#if __INCLUDE_LEVEL__ == 0

#include __BASE_FILE__

using Mint = atcoder::modint998244353;

void Solve() {
  string s;
  IN(s);
  int n = Sz(s);

  vector<int> pos;
  pos.reserve(ranges::count(s, 'A'));
  for (int i : Rep(0, n)) {
    if (s[i] == 'A') {
      pos.push_back(i);
    }
  }

  int N = Sz(pos);

  vector<int> A(N);
  vector<int> B(N);
  for (int i : Rep(0, N)) {
    B[i] = pos[i] - i + 1;
  }
  OUT(nachia::main(N, n, A, B));
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  Solve();
}

#elif __INCLUDE_LEVEL__ == 1

#include <bits/stdc++.h>

// https://judge.yosupo.jp/submission/214966

namespace nachia {

template <class Modint>
class Comb {
 private:
  std::vector<Modint> F;
  std::vector<Modint> iF;

 public:
  void extend(int newN) {
    int prevN = (int)F.size() - 1;
    if (prevN >= newN) return;
    F.resize(newN + 1);
    iF.resize(newN + 1);
    for (int i = prevN + 1; i <= newN; i++) F[i] = F[i - 1] * Modint::raw(i);
    iF[newN] = F[newN].inv();
    for (int i = newN; i > prevN; i--) iF[i - 1] = iF[i] * Modint::raw(i);
  }
  Comb(int n = 1) {
    F.assign(2, Modint(1));
    iF.assign(2, Modint(1));
    extend(n);
  }
  Modint factorial(int n) const { return F[n]; }
  Modint invFactorial(int n) const { return iF[n]; }
  Modint invOf(int n) const { return iF[n] * F[n - 1]; }
  Modint comb(int n, int r) const {
    if (n < 0 || n < r || r < 0) return Modint(0);
    return F[n] * iF[r] * iF[n - r];
  }
  Modint invComb(int n, int r) const {
    if (n < 0 || n < r || r < 0) return Modint(0);
    return iF[n] * F[r] * F[n - r];
  }
  Modint perm(int n, int r) const {
    if (n < 0 || n < r || r < 0) return Modint(0);
    return F[n] * iF[n - r];
  }
  Modint invPerm(int n, int r) const {
    if (n < 0 || n < r || r < 0) return Modint(0);
    return iF[n] * F[n - r];
  }
  Modint operator()(int n, int r) const { return comb(n, r); }
};

}  // namespace nachia

namespace nachia {

template <class Fps>
Fps countStairSequenseBetweenTwoSequences(
    std::vector<int> L,
    std::vector<int> U,
    Fps In) {
  assert(L.size() == U.size());
  using Elem = typename Fps::ElemTy;

  int length = int(L.size());
  for (int i = 0; i + 1 < length; i++)
    if (L[i + 1] < L[i]) L[i + 1] = L[i];
  for (int i = length - 2; i >= 0; i--)
    if (L[i] < L[i + 1] - 1) L[i] = L[i + 1] - 1;
  for (int i = 0; i + 1 < length; i++)
    if (U[i + 1] > U[i] + 1) U[i + 1] = U[i] + 1;
  for (int i = length - 2; i >= 0; i--)
    if (U[i] > U[i + 1]) U[i] = U[i + 1];

  if (L[length - 1] > U[length - 1]) return Fps(0);
  for (int i = 0; i < length; i++)
    if (L[i] > U[i]) return Fps(U[length - 1] - L[length - 1] + 1);

  auto comb = nachia::Comb<Elem>(length + 1);
  auto combFps = [&](int n) -> Fps {
    Fps res(n + 1);
    for (int i = 0; i <= n; i++) res[i] = comb(n, i);
    return res;
  };
  auto transition = [&](int l, int r, const Fps& I, int off) -> Fps {
    return I.convolve(combFps(r - l), I.size() + r - l);
  };
  auto dfs_low = [&](auto dfs, int l, int r, Fps I) -> Fps {
    if (r - l == 1) {
      auto res = transition(l, r, I, L[l]);
      if (L[l] != L[r]) res = res.clip(1);
      return res;
    }
    int m = l + (r - l) / 2;

