// https://judge.yosupo.jp/submission/319327

#include <bits/stdc++.h>
using namespace std;
#include<vector>
#include<assert.h>

//modint+畳み込み+逆元テーブル

// from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9
// (based on AtCoder STL)

#include <algorithm>
#include <array>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder



#include <utility>

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;
    
    barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
    
    unsigned int umod() const { return _m; }
    
    unsigned int mul(unsigned int a, unsigned int b) const {
        
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (long long a : {2, 7, 61}) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
    
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b
        
        
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

}  // namespace internal

}  // namespace atcoder


#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;

template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;

template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;

template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
                           std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;

template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder

#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;
    
public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    
    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }
    static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
    
    unsigned int val() const { return _v; }
    
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    
private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;
    
public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    
    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }
    dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
    
    unsigned int val() const { return _v; }
    
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    
private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder

#include <cassert>
#include <type_traits>
#include <vector>

namespace atcoder {

namespace internal {

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
    
    static bool first = true;
    static mint sum_e[30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
    }
    for (int ph = 1; ph <= h; ph++) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint now = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p] * now;
                a[i + offset] = l + r;
                a[i + offset + p] = l - r;
            }
            now *= sum_e[bsf(~(unsigned int)(s))];
        }
    }
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
    
    static bool first = true;
    static mint sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
    }
    
    for (int ph = h; ph >= 1; ph--) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint inow = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p];
                a[i + offset] = l + r;
                a[i + offset + p] =
                (unsigned long long)(mint::mod() + l.val() - r.val()) *
                inow.val();
            }
            inow *= sum_ie[bsf(~(unsigned int)(s))];
        }
    }
}

}  // namespace internal

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) {
        if (n < m) {
            std::swap(n, m);
            std::swap(a, b);
        }
        std::vector<mint> ans(n + m - 1);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
        return ans;
    }
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}

template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    
    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
        a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
        b2[i] = mint(b[i]);
    }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        c[i] = c2[i].val();
    }
    return c;
}

std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                      const std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    
    static constexpr unsigned long long MOD1 = 754974721;  // 2^24
    static constexpr unsigned long long MOD2 = 167772161;  // 2^25
    static constexpr unsigned long long MOD3 = 469762049;  // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
    
    static constexpr unsigned long long i1 =
    internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 =
    internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 =
    internal::inv_gcd(MOD1 * MOD2, MOD3).second;
    
    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);
    
    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        long long diff =
        c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {
            0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }
    
    return c;
}

}  // namespace atcoder

using mint=atcoder::modint998244353;

namespace po167{
template<class T>
struct Binomial{
    std::vector<T> fact_vec, fact_inv_vec;
    void extend(int m = -1){
        int n = fact_vec.size();
        if (m == -1) m = n * 2;
        if (n >= m) return;
        fact_vec.resize(m);
        fact_inv_vec.resize(m);
        for (int i = n; i < m; i++){
            fact_vec[i] = fact_vec[i - 1] * T(i);
        }
        fact_inv_vec[m - 1] = T(1) / fact_vec[m - 1];
        for (int i = m - 1; i > n; i--){
            fact_inv_vec[i - 1] = fact_inv_vec[i] * T(i);
        }
    }
    Binomial(int MAX = 0){
        fact_vec.resize(1, T(1));
        fact_inv_vec.resize(1, T(1));
        extend(MAX + 1);
    }
    
