#include #include using namespace std; using namespace atcoder; enum Mode { FAST = 1, NAIVE = -1, }; template struct FormalPowerSeries : std::vector { using std::vector::vector; using std::vector::size; using std::vector::resize; using F = FormalPowerSeries; F &operator+=(const F &g) { for(int i = 0; i < int(std::min((*this).size(), g.size())); i++) (*this)[i] += g[i]; return *this; } F &operator+=(const T &t) { assert(int((*this).size())); (*this)[0] += t; return *this; } F &operator-=(const F &g) { for(int i = 0; i < int(std::min((*this).size(), g.size())); i++) (*this)[i] -= g[i]; return *this; } F &operator-=(const T &t) { assert(int((*this).size())); (*this)[0] -= t; return *this; } F &operator*=(const T &t) { for(int i = 0; i < int((*this).size()); ++i) (*this)[i] *= t; return *this; } F &operator/=(const T &t) { T div = t.inv(); for(int i = 0; i < int((*this).size()); ++i) (*this)[i] *= div; return *this; } F &operator>>=(const int sz) const { assert(sz >= 0); int n = (*this).size(); (*this).erase((*this).begin(), (*this).begin() + std::min(sz, n)); (*this).resize(n); return *this; } F &operator<<=(const int sz) const { assert(sz >= 0); int n = (*this).size(); (*this).insert((*this).begin(), (*this).begin() + sz, 0); (*this).resize(n); return *this; } F &operator%=(const F &g) { return *this -= *this / g * g; } F &operator=(const std::vector &v) { int n = (*this).size(); for(int i = 0; i < n; ++i) (*this)[i] = v[i]; return *this; } F operator-() const { F ret = *this; return ret * -1; } F &operator*=(const F &g) { if(mode == FAST) { int n = (*this).size(); auto tmp = atcoder::convolution(*this, g); for(int i = 0; i < n; ++i) (*this)[i] = tmp[i]; return *this; } else { int n = (*this).size(), m = g.size(); for(int i = n - 1; i >= 0; --i) { (*this)[i] *= g[0]; for(int j = 1; j < std::min(i + 1, m); j++) (*this)[i] += (*this)[i - j] * g[j]; } return *this; } } F &operator/=(const F &g) { if(mode == FAST) { int n = (*this).size(); (*this) = atcoder::convolution(*this, g.inv()); return *this; } else { assert(g[0] != T(0)); T ig0 = g[0].inv(); int n = (*this).size(), m = g.size(); for(int i = 0; i < n; ++i) { for(int j = 1; j < std::min(i + 1, m); ++j) (*this)[i] -= (*this)[i - j] * g[j]; (*this)[i] *= ig0; } return *this; } } F operator+(const F &g) const { return F(*this) += g; } F operator+(const T &t) const { return F(*this) += t; } F operator-(const F &g) const { return F(*this) -= g; } F operator-(const T &t) const { return F(*this) -= t; } F operator*(const F &g) const { return F(*this) *= g; } F operator*(const T &t) const { return F(*this) *= t; } F operator/(const F &g) const { return F(*this) /= g; } F operator/(const T &t) const { return F(*this) /= t; } F operator%(const F &g) const { return F(*this) %= g; } T eval(const T &t) const { int n = (*this).size(); T res = 0, tmp = 1; for(int i = 0; i < n; ++i) res += (*this)[i] * tmp, tmp *= t; return res; } F inv(int deg = -1) const { int n = (*this).size(); assert(mode == FAST and n and (*this)[0] != 0); if(deg == -1) deg = n; assert(deg > 0); F res{(*this)[0].inv()}; while(int(res.size()) < deg) { int m = res.size(); F f((*this).begin(), (*this).begin() + std::min(n, m * 2)), r(res); f.resize(m * 2), atcoder::internal::butterfly(f); r.resize(m * 2), atcoder::internal::butterfly(r); for(int i = 0; i < m * 2; ++i) f[i] *= r[i]; atcoder::internal::butterfly_inv(f); f.erase(f.begin(), f.begin() + m); f.resize(m * 2), atcoder::internal::butterfly(f); for(int i = 0; i < m * 2; ++i) f[i] *= r[i]; atcoder::internal::butterfly_inv(f); T iz = T(m * 2).inv(); iz *= -iz; for(int i = 0; i < m; ++i) f[i] *= iz; res.insert(res.end(), f.begin(), f.begin() + m); } res.resize(deg); return