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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main {
	static ArrayList<Integer> xs, ys;
	static int x, y;
	static Boolean[][] mem1, mem2;
	static int offset = 8001;

	static boolean solve(int idx, int sum) {
		if (idx == xs.size())
			return sum == x;
		if (mem1[idx][sum + offset] != null)
			return mem1[idx][sum + offset];
		return mem1[idx][sum + offset] = solve(idx + 1, sum + xs.get(idx)) || solve(idx + 1, sum - xs.get(idx));
	}

	static boolean solve2(int idx, int sum) {
		if (idx == ys.size())
			return sum == y;
		if (mem2[idx][sum + offset] != null)
			return mem2[idx][sum + offset];
		return mem2[idx][sum + offset] = solve2(idx + 1, sum + ys.get(idx)) || solve2(idx + 1, sum - ys.get(idx));
	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		String s = sc.next();
		x = sc.nextInt();
		y = sc.nextInt();

		xs = new ArrayList<>();
		ys = new ArrayList<>();

		int start = 0;

		while (start < s.length() && s.charAt(start) == 'F') {
			x--;
			start++;
		}

		boolean inX = true;
		for (int i = start; i < s.length(); i++) {
			if (s.charAt(i) == 'T') {
				inX = !inX;
			}
			else {
				int cnt = 0;
				boolean in = false;
				while (i < s.length() && s.charAt(i) == 'F') {
					cnt++;
					i++;
					in = true;
				}
				if (in)
					i--;
				if (inX)
					xs.add(cnt);
				else
					ys.add(cnt);
			}
		}
		mem1 = new Boolean[xs.size() + 1][8002 * 2];
		mem2 = new Boolean[ys.size() + 1][8002 * 2];
		if (solve(0, 0) && solve2(0, 0))
			System.out.println("Yes");
		else
			System.out.println("No");

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}
	}
}