);
		else ys.add(tmp);

		Collections.sort(xs);
		Collections.sort(ys);

		HashSet<Integer> setX = new HashSet<>();
		setX.add(0);
		for (int dx : xs) {
			HashSet<Integer> tmpS = new HashSet<>();
			for (int xx : setX) {
				tmpS.add(xx + dx);
				tmpS.add(xx - dx);
			}
			setX = tmpS;
		}
		HashSet<Integer> setY = new HashSet<>();
		setY.add(0);
		for (int dy : ys) {
			HashSet<Integer> tmpS = new HashSet<>();
			for (int yy : setY) {
				tmpS.add(yy + dy);
				tmpS.add(yy - dy);
			}
			setY = tmpS;
		}

		out.println(setX.contains(x) && setY.contains(y) ? "Yes" : "No");
		out.flush();
	}

}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) return true;
		else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) return false;
		}
		return true;
	}

	private byte readByte() {
		if (hasNextByte()) return buffer[ptr++];
		return -1;
	}

	private boolean isPrintableChar(byte c) {
		return '!' <= c && c <= '~';
	}

	private void skipUnprintable() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
			ptr++;
		}
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		byte b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public int nextInt() {
		if (!hasNext()) throw new NoSuchElementException();
		int n = 0;
		boolean minus = false;
		byte b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		return a;
	}

	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		byte b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		return a;
	}
}