    auto resm = transition(l, m, I.clip(L[m] - L[l]), L[m]);
    auto buf = dfs(dfs, l, m, I.clip(0, L[m] - L[l]));
    for (int i = 0; i < buf.size(); i++) resm[i] += buf[i];

    auto resr = transition(m, r, resm.clip(L[r] - L[m]), L[r]);
    buf = dfs(dfs, m, r, resm.clip(0, L[r] - L[m]));
    for (int i = 0; i < buf.size(); i++) resr[i] += buf[i];
    return resr;
  };
  auto dfs_high = [&](auto& dfs, int l, int r, Fps I) -> Fps {
    if (r - l == 1) {
      if (U[l] == U[r]) return Fps(0);
      return transition(l, r, I, U[l] + 1 - (r - l)).clip(1);
    }
    int m = l + (r - l) / 2;

    auto resm = transition(l, m, I, U[l] + 1 - (r - l)).clip(m - l, r - l, 0, U[m] - U[l] + r - m);
    auto buf = dfs(dfs, l, m, I.clip(r - m));
    for (int i = 0; i < buf.size(); i++) resm[i + (r - m)] += buf[i];

    auto resr = transition(m, r, resm, U[l] + 1 - (r - m)).clip(r - m, r - m + U[m] - U[l], 0, U[r] - U[l]);
    buf = dfs(dfs, m, r, resm.clip(U[m] - U[l]));
    for (int i = 0; i < buf.size(); i++) resr[i + (U[m] - U[l])] += buf[i];
    return resr;
  };
  auto dfs = [&](auto dfs, int l, int r, Fps I) -> Fps {
    if (r - l == 1) {
      auto res = transition(l, r, I, L[l]);
      return res.clip(L[r] - L[l], U[r] + 1 - L[l]);
    }
    if (L[r] + (r - l) < U[l]) {
      Fps res1 = transition(l, r, I.clip(L[r] - L[l]), L[r]).clip(0, U[l] + 1 - L[r], 0, U[r] + 1 - L[r]);
      Fps res2 = dfs_low(dfs_low, l, r, I.clip(0, L[r] - L[l]));
      Fps res3 = dfs_high(dfs_high, l, r, I.clip(I.size() - (r - l)));
      for (int i = 0; i < res2.size(); i++) res1[i] += res2[i];
      for (int i = 0; i < res3.size(); i++) res1[res1.size() - 1 - i] += res3[res3.size() - 1 - i];
      return res1;
    }
    int m = (l + r) / 2;
    return dfs(dfs, m, r, dfs(dfs, l, m, I.move()));
  };
  return dfs(dfs, 0, length - 1, In.move());
}

}  // namespace nachia

namespace nachia {

template <unsigned int MOD>
struct PrimitiveRoot {
  using u64 = unsigned long long;
  static constexpr u64 powm(u64 a, u64 i) {
    u64 res = 1, aa = a;
    for (; i; i /= 2) {
      if (i & 1) res = res * aa % MOD;
      aa = aa * aa % MOD;
    }
    return res;
  }
  static constexpr bool ExamineVal(unsigned int g) {
    u64 t = MOD - 1;
    for (u64 d = 2; d * d <= t; d += 1 + (d & 1))
      if (t % d == 0) {
        if (powm(g, (MOD - 1) / d) == 1) return false;
        while (t % d == 0) t /= d;
      }
    if (t != 1)
      if (powm(g, (MOD - 1) / t) == 1) return false;
    return true;
  }
  static constexpr unsigned int GetVal() {
    for (u64 x = 2; x < MOD; x++)
      if (ExamineVal(x)) return x;
    return 0;
  }
  static const unsigned int val = GetVal();
};

}  // namespace nachia

namespace nachia {

int Popcount(unsigned long long c) noexcept {
  return __builtin_popcountll(c);
}

int MsbIndex(unsigned long long x) noexcept {
  return 63 - __builtin_clzll(x);
}

int LsbIndex(unsigned long long x) noexcept {
  return __builtin_ctzll(x);
}

}  // namespace nachia

namespace nachia {

template <class mint>
struct NttInterface {
  template <class Iter>
  void Butterfly(Iter, int) const {}

  template <class Iter>
  void IButterfly(Iter, int) const {}

  template <class Iter>
  void BitReversal(Iter a, int N) const {
    for (int i = 0, j = 0; j < N; j++) {
      if (i < j) std::swap(a[i], a[j]);
      for (int k = N >> 1; k > (i ^= k); k >>= 1)
        ;
    }
  }
};

