#if __INCLUDE_LEVEL__ == 0 #include __BASE_FILE__ namespace { using Fp = atcoder::modint998244353; Comb comb(1e6); void solve() { int n, m; scan(n, m); std::vector l(m), r(m); for (const int i : rep(m)) { scan(l[i], r[i]); --l[i]; } if (n & 1) { print(0); return; } const auto catalan = [&](int n) { return comb.binom(n * 2, n) * comb.recip(n + 1); }; std::vector> q; for (const int i : rep(m)) { if ((r[i] - l[i]) & 1) { continue; } const int t = (r[i] - l[i]) / 2; q.emplace_back(t + 1); q.back()[0] += 1; q.back()[t] -= catalan(t); } for (int qi = 0; qi + 2 <= len(q); qi += 2) { q.push_back(atcoder::convolution(q[qi], q[qi + 1])); } Fp ans = 0; for (const int i : rep(len(q.back()))) { ans += catalan(n / 2 - i) * q.back()[i]; } print(ans); } } // namespace int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); solve(); } #else // __INCLUDE_LEVEL__ #include #include template std::vector make_vector_for_overwrite(int n) { static_assert(std::is_trivially_destructible_v); std::vector v; static_assert(sizeof(v) == 3 * sizeof(T*)); v.reserve(n); T*(&a)[3] = reinterpret_cast(v); assert(a[0] == a[1] && a[1] + n == a[2]); a[1] = a[2]; return v; } template class Comb { public: Comb() = default; explicit Comb(int max_n) : fact_(make_vector_for_overwrite(max_n + 1)), recip_fact_(make_vector_for_overwrite(max_n + 1)) { fact_[0] = 1; for (const int n : std::views::iota(1, max_n + 1)) { fact_[n] = fact_[n - 1] * n; } recip_fact_[max_n] = 1 / fact_[max_n]; for (const int n : std::views::iota(1, max_n + 1) | std::views::reverse) { recip_fact_[n - 1] = n * recip_fact_[n]; } } T recip(int n) const { assert(n); return n < 0 ? -recip(-n) : recip_fact_[n] * fact_[n - 1]; } T fact(int n) const { assert(0 <= n); return fact_[n]; } T recip_fact(int n) const { return n < 0 ? 0 : recip_fact_[n]; } T falling_fact(int n, int k) const { assert(0 <= n || n < k); if (n < 0) { const T t = falling_fact(k - n - 1, k); return k & 1 ? -t : t; } return n < k ? 0 : recip_fact(n - k) * fact(n); } T recip_falling_fact(int n, int k) const { assert(n < 0 || k <= n); return falling_fact(n - k, -k); } T rising_fact(int n, int k) const { assert(n <= 0 || 0 < n + k); return falling_fact(n + k - 1, k); } T recip_rising_fact(int n, int k) const { assert(0 < n || n + k <= 0); return falling_fact(n - 1, -k); } T binom(int n, int k) const { if ((n < 0) ^ (k < 0) ^ (n < k)) { return 0; } if (n < 0 && k < 0) { k = n - k; } return recip_fact(k) * falling_fact(n, k); } T recip_binom(int n, int k) const { assert((0 <= n) ^ (0 <= k) ^ (k <= n)); k = std::max(k, n - k); return recip_falling_fact(n, k) * fact(k); } T multiset(int n, int k) const { return binom(n + k - 1, k); } T recip_multiset(int n, int k) const { assert((0 < n) ^ (0 <= k) ^ (0 < n + k)); return recip_binom(n + k - 1, k); } private: std::vector fact_; std::vector recip_fact_; }; template bool chmin(T& x, U&& y) { return y < x && (x = std::forward(y), true); } template bool chmax(T& x, U&& y) { return x < y && (x = std::forward(y), true); } template T inf() { T ret; std::memset(&ret, 0x3f, sizeof(ret)); return ret; } template T inf() { return std::numeric_limits::infinity(); } template concept Range = std::ranges::range && !std::convertible_to; template concept TupleLike = std::__is_tuple_like::value && !Range; namespace std { istream& operator>>(istream& is, Range auto&& r) { for (auto&& e : r) { is >> e; } return is; } istream& operator>>(istream& is, TupleLike auto&& t) { return