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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(non_snake_case)]
#![allow(dead_code)]
#![allow(unused_macros)]
#![allow(unused_imports)]

use std::str::FromStr;
use std::io::*;
use std::collections::*;
use std::cmp::*;

struct Scanner<I: Iterator<Item = char>> {
    iter: std::iter::Peekable<I>,
}

macro_rules! exit {
    () => {{
        exit!(0)
    }};
    ($code:expr) => {{
        if cfg!(local) {
            writeln!(std::io::stderr(), "===== Terminated =====")
                .expect("failed printing to stderr");
        }
        std::process::exit($code);
    }}
}

impl<I: Iterator<Item = char>> Scanner<I> {
    pub fn new(iter: I) -> Scanner<I> {
        Scanner {
            iter: iter.peekable(),
        }
    }

    pub fn safe_get_token(&mut self) -> Option<String> {
        let token = self.iter
            .by_ref()
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        if token.is_empty() {
            None
        } else {
            Some(token)
        }
    }

    pub fn token(&mut self) -> String {
        self.safe_get_token().unwrap_or_else(|| exit!())
    }

    pub fn get<T: FromStr>(&mut self) -> T {
        self.token().parse::<T>().unwrap_or_else(|_| exit!())
    }

    pub fn vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
        (0..len).map(|_| self.get()).collect()
    }

    pub fn mat<T: FromStr>(&mut self, row: usize, col: usize) -> Vec<Vec<T>> {
        (0..row).map(|_| self.vec(col)).collect()
    }

    pub fn char(&mut self) -> char {
        self.iter.next().unwrap_or_else(|| exit!())
    }

    pub fn chars(&mut self) -> Vec<char> {
        self.get::<String>().chars().collect()
    }

    pub fn mat_chars(&mut self, row: usize) -> Vec<Vec<char>> {
        (0..row).map(|_| self.chars()).collect()
    }

    pub fn line(&mut self) -> String {
        if self.peek().is_some() {
            self.iter
                .by_ref()
                .take_while(|&c| !(c == '\n' || c == '\r'))
                .collect::<String>()
        } else {
            exit!();
        }
    }

    pub fn peek(&mut self) -> Option<&char> {
        self.iter.peek()
    }
}

const MAX_BOUNDS: usize = 8000;

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin.bytes().map(|c| c.unwrap() as char));
    let s: Vec<char> = sc.chars();
    let n = s.len();
    let mut cur = 0;
    let mut xy = true;
    let mut xs = Vec::new();
    let mut ys = Vec::new();
    while cur < n {
        let mut cnt = 0;
        while cur < n && s[cur] == 'F' {
            cnt += 1;
            cur += 1;
        }
        if xy {
            xs.push(cnt);
        } else {
            ys.push(cnt);
        }
        xy = !xy;
        cur += 1;
    }
    let x: i64 = sc.get();
    let y: i64 = sc.get();
    let mut dp = vec![false; MAX_BOUNDS*2+2];
    dp[x.abs() as usize + xs[0]] = true;
    for i in 1..xs.len() {
        let mut ndp = vec![false; MAX_BOUNDS*2+2];
        for j in 0..MAX_BOUNDS * 2 {
            if j >= xs[i] {
                ndp[j - xs[i]] |= dp[j];
            }
            if j + xs[i] <= MAX_BOUNDS * 2 {
                ndp[j + xs[i]] |= dp[j];
            }
        }
        dp = ndp;
    }
    if !dp[(x.abs() + x) as usize] {
        println!("No");
        return;
    }
    let mut dp = vec![false; MAX_BOUNDS*2+2];
    dp[y.abs() as usize] = true;
    for i in 0..ys.len() {
        let mut ndp = vec![false; MAX_BOUNDS*2+2];
        for j in 0..MAX_BOUNDS * 2 {
            if j >= ys[i] {
                ndp[j - ys[i]] |= dp[j];
            }
            if j + ys[i] <= MAX_BOUNDS * 2 {
                ndp[j + ys[i]] |= dp[j];
            }
        }
        dp = ndp;
    }
    if !dp[(y.abs() + y) as usize] {
        println!("No");
        return;
    }
    println!("Yes");
}