}  // namespace nachia

namespace nachia {

template <class mint>
struct Ntt : NttInterface<mint> {
  using u32 = unsigned int;
  using u64 = unsigned long long;

  static int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (u32)(n)) x++;
    return x;
  }

  static constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
  }

  struct fft_info {
    static constexpr u32 g = nachia::PrimitiveRoot<mint::mod()>::val;
    static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
    using RootTable = std::array<mint, rank2 + 1>;
    RootTable root, iroot, rate3, irate3;

    fft_info() {
      root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
      iroot[rank2] = root[rank2].inv();
      for (int i = rank2 - 1; i >= 0; i--) {
        root[i] = root[i + 1] * root[i + 1];
        iroot[i] = iroot[i + 1] * iroot[i + 1];
      }
      mint prod = 1, iprod = 1;
      for (int i = 0; i <= rank2 - 3; i++) {
        rate3[i] = root[i + 3] * prod;
        irate3[i] = iroot[i + 3] * iprod;
        prod *= iroot[i + 3];
        iprod *= root[i + 3];
      }
    }
  };

  template <class RandomAccessIterator>
  void ButterflyLayered(RandomAccessIterator a, int n, int stride, int repeat) const {
    static const fft_info info;
    int h = n * stride;

    while (repeat--) {
      int len = 1;
      int p = h;
      if (ceil_pow2(n) % 2 == 1) {
        p >>= 1;
        for (int i = 0; i < p; i++) {
          mint l = a[i], r = a[i + p];
          a[i] = l + r;
          a[i + p] = l - r;
        }
        len <<= 1;
      }
      for (; p > stride;) {
        p >>= 2;
        mint rot = 1, imag = info.root[2];
        u64 mod2 = u64(mint::mod()) * mint::mod();
        int offset = p;
        for (int s = 0; s < len; s++) {
          if (s) rot *= info.rate3[LsbIndex(~(u32)(s - 1))];
          mint rot2 = rot * rot;
          mint rot3 = rot2 * rot;
          for (int i = offset - p; i < offset; i++) {
            u64 a0 = u64(a[i].val());
            u64 a1 = u64(a[i + p].val()) * rot.val();
            u64 a2 = u64(a[i + 2 * p].val()) * rot2.val();
            u64 a3 = u64(a[i + 3 * p].val()) * rot3.val();
            u64 a1na3imag = u64(mint(a1 + mod2 - a3).val()) * imag.val();
            u64 na2 = mod2 - a2;
            a[i] = a0 + a2 + a1 + a3;
            a[i + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
            a[i + 2 * p] = a0 + na2 + a1na3imag;
            a[i + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
          }
          offset += p << 2;
        }
        len <<= 2;
      }

      a += h;
    }
  }

  template <class RandomAccessIterator>
  void Butterfly(RandomAccessIterator a, int n) const {
    ButterflyLayered(a, n, 1, 1);
  }

  template <class RandomAccessIterator>
  void IButterflyLayered(RandomAccessIterator a, int n, int stride, int repeat) const {
    static const fft_info info;
    constexpr int MOD = mint::mod();

    while (repeat--) {
      int len = n;
      int p = stride;

      for (; 2 < len;) {
        len >>= 2;
        mint irot = 1, iimag = info.iroot[2];
        int offset = p;
        for (int s = 0; s < len; s++) {
          if (s) irot *= info.irate3[LsbIndex(~(u32)(s - 1))];
          mint irot2 = irot * irot;
          mint irot3 = irot2 * irot;
          for (int i = offset - p; i < offset; i++) {
            u64 a0 = a[i].val();
            u64 a1 = a[i + p].val();
            u64 a2 = a[i + 2 * p].val();
            u64 a3 = a[i + 3 * p].val();
            u64 a2na3iimag = mint((a2 + MOD - a3) * iimag.val()).val();
            a[i] = a0 + a1 + a2 + a3;
            a[i + p] = (a0 + (MOD - a1) + a2na3iimag) * irot.val();
            a[i + 2 * p] = (a0 + a1 + (MOD - a2) + (MOD - a3)) * irot2.val();
            a[i + 3 * p] = (a0 + (MOD - a1) + (MOD - a2na3iimag)) * irot3.val();
          }
          offset += p << 2;
        }
        p <<= 2;
      }
      if (len == 2) {
        for (int i = 0; i < p; i++) {
          mint l = a[i], r = a[i + p];
          a[i] = l + r;
          a[i + p] = l - r;
        }
        p <<= 1;
      }