apply([&](auto&... xs) -> istream& { return (is >> ... >> xs); }, t); } ostream& operator<<(ostream& os, Range auto&& r) { string_view sep = ""; for (auto&& e : r) { os << exchange(sep, " ") << e; } return os; } ostream& operator<<(ostream& os, TupleLike auto&& t) { const auto f = [&](auto&... xs) -> ostream& { [[maybe_unused]] string_view sep = ""; ((os << exchange(sep, " ") << xs), ...); return os; }; return apply(f, t); } #define DEF_INC_OR_DEC(op) \ auto& operator op(Range auto&& r) { \ for (auto&& e : r) { \ op e; \ } \ return r; \ } \ auto& operator op(TupleLike auto&& t) { \ apply([](auto&... xs) { (op xs, ...); }, t); \ return t; \ } DEF_INC_OR_DEC(++) DEF_INC_OR_DEC(--) #undef DEF_INC_OR_DEC } // namespace std namespace atcoder { template * = nullptr> std::istream& operator>>(std::istream& is, T& x) { int v; is >> v; x = T::raw(v); return is; } template * = nullptr> std::ostream& operator<<(std::ostream& os, const T& x) { return os << x.val(); } } // namespace atcoder void scan(auto&&... xs) { std::cin >> std::tie(xs...); } void print(auto&&... xs) { std::cout << std::tie(xs...) << '\n'; } #define FWD(...) static_cast(__VA_ARGS__) template class fix { public: explicit fix(F f) : f_(std::move(f)) {} decltype(auto) operator()(auto&&... xs) const { return f_(std::ref(*this), FWD(xs)...); } private: F f_; }; template concept LambdaExpr = std::is_placeholder_v> != 0 || std::is_bind_expression_v>; auto operator++(LambdaExpr auto&& x, int) { return std::bind([](auto&& x) -> decltype(auto) { return FWD(x)++; }, FWD(x)); } auto operator--(LambdaExpr auto&& x, int) { return std::bind([](auto&& x) -> decltype(auto) { return FWD(x)--; }, FWD(x)); } #define DEF_UNARY_OP(op) \ auto operator op(LambdaExpr auto&& x) { \ return std::bind([](auto&& x) -> decltype(auto) { return op FWD(x); }, FWD(x)); \ } DEF_UNARY_OP(++) DEF_UNARY_OP(--) DEF_UNARY_OP(+) DEF_UNARY_OP(-) DEF_UNARY_OP(~) DEF_UNARY_OP(!) DEF_UNARY_OP(*) DEF_UNARY_OP(&) #undef DEF_UNARY_OP #define DEF_BINARY_OP(op) \ template \ requires LambdaExpr || LambdaExpr \ auto operator op(T1&& x, T2&& y) { \ return std::bind([](auto&& x, auto&& y) -> decltype(auto) { return FWD(x) op FWD(y); }, \ FWD(x), FWD(y)); \ } DEF_BINARY_OP(+=) DEF_BINARY_OP(-=) DEF_BINARY_OP(*=) DEF_BINARY_OP(/=) DEF_BINARY_OP(%=) DEF_BINARY_OP(^=) DEF_BINARY_OP(&=) DEF_BINARY_OP(|=) DEF_BINARY_OP(<<=) DEF_BINARY_OP(>>=) DEF_BINARY_OP(+) DEF_BINARY_OP(-) DEF_BINARY_OP(*) DEF_BINARY_OP(/) DEF_BINARY_OP(%) DEF_BINARY_OP(^) DEF_BINARY_OP(&) DEF_BINARY_OP(|) DEF_BINARY_OP(<<) DEF_BINARY_OP(>>) DEF_BINARY_OP(==) DEF_BINARY_OP(!=) DEF_BINARY_OP(<) DEF_BINARY_OP(>) DEF_BINARY_OP(<=) DEF_BINARY_OP(>=) DEF_BINARY_OP(&&) DEF_BINARY_OP(||) #undef DEF_BINARY_OP template requires LambdaExpr || LambdaExpr auto at(T1&& x, T2&& y) { return std::bind([](auto&& x, auto&& y) -> decltype(auto) { return FWD(x)[FWD(y)]; }, FWD(x), FWD(y)); } template auto get(LambdaExpr auto&& x) { return std::bind([](auto&& x) -> decltype(auto) { return std::get(FWD(x)); }, FWD(x)); } inline auto rep(int l, int r) { return std::views::iota(std::min(l, r), r); } inline auto rep(int n) { return rep(0, n); } inline auto rep1(int l, int r) { return rep(l, r + 1); } inline auto rep1(int n) { return rep(1, n + 1); } using namespace std::literals; using namespace std::placeholders; namespace ranges = std::ranges; namespace views = std::views; using i64 = std::int64_t; #define len(...) static_cast(ranges::size(__VA_ARGS__)) #endif // __INCLUDE_LEVEL__