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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cstdint>
#include <utility>
#include <tuple>
#include <vector>
#include <stack>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <algorithm>
#include <limits>
#include <numeric>
#include <iomanip>

using namespace std;

// Type aliases
using i8  =  int8_t; using  u8 =  uint8_t;
using i16 = int16_t; using u16 = uint16_t;
using i32 = int32_t; using u32 = uint32_t;
using i64 = int64_t; using u64 = uint64_t;

template <class T> using V = vector<T>;

// Loops
#define REP(i, n) for (i64 i = 0; i < (n); ++i)
#define REPR(i, n) for (i64 i = (n) - 1; i >= 0; --i)
#define FOR(i, n, m) for (i64 i = (n); i < (m); ++i)
#define FORR(i, n, m) for (i64 i = (m) - 1; i >= (n); --i)

#define FORE(x, xs) for (auto &x: (xs))

// Macros
#define CTR(x) (x).begin(), (x).end()

// Utils for Tuple
namespace tuple_utils {
    template<size_t...> struct seq{};

    template<size_t N, size_t... Is>
    struct gen_seq : gen_seq<N - 1, N - 1, Is...>{};

    template<size_t... Is>
    struct gen_seq<0, Is...> : seq<Is...>{};

    template <class Tuple, size_t... Is>
    void read(istream &stream, Tuple &t, seq<Is...>) {
        static_cast<void>((int[]){0, (void(stream  >> get<Is>(t)), 0)...});
    }

    template<class Tuple, size_t... Is>
    void print(ostream& stream, Tuple const& t, seq<Is...>) {
        static_cast<void>((int[]){0, (void(stream << (Is == 0 ?  "" : ", ") << get<Is>(t)), 0)...});
    }

    template <size_t I, class F, class A, class... Elems>
    struct ForEach {
        void operator()(A &arg, tuple<Elems...> const& t) const {
            F()(arg, get<I>(t));
            ForEach<I - 1, F, A, Elems...>()(arg, t);
        };
        void operator()(A &arg, tuple<Elems...>& t) const {
            F()(arg, get<I>(t));
            ForEach<I - 1, F, A, Elems...>()(arg, t);
        };
    };
    template <class F, class A, class... Elems>
    struct ForEach<0, F, A, Elems...> {
        void operator()(A &arg, tuple<Elems...> const& t) const {
            F()(arg, get<0>(t));
        };
        void operator()(A &arg, tuple<Elems...>& t) const {
            F()(arg, get<0>(t));
        };
    };
    template <class F, class A, class... Elems>
    void for_each(A &arg, tuple<Elems...> const& t) {
        ForEach<tuple_size<tuple<Elems...>>::value - 1, F, A, Elems...>()(arg, t);
    };
    template <class F, class A, class... Elems>
    void for_each(A &arg, tuple<Elems...>& t) {
        ForEach<tuple_size<tuple<Elems...>>::value - 1, F, A, Elems...>()(arg, t);
    };

    struct hash_for_element {
        template <class V>
        void operator()(size_t &size, const V& v) const {
            size ^= hash<V>()(v);
        }
    };
}

// Input
template <class F, class S>
istream &operator>>(istream &stream, pair<F, S> &pair) {
    stream >> pair.first;
    stream >> pair.second;
    return stream;
}
template <class ...Args>
istream &operator>>(istream &stream, tuple<Args...> &tuple) {
    tuple_utils::read(stream, tuple, tuple_utils::gen_seq<sizeof...(Args)>());
    return stream;
}

template <class T>
T read() {
    T t;
    cin >> t;
    return t;
}
template <class F, class S>
pair<F, S> read() {
    pair<F, S> p;
    cin >> p;
    return p;
}
template <class T1, class T2, class T3, class ...Args>
tuple<T1, T2, T3, Args...> read() {
    tuple<T1, T2, T3, Args...> t;
    cin >> t;
    return t;
}

template <class T>
V<T> read(const int length) {
    V<T> ts(length);
    for (auto& t: ts) {
        cin >> t;
    }
    return ts;
}
template <class F, class S>
V<pair<F, S>> read(const int length) {
    V<pair<F, S>> ps(length);
    for (auto& p: ps) {
        cin >> p;
    }
    return ps;
}
template <class T1, class T2, class T3, class ...Args>
V<tuple<T1, T2, T3, Args...>> read(const int length) {
    V<tuple<T1, T2, T3, Args...>> ts(length);
    for (auto& t: ts) {
        cin >> t;
    }
    return ts;
}