      a += p;
    }
  }

  template <class RandomAccessIterator>
  void IButterfly(RandomAccessIterator a, int n) const {
    IButterflyLayered(a, n, 1, 1);
  }
};

}  // namespace nachia

namespace nachia {

template <class Elem, class NttInst = Ntt<Elem>>
struct FpsNtt {
 public:
  using Fps = FpsNtt;
  using ElemTy = Elem;
  static constexpr unsigned int MOD = Elem::mod();
  static constexpr int CONV_THRES = 30;
  static const NttInst nttInst;
  static const unsigned int zeta = nachia::PrimitiveRoot<MOD>::GetVal();

 private:
  using u32 = unsigned int;
  static Elem ZeroElem() noexcept { return Elem(0); }
  static Elem OneElem() noexcept { return Elem(1); }
  static Comb<Elem> comb;
  std::vector<Elem> a;
  int RSZ(int& sz) const { return sz = (sz < 0 ? size() : sz); }

 public:
  int size() const noexcept { return a.size(); }
  Elem& operator[](int x) noexcept { return a[x]; }
  const Elem& operator[](int x) const noexcept { return a[x]; }
  Elem getCoeff(int x) const noexcept { return (0 <= x && x < size()) ? a[x] : ZeroElem(); }
  static Comb<Elem>& GetComb() { return comb; }
  static int BestNttSize(int x) noexcept {
    assert(x);
    return 1 << MsbIndex(x * 2 - 1);
  }
  Fps move() { return std::move(*this); }
  Fps& set(int i, Elem c) {
    a[i] = c;
    return *this;
  }

  Fps& removeLeadingZeros() {
    int newsz = size();
    while (newsz && a[newsz - 1].val() == 0) newsz--;
    a.resize(newsz);
    if ((int)a.capacity() / 4 > newsz) a.shrink_to_fit();
    return *this;
  }

  FpsNtt() {}
  FpsNtt(int sz) : a(sz, ZeroElem()) {}
  FpsNtt(int sz, Elem e) : a(sz, e) {}
  FpsNtt(std::vector<Elem>&& src) : a(std::move(src)) {}
  FpsNtt(const std::vector<Elem>& src) : a(src) {}

  Fps& ntt() {
    capSize(BestNttSize(size()));
    nttInst.Butterfly(a.begin(), size());
    return *this;
  }
  Fps& intt() {
    nttInst.IButterfly(a.begin(), a.size());
    return times(Elem::raw(size()).inv());
  }
  Fps nttDouble(Fps vanilla) const {
    int n = size();
    assert(n != 0 && n == (n & -n));
    Elem q = Elem::raw(zeta).pow((Elem::mod() - 1) / (n * 2));
    Elem qq = OneElem();
    for (int i = 0; i < n; i++) {
      vanilla[i] *= qq;
      qq *= q;
    }
    vanilla.ntt();
    Fps res = clip(0, n * 2);
    for (int i = 0; i < n; i++) res[n + i] = vanilla[i];
    return res;
  }
  Fps nttDouble() const { return nttDouble(clip().intt().move()); }

  Fps clip(int srcL, int srcR = -1, int destL = 0, int resSz = -1) const {
    srcR = RSZ(srcR);
    if (resSz < 0) resSz = destL + srcR - srcL;
    int rj = std::min(std::min(srcR, size()) - srcL, resSz - destL);
    Fps res(resSz);
    for (int j = std::max(0, -srcL); j < rj; j++) res[j + destL] = a[j + srcL];
    return res;
  }
  Fps clip() const { return *this; }

