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)

use std::cmp;
use std::collections::HashMap;
use std::collections::VecDeque;
use std::io::Read;
use std::usize::MAX;

macro_rules! input {(source = $s:expr, $($r:tt)*) => {let mut iter = $s.split_whitespace();let mut next = || { iter.next().unwrap() };input_inner!{next, $($r)*}};($($r:tt)*) => {let stdin = std::io::stdin();let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));let mut next = move || -> String{bytes.by_ref().map(|r|r.unwrap() as char).skip_while(|c|c.is_whitespace()).take_while(|c|!c.is_whitespace()).collect()};input_inner!{next, $($r)*}};}
macro_rules! input_inner {($next:expr) => {};($next:expr, ) => {};($next:expr, $var:ident : $t:tt $($r:tt)*) => {let $var = read_value!($next, $t);input_inner!{$next $($r)*}};}
macro_rules! read_value {($next:expr, ( $($t:tt),* )) => {( $(read_value!($next, $t)),* )};($next:expr, [ $t:tt ; $len:expr ]) => {(0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()};($next:expr, chars) => {read_value!($next, String).chars().collect::<Vec<char>>()};($next:expr, usize1) => {read_value!($next, usize) - 1};($next:expr, [ $t:tt ]) => {{let len = read_value!($next, usize);(0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()}};($next:expr, $t:ty) => {$next().parse::<$t>().expect("Parse error")};}

fn solve() {
    input! {
        s: chars,
        x: i64,
        y: i64
    }

    let mut x = x;
    let y = y;

    let mut x_moves: Vec<usize> = Vec::new();
    let mut y_moves: Vec<usize> = Vec::new();

    let mut count = 0;
    let mut isX = true;

    let mut init_pos = 0;
    for i in 0..s.len() {
        if s[i] == 'T' || i == s.len() - 1 {
            init_pos = i;
            x = x - i as i64;
            break;
        }
    }

    for i in init_pos..s.len() {
        if s[i] == 'T' {
            if isX {
                x_moves.push(count);
                isX = !isX
            } else {
                y_moves.push(count);
                isX = !isX
            }
            count = 0;
        } else {
            count += 1;
        }
    }
    if isX {
        x_moves.push(count);
    } else {
        y_moves.push(count);
    }

    let ok_x = is_arrivable(&x_moves, x);
    let ok_y = is_arrivable(&y_moves, y);

    if ok_x && ok_y {
        println!("Yes");
    } else {
        println!("No");
    }
}

// x,y座標に対して、移動量の配列からposの位置にいることができるか調べる
fn is_arrivable(moves: &Vec<usize>, pos: i64) -> bool {
    let mut dp = vec![vec![false; 16000 + 1]; moves.len() + 1];

    dp[0][8000] = true;

    for i in 1..moves.len() + 1 {
        let index = i - 1;
        for j in 0..16000 {
            let plus_pattern = if j > moves[index] {
                if dp[index][j - moves[index]] {
                    true
                } else {
                    false
                }
            } else {
                false
            };

            let minus_pattern = if j + moves[index] <= 16000 {
                if dp[index][j + moves[index]] {
                    true
                } else {
                    false
                }
            } else {
                false
            };

            if plus_pattern || minus_pattern {
                dp[i][j] = true;
            }
        }
    }

    if pos + 8000 < 0 {
        false
    } else {
        dp[moves.len()][(pos + 8000) as usize]
    }
}

fn main() {
    let thd = std::thread::Builder::new().stack_size(104_857_600);
    thd.spawn(|| solve()).unwrap().join().unwrap();

    /*
    // 入力を一括で読み込む場合
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut input = buf.split_whitespace();

    // inputに対しnext()で読み込んでいく
    let q: usize = input.next().unwrap().parse().unwrap();
    */
}

const LARGE_PRIME: u64 = 1_000_000_007;

// @〜でsnippet