    T fact(int i){
        if (i < 0) return 0;
        while (int(fact_vec.size()) <= i) extend();
        return fact_vec[i];
    }
    T invfact(int i){
        if (i < 0) return 0;
        while (int(fact_inv_vec.size()) <= i) extend();
        return fact_inv_vec[i];
    }
    T C(int a, int b){
        if (a < b || b < 0) return 0;
        return fact(a) * invfact(b) * invfact(a - b);
    }
    T invC(int a, int b){
        if (a < b || b < 0) return 0;
        return fact(b) * fact(a - b) *invfact(a);
    }
    T P(int a, int b){
        if (a < b || b < 0) return 0;
        return fact(a) * invfact(a - b);
    }
    T inv(int a){
        if (a < 0) return inv(-a) * T(-1);
        if (a == 0) return 1;
        return fact(a - 1) * invfact(a);
    }
    T Catalan(int n){
        if (n < 0) return 0;
        return fact(2 * n) * invfact(n + 1) * invfact(n);
    }
    T narayana(int n, int k){
        if (n <= 0 || n < k || k < 1) return 0;
        return C(n, k) *  C(n, k - 1) * inv(n);
    }
    T Catalan_pow(int n,int d){
        if (n < 0 || d < 0) return 0;
        if (d == 0){
            if (n == 0) return 1;
            return 0;
        }
        return T(d) * inv(d + n) * C(2 * n + d - 1, n);
    }
    // retrun [x^a] 1/(1-x)^b
    T ruiseki(int a,int b){
        if (a < 0 || b < 0) return 0;
        if (a == 0){
            return 1;
        }
        return C(a + b - 1, b - 1);
    }
    // (a, b) -> (c, d)
    // always x + e >= y
    T mirror(int a, int b, int c, int d, int e = 0){
        if (a + e < b || c + e < d) return 0;
        if (a > c || b > d) return 0;
        a += e;
        c += e;
        return C(c + d - a - b, c - a) - C(c + d - a - b, c - b + 1);
    }
    // return sum_{i = 0, ... , a} sum_{j = 0, ... , b} C(i + j, i)
    // return C(a + b + 2, a + 1) - 1;
    T gird_sum(int a, int b){
        if (a < 0 || b < 0) return 0;
        return C(a + b + 2, a + 1) - 1;
    }
    // return sum_{i = a, ..., b - 1} sum_{j = c, ... , d - 1} C(i + j, i)
    // AGC 018 E
    T gird_sum_2(int a, int b, int c, int d){
        if (a >= b || c >= d) return 0;
        a--, b--, c--, d--;
        return gird_sum(a, c) - gird_sum(a, d) - gird_sum(b, c) + gird_sum(b, d);
    }
    
    // the number of diagonal dissections of a convex n-gon into k+1 regions.
    // OEIS A033282
    // AGC065D
    T diagonal(int n, int k){
        if (n <= 2 || n - 3 < k || k < 0) return 0;
        return C(n - 3, k) * C(n + k - 1, k) * inv(k + 1);
    }
};
}
#line 4 "fps/FPS_cyclic_convolution.hpp"