  Fps& capSize(int l, int r) {
    if (r <= (int)size()) a.resize(r);
    if (size() <= l) a.resize(l, ZeroElem());
    return *this;
  }
  Fps& capSize(int z) {
    a.resize(RSZ(z), ZeroElem());
    return *this;
  }
  Fps& times(Elem x) {
    for (int i = 0; i < size(); i++) {
      a[i] *= x;
    }
    return *this;
  }
  Fps& timesFactorial(int z = -1) {
    comb.extend(RSZ(z));
    for (int i = 0; i < z; i++) {
      a[i] *= comb.factorial(i);
    }
    return *this;
  }
  Fps& timesInvFactorial(int z = -1) {
    comb.extend(RSZ(z));
    for (int i = 0; i < z; i++) {
      a[i] *= comb.invFactorial(i);
    }
    return *this;
  }
  Fps& clrRange(int l, int r) {
    for (int i = l; i < r; i++) {
      a[i] = ZeroElem();
    }
    return *this;
  }
  Fps& negate() {
    for (auto& e : a) {
      e = -e;
    }
    return *this;
  }
  Fps& mulEach(const Fps& other, int maxi = -1) {
    maxi = std::min(RSZ(maxi), std::min(size(), other.size()));
    for (int i = 0; i < maxi; i++) a[i] *= other[i];
    return *this;
  }
  Fps& reverse(int sz = -1) {
    RSZ(sz);
    std::reverse(a.begin(), a.begin() + sz);
    return *this;
  }
  Fps& revRange(int l, int r = -1) {
    RSZ(r);
    std::reverse(a.begin() + l, a.begin() + r);
    return *this;
  }

  static Fps convolution(const Fps& a, const Fps& b, int sz = -1) {
    if (std::min(a.size(), b.size()) <= CONV_THRES) {
      if (a.size() > b.size()) return convolution(b, a, sz);
      if (sz < 0) sz = std::max(0, a.size() + b.size() - 1);
      std::vector<Elem> res(sz);
      for (int i = 0; i < a.size(); i++)
        for (int j = 0; j < b.size() && i + j < sz; j++) res[i + j] += a[i] * b[j];
      return res;
    }
    int Z = BestNttSize(a.size() + b.size() - 1);
    return a.clip(0, Z).ntt().mulEach(b.clip(0, Z).ntt()).intt().capSize(sz).move();
  }
  Fps convolve(const Fps& r, int sz = -1) const { return convolution(*this, r, sz); }

  Fps powerSum(int sz) const {
    RSZ(sz);
    if (sz == 0) return {};
    int q = std::min(sz, 32);
    Fps x = Fps(q).set(0, OneElem()).move();
    for (int i = 1; i < q; i++)
      for (int j = 1; j <= std::min(i, (int)a.size() - 1); j++) x[i] += x[i - j] * a[j];
    while (x.size() < sz) {
      int hN = x.size(), N = hN * 2;
      Fps a = x.clip(0, N).ntt().move();
      Fps b = clip(0, N).ntt().mulEach(a).intt().clrRange(0, hN).ntt().mulEach(a).intt().move();
      for (int i = 0; i < hN; i++) b[i] = x[i];
      std::swap(b, x);
    }
    return x.capSize(sz).move();
  }

  Fps inv(int sz = -1) const {
    RSZ(sz);
    Elem iA0 = a[0].inv();
    return clip(0, std::min(sz, size())).times(-iA0).set(0, ZeroElem()).powerSum(sz).times(iA0).move();
  }

  Fps& difference() {
    if (size() == 0) return *this;
    for (int i = 0; i + 1 < size(); i++) a[i] = a[i + 1] * Elem::raw(i + 1);
    return capSize(size() - 1);
  }
  Fps& integral() {
    if (size() == 0) return capSize(1);
    capSize(size() + 1);
    comb.extend(size());
    for (int i = size() - 1; i >= 1; i--) a[i] = a[i - 1] * comb.invOf(i);
    return set(0, ZeroElem());
  }

  Fps log(int sz = -1) {
    RSZ(sz);
    assert(sz != 0);
    assert(a[0].val() == 1);
    return convolution(inv(sz), clip().difference(), sz - 1).integral();
  }

