#include using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using isize = std::ptrdiff_t; using usize = std::size_t; class rep { struct Iter { usize itr; constexpr Iter(const usize pos) noexcept : itr(pos) {} constexpr void operator++() noexcept { ++itr; } constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; } constexpr usize operator*() const noexcept { return itr; } }; const Iter first, last; public: explicit constexpr rep(const usize first, const usize last) noexcept : first(first), last(std::max(first, last)) {} constexpr Iter begin() const noexcept { return first; } constexpr Iter end() const noexcept { return last; } }; template constexpr T totient(T x) { T ret = x; for (T i = 2; i * i <= x; ++i) { if (x % i == 0) { ret /= i; ret *= i - 1; while (x % i == 0) x /= i; } } if (x > 1) { ret /= x; ret *= x - 1; } return ret; } template constexpr T rem_euclid(T value, const T& mod) { return (value %= mod) >= 0 ? value : value + mod; } template * = nullptr> class StaticModint { using Mint = StaticModint; static inline constexpr u32 PHI = totient(MOD); u32 v; public: static constexpr u32 mod() noexcept { return MOD; } template and std::is_integral_v>* = nullptr> static constexpr T normalize(const T x) noexcept { return rem_euclid>(x, MOD); } template and std::is_integral_v>* = nullptr> static constexpr T normalize(const T x) noexcept { return x % MOD; } constexpr StaticModint() noexcept : v(0) {} template constexpr StaticModint(const T x) noexcept : v(normalize(x)) {} template static constexpr Mint raw(const T x) noexcept { Mint ret; ret.v = x; return ret; } constexpr u32 get() const noexcept { return v; } constexpr Mint neg() const noexcept { return raw(v == 0 ? 0 : MOD - v); } constexpr Mint inv() const noexcept { return pow(PHI - 1); } constexpr Mint pow(u64 exp) const noexcept { Mint ret(1), mult(*this); for (; exp > 0; exp >>= 1) { if (exp & 1) ret *= mult; mult *= mult; } return ret; } constexpr Mint operator-() const noexcept { return neg(); } constexpr Mint operator~() const noexcept { return inv(); } constexpr Mint operator+(const Mint& rhs) const noexcept { return Mint(*this) += rhs; } constexpr Mint& operator+=(const Mint& rhs) noexcept { if ((v += rhs.v) >= MOD) v -= MOD; return *this; } constexpr Mint operator-(const Mint& rhs) const noexcept { return Mint(*this) -= rhs; } constexpr Mint& operator-=(const Mint& rhs) noexcept { if (v < rhs.v) v += MOD; v -= rhs.v; return *this; } constexpr Mint operator*(const Mint& rhs) const noexcept { return Mint(*this) *= rhs; } constexpr Mint& operator*=(const Mint& rhs) noexcept { v = (u64)v * rhs.v % MOD; return *this; } constexpr Mint operator/(const Mint& rhs) const noexcept { return Mint(*this) /= rhs; } constexpr Mint& operator/=(const Mint& rhs) noexcept { return *this *= rhs.inv(); } constexpr bool operator==(const Mint& rhs) const noexcept { return v == rhs.v; } constexpr bool operator!=(const Mint& rhs) const noexcept { return v != rhs.v; } friend std::ostream& operator<<(std::ostream& stream, const Mint& rhs) { return stream << rhs.v; } }; using Modint1000000007 = StaticModint<1000000007>; using Modint998244353 = StaticModint<998244353>; __attribute__((target("avx2"))) constexpr u64 ceil_log2(const u64 x) { u64 e = 0; while (((u64)1 << e) < x) ++e; return e; } template class AutoReallocation { using R = typename decltype(std::declval()((usize)0))::value_type; F func; mutable std::vector data; public: explicit AutoReallocation(F&& f) : func(std::forward(f)), data() {} void reserve(const usize size) const { if (data.size() < size) data = func(((usize)1 << ceil_log2(size))); } R operator[](const usize i) const { reserve(i + 1); return data[i]; } }; template decltype(auto) auto_realloc(F&& f) { using G = std::decay_t; return AutoReallocation(std::forward(f)); } template struct ModintUtil { static inline const auto fact = auto_realloc([](const usize n) { std::vector ret(n); ret[0] = M(1); for (const usize i : rep(1, n)) { ret[i] = ret[i - 1] * M(i); } return ret; }); static inline const auto inv = auto_realloc([](const usize n) { std::vector ret(n); if (n == 1) return ret; ret[1] = M(1); for (const usize i : rep(2, n)) { ret[i] = -M(M::mod() / i) * ret[M::mod() % i]; } return ret; }); static inline const auto inv_fact = auto_realloc([](const usize n) { std::vector ret(n); ret[0] = M(1); for (const usize i : rep(1, n)) { ret[i] = ret[i - 