// Output
namespace debug {
    template <class F, class S>
    ostream &operator<<(ostream& stream, const pair<F, S> &pair) {
        stream << "{" << pair.first << ", " << pair.second << "}";
        return stream;
    }
    template <class ...Args>
    ostream &operator<<(ostream& stream, const tuple<Args...> &tuple) {
        stream << "{";
        tuple_utils::print(stream, tuple, tuple_utils::gen_seq<sizeof...(Args)>());
        stream << "}";
        return stream;
    }

    template <class Iterator>
    struct Container {
        Container(const Iterator &begin, const Iterator &end) : begin(begin), end(end) {}
        const Iterator &begin;
        const Iterator &end;
    };

    template <class Iterator>
    Container<Iterator> container(const Iterator &begin, const Iterator &end) {
        return Container<Iterator>(begin, end);
    }

    template <class Iterator>
    ostream &operator<<(ostream &stream, const Container<Iterator> &container) {
        stream << "[";

        size_t cnt = 0;
        for (auto it = container.begin; it != container.end; ++it) {
            stream << *it;
            stream << "," << ((cnt % 10 == 9) ? "\n " : "\t");

            cnt += 1;
        }

        stream << "\b\b]";
        return stream;
    }

    template <class T, class Alloc>
    ostream &operator<<(ostream& stream, const vector<T, Alloc> &vector) {
        return stream << container(vector.begin(), vector.end());
    }
}

// Hash
namespace std {
    template <class F, class S>
    struct hash<pair<F, S>> {
        size_t operator ()(const pair<F, S> &p) const {
            return hash<F>()(p.first) ^ hash<S>()(p.second);
        }
    };

    template <class ...Args>
    struct hash<tuple<Args...>> {
        size_t operator ()(const tuple<Args...> &t) const {
            size_t retval = 0;

            tuple_utils::for_each<tuple_utils::hash_for_element, size_t, Args...>(retval, t);

            return retval;
        }
    };
}

#define MAIN
void body();

// main function (DO NOT EDIT)
int main (int argc, char **argv) {
    cin.tie(0);
    ios_base::sync_with_stdio(false);

    cout << fixed;
    body();

    return 0;
}

void body() {
    using namespace debug;
    auto s = read<string>();
    auto x = read<i32>();
    auto y = read<i32>();

    V<i32> dx;
    V<i32> dy;

    bool is_x = true;
    i32 cnt = 0;
    FORE (c, s) {
        if (c == 'F') {
            cnt ++;
        } else {
            if (is_x) {
                dx.push_back(cnt);
            } else {
                dy.push_back(cnt);
            }

            cnt = 0;
            is_x = !is_x;
        }
    }

    if (is_x) {
        dx.push_back(cnt);
    } else {
        dy.push_back(cnt);
    }

    sort(CTR(dx), std::greater<i32>());
    sort(CTR(dy), std::greater<i32>());

    bool ans = true;

    // xについて調査
    i64 x_curr = 0;
    FORE (d, dx) {
        if (x > x_curr) {
            x_curr += d;
        } else {
            x_curr -= d;
        }
    }
    if (x_curr != x) {
        ans = false;
    }

    // yについて
    i64 y_curr = 0;
    FORE (d, dy) {
        if (y > y_curr) {
            y_curr += d;
        } else {
            y_curr -= d;
        }
    }
    if (y_curr != y) {
        ans = false;
    }


    cout << (ans ? "Yes" : "No") << endl;
}