  Fps exp(int sz = -1) {
    RSZ(sz);
    Fps res = Fps(1).set(0, OneElem());
    while (res.size() < sz) {
      auto z = res.size();
      auto tmp = res.capSize(z * 2).log().set(0, -OneElem()).move();
      for (int i = 0; i < z * 2 && i < size(); i++) tmp[i] -= a[i];
      auto resntt = res.clip().ntt().mulEach(tmp.ntt()).intt().move();
      for (int i = z; i < z * 2; i++) res[i] = -resntt[i];
    }
    return res.capSize(0, sz).move();
  }

  Fps pow(unsigned long long k, int sz = -1) {
    int n = RSZ(sz);
    if (k == 0) return Fps(n).set(0, OneElem()).move();
    int ctz = 0;
    while (ctz < n && a[ctz].val() == 0) ctz++;
    if ((unsigned long long)ctz >= (n - 1) / k + 1) return Fps(n);
    Elem a0 = a[ctz];
    return clip(ctz, ctz + n - ctz * k).times(a0.inv()).log().times(Elem(k)).exp().times(a0.pow(k)).clip(0, -1, ctz * k);
  }

  auto begin() { return a.begin(); }
  auto end() { return a.end(); }
  auto begin() const { return a.begin(); }
  auto end() const { return a.end(); }

  std::string toString(std::string beg = "[ ", std::string delim = " ", std::string en = " ]") const {
    std::string res = beg;
    bool f = false;
    for (auto x : a) {
      if (f) {
        res += delim;
      }
      f = true;
      res += std::to_string(x.val());
    }
    res += en;
    return res;
  }

  std::vector<Elem> getVectorMoved() { return std::move(a); }

  Fps& operator+=(const Fps& r) {
    capSize(std::max(size(), r.size()));
    for (int i = 0; i < r.size(); i++) a[i] += r[i];
    return *this;
  }
  Fps& operator-=(const Fps& r) {
    capSize(std::max(size(), r.size()));
    for (int i = 0; i < r.size(); i++) a[i] -= r[i];
    return *this;
  }
  Fps operator+(const Fps& r) const { return (clip(0, std::max(size(), r.size())) += r).move(); }
  Fps operator-(const Fps& r) const { return (clip(0, std::max(size(), r.size())) -= r).move(); }
  Fps operator-() const { return (clip().negate()).move(); }
  Fps operator*(const Fps& r) const { return convolve(r).removeLeadingZeros().move(); }
  Fps& operator*=(const Fps& r) { return (*this) = operator*(r); }
  Fps& operator*=(Elem m) { return times(m); }
  Fps operator*(Elem m) const { return (clip() *= m).move(); }

  Elem eval(Elem x) const {
    Elem res = 0;
    for (int i = size() - 1; i >= 0; i--) res = res * x + a[i];
    return res;
  }
};

template <class Elem, class NttInst> Comb<Elem> FpsNtt<Elem, NttInst>::comb;
template <class Elem, class NttInst> const NttInst FpsNtt<Elem, NttInst>::nttInst;

}  // namespace nachia

namespace nachia {

std::pair<long long, long long> ExtGcd(long long a, long long b) {
  long long x = 1, y = 0;
  while (b) {
    long long u = a / b;
    std::swap(a -= b * u, b);
    std::swap(x -= y * u, y);
  }
  return std::make_pair(x, a);
}

}  // namespace nachia

namespace nachia {

template <unsigned int MOD>
struct StaticModint {
 private:
  using u64 = unsigned long long;
  unsigned int x;

 public:
  using my_type = StaticModint;
  template <class Elem>
  static Elem safe_mod(Elem x) {
    if (x < 0) {
      if (0 <= x + MOD) return x + MOD;
      return MOD - ((-(x + MOD) - 1) % MOD + 1);
    }
    return x % MOD;
  }