namespace po167{
// |f| = |g| = 2 ^ n
template<class T>
std::vector<T> FPS_cyclic_convolution(std::vector<T> f, std::vector<T> g){
    atcoder::internal::butterfly(f);
    atcoder::internal::butterfly(g);
    for (int i = 0; i < (int)f.size(); i++) f[i] *= g[i];
    atcoder::internal::butterfly_inv(f);
    T iz = (T)(1) / (T)(f.size());
    for (int i = 0; i < (int)f.size(); i++) f[i] *= iz;
    return f;
}
}
#line 5 "fps/count_increasing_sequences.hpp"
namespace po167{
template<class T>
std::pair<std::vector<T>, std::vector<T>> count_square(std::vector<T> L, std::vector<T> D){
    assert(!L.empty() && !D.empty());
    int N = L.size();
    int M = D.size();
    if (std::min(N, M) <= 200){
        int sw = 0;
        if (N > M) std::swap(N, M), std::swap(L, D), sw = 1;
        std::vector<T> R(N);
        for (int i = 0; i < N; i++){
            D[0] += L[i];
            for (int j = 1; j < M; j++) D[j] += D[j - 1];
            R[i] = D.back();
        }
        if (sw) std::swap(R, D);
        return {R, D};
    }
    po167::Binomial<T> table(N + M);
    std::vector<T> R(N), U(M);
    int z = 0;
    while ((1 << z) < (N + M - 1)) z++;
    // 左から右
    {
        std::vector<T> tmp(N);
        for (int i = 0; i < N; i++) tmp[i] = table.C(M - 1 + i, i);
        tmp = atcoder::convolution(tmp, L);
        for (int i = 0; i < N; i++) R[i] += tmp[i];
    }
    // 左から上
    {
        std::vector<T> tmp(1 << z);
        for (int i = 0; i < N; i++) L[i] *= table.invfact(N - 1 - i);
        for (int i = 0; i < N + M - 1; i++) tmp[i] = table.fact(i);
        L.resize(1 << z, 0);
        tmp = po167::FPS_cyclic_convolution(tmp, L);
        for (int i = 0; i < M; i++) U[i] += tmp[N - 1 + i] * table.invfact(i);
    }
    // 下から上
    {
        std::vector<T> tmp(M);
        for (int i = 0; i < M; i++) tmp[i] = table.C(N - 1 + i, i);
        tmp = atcoder::convolution(tmp, D);
        for (int i = 0; i < M; i++) U[i] += tmp[i];
    }
    // 下から右
    {
        std::vector<T> tmp(1 << z);
        for (int i = 0; i < M; i++) D[i] *= table.invfact(M - i - 1);
        for (int i = 0; i < N + M - 1; i++) tmp[i] = table.fact(i);
        D.resize(1 << z, 0);
        tmp = po167::FPS_cyclic_convolution(tmp, D);
        for (int i = 0; i < N; i++) R[i] += tmp[M - 1 + i] * table.invfact(i);
    }
    return {R, U};
}
template<class T>
/*
 * g(A, x) を
 * 0 <= B[i] < A[i] かつ B[i] = x を満たす
 * 広義単調増加列 B の数とする
 * res[x] = sum C[i] * g(A[i:N], x)
 * を返す
 */
std::vector<T> count_increase_sequences_with_upper_bounds(std::vector<int> A, std::vector<T> C){
    int N = A.size();
    assert((int)C.size() == N);
    assert(N);
    for (int i = (int)(A.size()) - 1; i > 0; i--) A[i - 1] = std::min(A[i - 1], A[i]);
    if (A.back() == 0) return {};
    if (std::min(A.back(), N) <= 200){
        std::vector<T> dp(0);
        dp.reserve(A.back());
        for (int i = 0; i < N; i++){
            dp.resize(A[i], 0);
            if (A[i]) dp[0] += C[i];
            for (int j = 1; j < (int)dp.size(); j++){
                dp[j] += dp[j - 1];
            }
        }
        return dp;
    }
    if (N == 1){
        std::vector<T> res(A[0]);
        for (int i = 0; i < A[0]; i++) res[i] = C[0];
        return res;
    }
    int m = N / 2;
    std::vector<int> LA(m), RA(N - m);
    std::vector<T> LC(m), RC(N - m);
    for (int i = 0; i < m; i++){
        LA[i] = A[i];
        LC[i] = C[i];
    }
    for (int i = 0; i < N - m; i++){
        RA[i] = A[i + m] - A[m - 1];
        RC[i] = C[i + m];
    }
    std::vector<T> res;
    res.reserve(A.back());
    auto L = count_increase_sequences_with_upper_bounds(LA, LC);
    if (!L.empty()){
        auto [R, U] = count_square(L, RC);
        for (int i = 0; i < (int)R.size(); i++) res.push_back(R[i]);
        std::swap(U, RC);
    }
    auto R = count_increase_sequences_with_upper_bounds(RA, RC);
    for (auto x : R) res.push_back(x);
    return res;
}
template<class T>
std::vector<T> NAIVE_count_increase_sequences_with_upper_lower_bounds(std::vector<int> A, std::vector<int> B, std::vector<T> C = {}){
    std::vector<T> tmp(B.back() - A[0]);
    if (C.empty()){
        int b = B[0];
        for (int i = 1; i < (int)B.size(); i++) b = std::min(b, B[i]);
        for (int i = 0; i < b - A[0]; i++) tmp[i] = 1;
    }
    else for (int i = 0; i < (int)std::min(tmp.size(), C.size()); i++) tmp[i] = C[i];
    int N = A.size();
    for (int i = 1; i < N; i++){
        for (int j = 1; j < (int)tmp.size(); j++){
            tmp[j] += tmp[j - 1];
        }
        for (int j = 0; j < (int)tmp.size(); j++){
            if (j < A[i] - A[0] || B[i] - A[0] <= j) tmp[j] = 0;
        }
    }
    std::vector<T> res(B.back() - A.back());
    for (int i = 0; i < B.back() - A.back(); i++){
        res[i] = tmp[A.back() - A[0] + i];
    }
    return res;
}