res; } F &diff_inplace() { int n = (*this).size(); for(int i = 1; i < n; ++i) (*this)[i - 1] = (*this)[i] * i; (*this)[n - 1] = 0; return *this; } F diff() const { F(*this).diff_inplace(); } F &integral_inplace() { int n = (*this).size(), mod = T::mod(); std::vector inv(n); { inv[1] = 1; for(int i = 2; i < n; ++i) inv[i] = T(mod) - inv[mod % i] * (mod / i); } for(int i = n - 2; i >= 0; --i) (*this)[i + 1] = (*this)[i] * inv[i + 1]; (*this)[0] = 0; return *this; } F integral() const { return F(*this).integral_inplace(); } F &log_inplace() { int n = (*this).size(); assert(n and (*this)[0] == 1); F f_inv = (*this).inv(); (*this).diff_inplace(); (*this) *= f_inv; (*this).integral_inplace(); return *this; } F log() const { return F(*this).log_inplace(); } F &deriv_inplace() { int n = (*this).size(); assert(n); for(int i = 2; i < n; ++i) (*this)[i] *= i; (*this).erase((*this).begin()); (*this).push_back(0); return *this; } F deriv() const { return F(*this).deriv_inplace(); } F &exp_inplace() { int n = (*this).size(); assert(n and (*this)[0] == 0); F g{1}; (*this)[0] = 1; F h_drv((*this).deriv()); for(int m = 1; m < n; m *= 2) { F f((*this).begin(), (*this).begin() + m); f.resize(2 * m), atcoder::internal::butterfly(f); auto mult_f = [&](F &p) { p.resize(2 * m); atcoder::internal::butterfly(p); for(int i = 0; i < 2 * m; ++i) p[i] *= f[i]; atcoder::internal::butterfly_inv(p); p /= 2 * m; }; if(m > 1) { F g_(g); g_.resize(2 * m), atcoder::internal::butterfly(g_); for(int i = 0; i < 2 * m; ++i) g_[i] *= g_[i] * f[i]; atcoder::internal::butterfly_inv(g_); T iz = T(-2 * m).inv(); g_ *= iz; g.insert(g.end(), g_.begin() + m / 2, g_.begin() + m); } F t((*this).begin(), (*this).begin() + m); t.deriv_inplace(); { F r{h_drv.begin(), h_drv.begin() + m - 1}; mult_f(r); for(int i = 0; i < m; ++i) t[i] -= r[i] + r[m + i]; } t.insert(t.begin(), t.back()); t.pop_back(); t *= g; F v((*this).begin() + m, (*this).begin() + std::min(n, 2 * m)); v.resize(m); t.insert(t.begin(), m - 1, 0); t.push_back(0); t.integral_inplace(); for(int i = 0; i < m; ++i) v[i] -= t[m + i]; mult_f(v); for(int i = 0; i < std::min(n - m, m); ++i) (*this)[m + i] = v[i]; } return *this; } F exp() const { return F(*this).exp_inplace(); } F &pow_inplace(long long k) { int n = (*this).size(), l = 0; assert(k >= 0); if(!k) { for(int i = 0; i < n; ++i) (*this)[i] = !i; return *this; } while(l < n and (*this)[l] == 0) ++l; if(l > (n - 1) / k or l == n) return *this = F(n); T c = (*this)[l]; (*this).erase((*this).begin(), (*this).begin() + l); (*this) /= c; (*this).log_inplace(); (*this).resize(n - l * k); (*this) *= k; (*this).exp_inplace(); (*this) *= c.pow(k); (*this).insert((*this).begin(), l * k, 0); return *this; } F pow(const long long k) const { return F(*this).pow_inplace(); } }; using mint = modint998244353; using fps = FormalPowerSeries; fps product_of_polynomial_sequence(vector F){ queue Q; Q.push({1}); for(auto f : F) Q.push(f); int cnt = 0; while((int)Q.size()>1){ fps f = Q.front(); Q.pop(); fps g = Q.front(); Q.pop(); for(int i=0; i<(int)g.size(); i++) f.push_back(0); f *= g; Q.push(f); } return Q.front(); }; int main(){ int n, m; cin >> n >> m; vector fac(2*n+1, 1); for(int i=2; i<=2*n; i++) fac[i] = fac[i-1]*mint(i); vector C(n+1, 1); for(int i=1; i<=n; i++) C[i] = fac[2*i]/(fac[i+1]*fac[i]); vector F; int D = 0; for(int i=0; i> L >> R; if((R-L+1)%2==1) continue; D += R-L+1; fps f(R-L+2, 0); f[0] = 1; f[R-L+1] = -C[(R-L+1)/2]; F.push_back(f); } if(n%2==1){ cout << 0 << '\n'; return 0; } fps v = product_of_polynomial_sequence(F); mint ans = 0; for(int i=0; i<=D; i++){ if(i%2==1) continue; ans += v[i] * C[(n-i)/2]; } cout << ans.val() << '\n'; }