  StaticModint() : x(0) {}
  StaticModint(const my_type& a) : x(a.x) {}
  StaticModint& operator=(const my_type&) = default;
  template <class Elem>
  StaticModint(Elem v) : x(safe_mod(v)) {}
  unsigned int operator*() const noexcept { return x; }
  my_type& operator+=(const my_type& r) noexcept {
    auto t = x + r.x;
    if (t >= MOD) t -= MOD;
    x = t;
    return *this;
  }
  my_type operator+(const my_type& r) const noexcept {
    my_type res = *this;
    return res += r;
  }
  my_type& operator-=(const my_type& r) noexcept {
    auto t = x + MOD - r.x;
    if (t >= MOD) t -= MOD;
    x = t;
    return *this;
  }
  my_type operator-(const my_type& r) const noexcept {
    my_type res = *this;
    return res -= r;
  }
  my_type operator-() const noexcept {
    my_type res = *this;
    res.x = ((res.x == 0) ? 0 : (MOD - res.x));
    return res;
  }
  my_type& operator*=(const my_type& r) noexcept {
    x = (u64)x * r.x % MOD;
    return *this;
  }
  my_type operator*(const my_type& r) const noexcept {
    my_type res = *this;
    return res *= r;
  }
  my_type pow(unsigned long long i) const noexcept {
    my_type a = *this, res = 1;
    while (i) {
      if (i & 1) {
        res *= a;
      }
      a *= a;
      i >>= 1;
    }
    return res;
  }
  my_type inv() const { return my_type(ExtGcd(x, MOD).first); }
  unsigned int val() const noexcept { return x; }
  static constexpr unsigned int mod() { return MOD; }
  static my_type raw(unsigned int val) noexcept {
    auto res = my_type();
    res.x = val;
    return res;
  }
  my_type& operator/=(const my_type& r) { return operator*=(r.inv()); }
  my_type operator/(const my_type& r) const { return operator*(r.inv()); }
};

}  // namespace nachia
namespace nachia {
using Modint = nachia::StaticModint<998244353>;
using Fps = nachia::FpsNtt<Modint>;

int main(int N, int M, std::vector<int> A, std::vector<int> B) {
  for (int i = 0; i < N; i++) {
    std::swap(A[i], B[i]);
    A[i] = M - A[i];
    B[i] = M - B[i];
  }
  std::reverse(A.begin(), A.end());
  std::reverse(B.begin(), B.end());
  std::vector<int> L(N + M, 0), U(N + M, M - 1);
  U[0] = 0;
  L[N + M - 1] = M - 1;
  for (int i = 0; i < N; i++)
    if (L[i + A[i]] < A[i]) L[i + A[i]] = A[i];
  for (int i = 0; i < N; i++)
    if (U[i + B[i]] > B[i] - 1) U[i + B[i]] = B[i] - 1;

  auto ans = countStairSequenseBetweenTwoSequences(std::move(L), std::move(U), Fps(1).set(0, 1))[0];
  return ans.val();
}
}  // namespace nachia

#include <atcoder/modint.hpp>

template <class T> concept MyRange = std::ranges::range<T> && !std::convertible_to<T, std::string_view>;
template <class T> concept MyTuple = std::__is_tuple_like<T>::value && !MyRange<T>;

namespace std {

istream& operator>>(istream& is, MyRange auto&& r) {
  for (auto&& e : r) is >> e;
  return is;
}
istream& operator>>(istream& is, MyTuple auto&& t) {
  apply([&](auto&... xs) { (is >> ... >> xs); }, t);
  return is;
}

ostream& operator<<(ostream& os, MyRange auto&& r) {
  auto sep = "";
  for (auto&& e : r) os << exchange(sep, " ") << e;
  return os;
}
ostream& operator<<(ostream& os, MyTuple auto&& t) {
  auto sep = "";
  apply([&](auto&... xs) { ((os << exchange(sep, " ") << xs), ...); }, t);
  return os;
}

template <class T, atcoder::internal::is_modint_t<T>* = nullptr>
istream& operator>>(istream& is, T& x) {
  int v;
  is >> v;
  x = T::raw(v);
  return is;
}

template <class T, atcoder::internal::is_modint_t<T>* = nullptr>
ostream& operator<<(ostream& os, const T& x) {
  return os << x.val();
}

}  // namespace std

using namespace std;

#define Rep(...) [](int l, int r) { return views::iota(min(l, r), r); }(__VA_ARGS__)
#define Sz(r) int(size(r))
#define IN(...) (cin >> forward_as_tuple(__VA_ARGS__))
#define OUT(...) (cout << forward_as_tuple(__VA_ARGS__) << '\n')

#endif  // __INCLUDE_LEVEL__ == 1