template<class T>
/*
 * f(a, b) を X[0] = a, X[N - 1] = b であるような、A, B に挟まれたものとする
 * 長さ B[N - 1] - A[N - 1] を返す
 * res[b - A.back()] = sum C[a - A[0]] * f(a, b)
 * A, B は広義単調増加が嬉しい
 */
std::vector<T> count_increase_sequences_with_upper_lower_bounds(std::vector<int> A, std::vector<int> B, std::vector<T> C = {}){
    int N = A.size();
    assert(A.size() == B.size());
    for (int i = 0; i < N - 1; i++){
        A[i + 1] = std::max(A[i], A[i + 1]);
    }
    for (int i = N - 1; i > 0; i--){
        B[i - 1] = std::min(B[i], B[i - 1]);
    }
    if (A.back() >= B.back()) return {};
    // A[0] == 0 にする
    std::vector<T> res(B.back() - A.back(), 0);
    {
        int tmp = A[0];
        for (int i = 0; i < N; i++){
            A[i] -= tmp;
            B[i] -= tmp;
            if (A[i] >= B[i]) return res;
        }
    }
    if (C.empty()){
        C.resize(B[0] - A[0], 1);
    }
    else assert((int)(C.size()) == B[0] - A[0]);
    int l = 0;
    while (B[l] <= A.back()){
        for (int i = (int)(C.size()) - 1; i > 0; i--) C[i] -= C[i - 1];
        int nl = l;
        while (A[nl] < B[l]) nl++;
        std::vector<int> tmp(B[l] - A[l]);
        tmp[0] = 1;
        for (int i = l; i < nl; i++){
            tmp[A[i] - A[l]]++;
        }
        for (int i = 1; i < B[l] - A[l]; i++) tmp[i] += tmp[i - 1];
        auto X = count_increase_sequences_with_upper_bounds(tmp, C);
        std::vector<int> nB(nl - l + 1);
        for (int i = l; i <= nl; i++){
            nB[i - l] = B[i] - B[l];
        }
        auto Y = count_increase_sequences_with_upper_bounds(nB, X);
        C.resize(B[nl] - A[nl]);
        for (int i = 0; i < B[nl] - A[nl]; i++){
            C[i] = Y[i + A[nl] - B[l]];
        }
        l = nl;
    }
    // A を揃えてしまえ
    {
        int a = A[l];
        for (int i = l; i < N; i++){
            A[i] -= a;
            B[i] -= a;
        }
    }
    for (int i = (int)(C.size()) - 1; i > 0; i--) C[i] -= C[i - 1];
    std::vector<T> D(N - l, 0);
    if (A.back() != 0){
        std::vector<T> L(A.back());
        for (int i = 0; i < (int)L.size(); i++) L[i] = C[i];
        std::vector<int> tmp(L.size());
        tmp[0] = 1;
        for (int i = l; i < N; i++){
            if (A[i] < (int)tmp.size()) tmp[A[i]]++;
        }
        for (int i = 1; i < (int)tmp.size(); i++){
            tmp[i] += tmp[i - 1];
        }
        auto nD = count_increase_sequences_with_upper_bounds(tmp, L);
        for (int i = 0; i < (int)nD.size(); i++) D[i] = nD[i];
    }
    for (int i = A.back(); i < B[l]; i++) C[i - A.back()] = C[i];
    C.resize(B[l] - A.back());
    auto [R, U] = count_square(C, D);
    res = R;
    std::vector<int> nB(N - l);
    for (int i = 0; i < N - l; i++) nB[i] = B[i + l] - B[l];
    R = count_increase_sequences_with_upper_bounds(nB, U);
    for (auto x : R) res.push_back(x);
    return res;
}
}
#line 2 "a.cpp"
#include <iostream>
int main() {
    string S;cin>>S;
    int la=-1;
    vector<int> A,B;
    for(int i=0;i<S.size();i++){
        if(S[i]=='A'){
            A.push_back(0);
            B.push_back(i-la-1);
            la=i;
        }
    }
    for(int i=1;i<B.size();i++) B[i]+=B[i-1];
    for(int i=0;i<B.size();i++) B[i]++;
    if(A.size()==0){
        cout<<1<<"\n";
    }else{
        int N=A.size();
        int M=B.back()+1;
        using mint = atcoder::modint998244353;
        auto tmp = po167::count_increase_sequences_with_upper_lower_bounds<mint>(A, B);
        mint ans = 0;
        for (auto x : tmp) ans += x;
        std::cout << ans.val() << "\n";
    }
}