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: Runtime Error)

import java.util.*;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		String s = sc.next();
		int x = sc.nextInt(); int y = sc.nextInt();
		ArrayList<Integer> a = new ArrayList<>(); // migi hidari
		ArrayList<Integer> b = new ArrayList<>(); // ue shita
		int state = 0;
		int acc = 0;
		for(int i=0; i<s.length(); i++) {
			if(state==0) { // migi(start)
				if(s.charAt(i)=='F') {
					acc++;
				} else {
					x -= acc;
					acc = 0;
					state = 2;
				}
				continue;
			}
			if(state==1) { // migi hidari
				if(s.charAt(i)=='F') {
					acc++;
				} else {
					a.add(acc);
					acc = 0;
					state = 2;
				}
				continue;
			}
			if(state==2) { // ue shita
				if(s.charAt(i)=='F') {
					acc++;
				} else {
					b.add(acc);
					acc = 0;
					state = 1;
				}
				continue;
			} else {
				throw new RuntimeException();
			}
		}
		if (state==0){
			if(x==acc&&y==0) {
				System.out.println("Yes");
				return;
			} else {
				System.out.println("No");
				return;
			}
		} else if(state==1) { // migi hidari
			a.add(acc);
			acc = 0;
			state = 2;
		} else if(state==2) { // ue shita
			b.add(acc);
			acc = 0;
			state = 1;
		} else {
			throw new RuntimeException();
		}
		// solve
		boolean[][] dpa = new boolean[a.size()+1][20000];
		boolean[][] dpb = new boolean[b.size()+1][20000];
		for(int i=0; i<a.size()+1; i++) {
			Arrays.fill(dpa[i], false);
		}
		for(int i=0; i<b.size()+1; i++) {
			Arrays.fill(dpb[i], false);
		}
		final int GEN = 10000;
		final int UPPPER = 20000;
		dpa[0][GEN] = true;
		dpb[0][GEN] = true;
		for(int i=1; i<a.size()+1; i++) {
			for(int j=0; j<20000; j++) {
				if(dpa[i-1][j]) {
					dpa[i][j] = true;
				}
				if(j-a.get(i-1)>=0&&j-a.get(i-1)<20000&&dpa[i-1][j-a.get(i-1)]) {
					dpa[i][j]=true;
				}
				if(j+a.get(i-1)>=0&&j+a.get(i-1)<20000&&dpa[i-1][j+a.get(i-1)]) {
					dpa[i][j] = true;
				}
			}
		}
		if(!dpa[a.size()][x+GEN]) {
			System.out.println("No");
			return;
		}
		for(int i=1; i<b.size()+1; i++) {
			for(int j=0; j<20000; j++) {
				if(dpb[i-1][j]) {
					dpb[i][j] = true;
				}
				if(j-b.get(i-1)>=0&&j-b.get(i-1)<20000&&dpb[i-1][j-b.get(i-1)]) {
					dpb[i][j]=true;
				}
				if(j+a.get(i-1)>=0&&j+b.get(i-1)<20000&&dpb[i-1][j+b.get(i-1)]) {
					dpb[i][j] = true;
				}
			}
		}
		if(!dpb[b.size()][y+GEN]) {
			System.out.println("No");
			return;
		}
		System.out.println("Yes");
	}
	
	static int binarySearch(int[] A, int x) {
		int l = 0;
		int r = A.length;
		while(l<r) {
			int mid = (l+r)/2;
			if(A[mid] == x) return mid;
			else if(x<A[mid]) r = mid;
			else l = mid+1;
		}
		return -1;
	}
	
	static long upper_bound(int[] A, int b) {
		// bよりおおきい値がはじめて出てくるindexを返す
		return lower_bound(A, b+1);
	}

	static long lower_bound(int[] A, int b) {
		// b以上の値がはじめて出てくるindexを返す
		int lb=0;
		int ub=A.length;
		while(ub>lb) {
			int mid = (lb+ub)/2;
			if(A[mid]>=b) ub = mid;
			else lb = mid+1;
		}
		return lb;
	}
	
	// union find lib
	// usage:
	// 最初にinitを呼ぶ
	// root: 直接は呼ばないで
	// unite: まとめる
	// same: グループ判定
	static void init(int par[], int N) {
		for(int i=0; i<N; i++) {
			par[i] = i;
		}
	}
	
	static int root(int x, int [] par) {
		if(par[x] == x) {
			return x;
		} else {
			return (par[x] = root(par[x], par));
		}
	}
	
	static boolean same(int x, int y, int[] par) {
		return root(x, par) == root(y, par);
	}
	
	static void unite(int x, int y, int[] par) {
		x = root(x, par);
		y = root(y, par);
		if(x == y) return;
		par[x] = y;
	}
	
	// end union find lib
	
	// number lib
	
	static int max(int...ls) {
		int ans = Integer.MIN_VALUE;
		for(int i=0; i<ls.length; i++) {
			ans = Math.max(ans, ls[i]);
		}
		return ans;
	}
	
	static int min(int...ls) {
		int ans = Integer.MAX_VALUE;
		for(int i=0; i<ls.length; i++) {
			ans = Math.min(ans, ls[i]);
		}
		return ans;
	}
	
	static long lcm(long a, long b) {
		return a*(b/gcd(a, b));
	}
	
	static long gcd(long a, long b) {
		long ta = Math.max(a, b);
		long tb = Math.min(a, b);
		long tmp;
		while((tmp = ta%tb) != 0) {
			ta = tb;
			tb = tmp;
		}
		return tb;
	}
	
	static long modcomb(long n, long k, long mod) {
		if(k==1) {
			return n;
		}
		
		long ans = 1;
		for(long i=n; i>=n-k+1; i--) {
			ans = (ans * i)%mod;
		}
		for(long i=k; 0<i; i--) {
			ans = (ans * modpow(i, mod-2, mod)) % mod;
		}
		return ans;
	}
	
	static long modpow(long a, long b, long mod) {
		if(b==0) return 1;
		if(b%2==0) {
			long d = modpow(a, b/2, mod);
			return (d*d)%mod;
		} else {
			return (a*modpow(a, b-1, mod))%mod;
		}
	}
	
	static int disit(long a, long d) {
		int count = 0;
		while(a!=0) {
			a = a/d;
			count++;
		}
		return count;
	}
	
	// end number lib
}