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 (1.42.0) (judge verdict: Accepted)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use std::cmp::*;
use std::collections::*;
use std::mem::*;

fn main() {
    let (r, w, e) = (std::io::stdin(), std::io::stdout(), std::io::stderr());
    let mut io = IO::new(r.lock(), w.lock(), e.lock());
    let mut s = io.chars();
    s.push('T');
    let n = s.len();
    let base = 8000usize;
    let (x, y) = (
        io.read::<i64>() + base as i64,
        io.read::<i64>() + base as i64,
    );
    let mut arms = Vec::new();
    let mut fcnt = 0;
    let mut tcnt = 0;
    arms.push(0);
    let mut t = Vec::new();
    for &c in s.iter() {
        if c == 'F' {
            fcnt += 1;
        } else {
            // t.push(fcnt);
            // t.push(0);
            // fcnt = 0;
            if fcnt != 0 {
                t.push(fcnt);
            }
            t.push(0);
            fcnt = 0;
        }
    }

    let mut dpx = vec![vec![false; base * 2 + 2 + 100]; base + 100];
    let mut dpy = vec![vec![false; base * 2 + 2 + 100]; base + 100];
    dpx[0][base] = true;
    dpy[0][base] = true;
    let mut flg = false;
    let mut xy = true;
    let mut cntx = 0;
    let mut cnty = 0;
    for (i, &ti) in t.iter().enumerate() {
        if ti == 0 {
            xy = !xy;
        } else if xy {
            cntx += 1;
            for j in 0..base * 2 + 50 {
                if dpx[cntx - 1][j] {
                    if j + ti < base * 2 + 50 {
                        dpx[cntx][j + ti] = true;
                    }
                    if (j >= ti) && flg {
                        dpx[cntx][j - ti] = true;
                    }
                }
            }
        } else {
            cnty += 1;
            for j in 0..base * 2 + 50 {
                if dpy[cnty - 1][j] {
                    if j + ti < base * 2 + 50 {
                        dpy[cnty][j + ti] = true;
                    }
                    if j >= ti {
                        dpy[cnty][j - ti] = true;
                    }
                }
            }
        }
        if !flg {
            flg = true;
        }
    }
    io.writeln(if dpx[cntx][x as usize] && dpy[cnty][y as usize] {
        "Yes"
    } else {
        "No"
    });
}

static MX: usize = 1010101;
static MOD: i64 = 1000000007;
static INF: i64 = std::i64::MAX >> 1;
// IO
use std::io::*;
struct IO<R: Read, W: Write, E: Write> {
    Read: R,
    Write: BufWriter<W>,
    Error: BufWriter<E>,
}
impl<R: Read, W: Write, E: Write> IO<R, W, E> {
    fn new(r: R, w: W, e: E) -> IO<R, W, E> {
        IO {
            Read: r,
            Write: BufWriter::new(w),
            Error: BufWriter::new(e),
        }
    }
    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
    {
        let next: String = self
            .Read
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect();
        next.parse().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
    fn chari(&mut self) -> Vec<i64> {
        self.chars()
            .iter()
            .map(|&c| (c as u8 - b'0') as i64)
            .collect::<Vec<i64>>()
    }
    fn readn<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect::<Vec<_>>()
    }
    fn readmat<T: std::str::FromStr>(&mut self, n: usize, m: usize) -> Vec<Vec<T>> {
        (0..n).map(|_| self.readn(m)).collect()
    }
    fn write<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
    }
    fn writeln<S: ToString>(&mut self, val: S) {
        self.Write.write(val.to_string().as_bytes());
        self.Write.write(b"\n");
    }
    fn debug<S: std::fmt::Debug>(&mut self, val: S) {
        writeln!(self.Error, "(debug) {:?}", &val);
    }
    fn debug2<S: std::fmt::Debug, T: std::fmt::Debug>(&mut self, val1: S, val2: T) {
        writeln!(self.Error, "(debug2) {:?} -> {:?}", val1, val2);
    }
    fn debug3<S: std::fmt::Debug, T: std::fmt::Debug, U: std::fmt::Debug>(
        &mut self,
        val1: S,
        val2: T,
        val3: U,
    ) {
        writeln!(
            self.Error,
            "(debug3) {:?} -> {:?} -> {:?}",
            val1, val2, val3
        );
    }
}