Buggy python submission (verdict: Time Limit Exceeded):

S = input()
P = tuple(map(int, input().split()))

dis = abs(P[0]) + abs(P[1])
forward = S.count("F")

S = S.split("T")

def add(p, d, L):
    return (p[0] + L * d[0], p[1] + L * d[1])

if dis > forward or (forward - dis) % 2 == 1:
    print("No")

else:
    now = {((0, 0), (1, 0), forward)} # (X, Y), dir
    for s in S:
        ne = set()
        L = len(s)
        for p, d, f in now:
            #Fのとき
            f -= L
            p = add(p, d, L)
            dis = abs(P[0] - p[0]) + abs(P[1] - p[1])

            if dis <= forward:
                #ne = ne | {(p, d, f)}
                ne = ne | {(p, (d[1], -d[0]), f), (p, (-d[1], d[0]), f) }
        now = ne
    
    for p,d,f in now:
        if p == P:
            print("Yes")
            break
    else:
        print("No")

Fixed submission:
import bisect
import copy
import heapq
import sys
import itertools
import math
import queue
input = sys.stdin.readline
sys.setrecursionlimit(1000000)
mod = 10 ** 9 + 7

def read_values(): return map(int, input().split())
def read_index(): return map(lambda x: int(x) - 1, input().split())
def read_list(): return list(read_values())
def read_lists(N): return [read_list() for n in range(N)]
def init_dp1(init, N): return [init for _ in range(N)]
def init_dp2(init, N, M): return [[init for _ in range(M)] for _ in range(N)]


class V:
    def __init__(self, f, v=None):
        self.f = f
        self.v = v
 
    def __str__(self):
        return str(self.v)
 
    def ud(self, n):
        if n is None:
            return

        if self.v is None:
            self.v = n
            return
        self.v = self.f(self.v, n) 


def main():
    S = input().strip()
    X, Y = read_values()
    F = list(map(len, S.split("T")))

    S = {F[0]}
    if len(F) >= 2:
        for x in F[2::2]:
            SS = set()
            for s in S:
                SS.add(s + x)
                SS.add(s - x)
            S = SS

    if not X in S:
        print("No")
        return
    
    S = {0}
    if len(F) >= 1:
        for x in F[1::2]:
            SS = set()
            for s in S:
                SS.add(s + x)
                SS.add(s - x)
            S = SS
    
    if not Y in S:
        print("No")
        return 
    
    print("Yes")


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):

S = input()
P = tuple(map(int, input().split()))

dis = abs(P[0]) + abs(P[1])
forward = S.count("F")

def add(p, d):
    return (p[0] + d[0], p[1] + d[1])

if dis > forward or (forward - dis) % 2 == 1:
    print("No")

else:
    now = {((0, 0), (1, 0), forward)} # (X, Y), dir
    for s in S:
        ne = set()
        for p, d, f in now:
            #Fのとき
            if s == "F":
                f -= 1
                p = add(p, d)
                dis = abs(P[0] - p[0]) + abs(P[1] - p[1])
                if dis <= forward:
                    ne = ne | {(p, d, f)}
            #Tのとき
            elif s == "T":
                ne = ne | {(p, (d[1], -d[0]), f), (p, (-d[1], d[0]), f) }
        now = ne
    
    for p,d,f in now:
        if p == P:
            print("Yes")
            break
    else:
        print("No")


Fixed submission:
import bisect
import copy
import heapq
import sys
import itertools
import math
import queue
input = sys.stdin.readline
sys.setrecursionlimit(1000000)
mod = 10 ** 9 + 7

def read_values(): return map(int, input().split())
def read_index(): return map(lambda x: int(x) - 1, input().split())
def read_list(): return list(read_values())
def read_lists(N): return [read_list() for n in range(N)]
def init_dp1(init, N): return [init for _ in range(N)]
def init_dp2(init, N, M): return [[init for _ in range(M)] for _ in range(N)]


class V:
    def __init__(self, f, v=None):
        self.f = f
        self.v = v
 
    def __str__(self):
        return str(self.v)
 
    def ud(self, n):
        if n is None:
            return

        if self.v is None:
            self.v = n
            return
        self.v = self.f(self.v, n) 


def main():
    S = input().strip()
    X, Y = read_values()
    F = list(map(len, S.split("T")))

    S = {F[0]}
    if len(F) >= 2:
        for x in F[2::2]:
            SS = set()
            for s in S:
                SS.add(s + x)
                SS.add(s - x)
            S = SS

    if not X in S:
        print("No")
        return
    
    S = {0}
    if len(F) >= 1:
        for x in F[1::2]:
            SS = set()
            for s in S:
                SS.add(s + x)
                SS.add(s - x)
            S = SS
    
    if not Y in S:
        print("No")
        return 
    
    print("Yes")


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
P = tuple(map(int, input().split()))

def add(p, d):
    return (p[0] + d[0], p[1] + d[1])

now = {((0, 0), (1, 0))} # (X, Y), dir
for s in S:
    ne = set()
    for p, d in now:

        #Fのとき
        if s == "F":
            ne = ne | {(add(p, d), d)}
        
        #Tのとき
        elif s == "T":
            ne = ne | {(p, (d[1], -d[0])), (p, (-d[1], d[0])) }

    now = ne

for p,d in now:
    if p == P:
        print("Yes")
        break
else:
    print("No")

Fixed submission:
import bisect
import copy
import heapq
import sys
import itertools
import math
import queue
input = sys.stdin.readline
sys.setrecursionlimit(1000000)
mod = 10 ** 9 + 7

def read_values(): return map(int, input().split())
def read_index(): return map(lambda x: int(x) - 1, input().split())
def read_list(): return list(read_values())
def read_lists(N): return [read_list() for n in range(N)]
def init_dp1(init, N): return [init for _ in range(N)]
def init_dp2(init, N, M): return [[init for _ in range(M)] for _ in range(N)]


class V:
    def __init__(self, f, v=None):
        self.f = f
        self.v = v
 
    def __str__(self):
        return str(self.v)
 
    def ud(self, n):
        if n is None:
            return

        if self.v is None:
            self.v = n
            return
        self.v = self.f(self.v, n) 


def main():
    S = input().strip()
    X, Y = read_values()
    F = list(map(len, S.split("T")))

    S = {F[0]}
    if len(F) >= 2:
        for x in F[2::2]:
            SS = set()
            for s in S:
                SS.add(s + x)
                SS.add(s - x)
            S = SS

    if not X in S:
        print("No")
        return
    
    S = {0}
    if len(F) >= 1:
        for x in F[1::2]:
            SS = set()
            for s in S:
                SS.add(s + x)
                SS.add(s - x)
            S = SS
    
    if not Y in S:
        print("No")
        return 
    
    print("Yes")


if __name__ == "__main__":
    main()