1] * inv[i]; } return ret; }); static M binom(const usize n, const usize k) { assert(k <= n); return fact[n] * inv_fact[n - k] * inv_fact[k]; } static M factpow(const usize n, const usize k) { assert(k <= n); return fact[n] * inv_fact[n - k]; } static M homo(const usize n, const usize k) { if (n == 0 and k == 0) return M(1); return binom(n + k - 1, k); } }; class revrep { struct Iter { usize itr; constexpr Iter(const usize pos) noexcept : itr(pos) {} constexpr void operator++() noexcept { --itr; } constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; } constexpr usize operator*() const noexcept { return itr; } }; const Iter first, last; public: explicit constexpr revrep(const usize first, const usize last) noexcept : first(last - 1), last(std::min(first, last) - 1) {} constexpr Iter begin() const noexcept { return first; } constexpr Iter end() const noexcept { return last; } }; template class SegmentTree { using T = typename M::Type; usize internal_size, seg_size; std::vector data; void fetch(const usize k) { data[k] = M::operation(data[2 * k], data[2 * k + 1]); } public: explicit SegmentTree(const usize size = 0, const T& value = M::identity()) : SegmentTree(std::vector(size, value)) {} explicit SegmentTree(const std::vector& vec) : internal_size(vec.size()) { seg_size = 1 << ceil_log2(internal_size); data = std::vector(2 * seg_size, M::identity()); for (const usize i : rep(0, internal_size)) data[seg_size + i] = vec[i]; for (const usize i : revrep(1, seg_size)) fetch(i); } usize size() const { return internal_size; } void assign(usize i, const T& value) { assert(i < internal_size); i += seg_size; data[i] = value; while (i > 1) { i >>= 1; fetch(i); } } T fold() const { return data[1]; } T fold(usize l, usize r) const { assert(l <= r and r <= internal_size); l += seg_size; r += seg_size; T ret_l = M::identity(), ret_r = M::identity(); while (l < r) { if (l & 1) ret_l = M::operation(ret_l, data[l++]); if (r & 1) ret_r = M::operation(data[--r], ret_r); l >>= 1; r >>= 1; } return M::operation(ret_l, ret_r); } template usize max_right(usize l, const F& f) const { assert(l <= internal_size); assert(f(M::identity())); if (l == internal_size) return internal_size; l += seg_size; T sum = M::identity(); do { while (!(l & 1)) l >>= 1; if (!f(M::operation(sum, data[l]))) { while (l < seg_size) { l = 2 * l; if (f(M::operation(sum, data[l]))) sum = M::operation(sum, data[l++]); } return l - seg_size; } sum = M::operation(sum, data[l++]); } while ((l & -l) != l); return internal_size; } template usize min_left(usize r, const F& f) const { assert(r <= internal_size); assert(f(M::identity())); if (r == 0) return 0; r += seg_size; T sum = M::identity(); do { r -= 1; while (r > 1 and (r & 1)) r >>= 1; if (!f(M::operation(data[r], sum))) { while (r < seg_size) { r = 2 * r + 1; if (f(M::operation(data[r], sum))) sum = M::operation(data[r--], sum); } return r + 1 - seg_size; } sum = M::operation(data[r], sum); } while ((r & -r) != r); return 0; } }; #include template struct OptionalMonoid { using Type = std::optional; static constexpr Type identity() { return std::nullopt; } static constexpr Type operation(const Type& l, const Type& r) { if (!l) return r; if (!r) return l; return Type(std::in_place, S::operation(*l, *r)); } }; template bool setmax(T& lhs, const T& rhs) { if (lhs < rhs) { lhs = rhs; return true; } return false; } template using Vec = std::vector; using Fp = Modint998244353; using Util = ModintUtil; struct Add { using Type = std::valarray; static Type operation(const Type& l, const Type& r) { return l + r; } }; using Monoid = OptionalMonoid; void main_() { usize N, K, M; std::cin >> N >> K >> M; Vec max(K + 1); while (M--) { usize l, r; std::cin >> l >> r; setmax(max[r], l); } SegmentTree seg(K + 1); { std::valarray tmp(K + 1); tmp[0] = 1; seg.assign(0, tmp); } usize left = 0; for (const auto r : rep(1, K + 1)) { seg.assign(r, seg.fold(left, r)->cshift(-1)); setmax(left, max[r]); } Vec pow(K + 1); for (const auto k : rep(0, K + 1)) { pow[k] = Fp(k).pow(N); } std::valarray coeff(K + 1); for (const auto k : rep(0, K + 1)) { for (const auto i : rep(0, k + 1)) { if ((k - i) & 1) coeff[k] -= Util::binom(k, i) * pow[i]; else coeff[k] += Util::binom(k, i) * pow[i]; } } std::cout << (*seg.fold(left, K + 1) * coeff).sum() << '\n'; } int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(nullptr); main_(); return 0; }