// #define _GLIBCXX_DEBUG #pragma GCC optimize("O2,no-stack-protector,unroll-loops,fast-math") #include using namespace std; #define rep(i, n) for (int i = 0; i < int(n); i++) #define per(i, n) for (int i = (n)-1; 0 <= i; i--) #define rep2(i, l, r) for (int i = (l); i < int(r); i++) #define per2(i, l, r) for (int i = (r)-1; int(l) <= i; i--) #define each(e, v) for (auto& e : v) #define MM << " " << #define pb push_back #define eb emplace_back #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define sz(x) (int)x.size() template void print(const vector& v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } using ll = long long; using pii = pair; using pll = pair; template bool chmax(T& x, const T& y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T& x, const T& y) { return (x > y) ? (x = y, true) : false; } template using minheap = std::priority_queue, std::greater>; template using maxheap = std::priority_queue; template int lb(const vector& v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector& v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector& v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } // __int128_t gcd(__int128_t a, __int128_t b) { // if (a == 0) // return b; // if (b == 0) // return a; // __int128_t cnt = a % b; // while (cnt != 0) { // a = b; // b = cnt; // cnt = a % b; // } // return b; // } struct Union_Find_Tree { vector data; const int n; int cnt; Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {} int root(int x) { if (data[x] < 0) return x; return data[x] = root(data[x]); } int operator[](int i) { return root(i); } bool unite(int x, int y) { x = root(x), y = root(y); if (x == y) return false; if (data[x] > data[y]) swap(x, y); data[x] += data[y], data[y] = x; cnt--; return true; } int size(int x) { return -data[root(x)]; } int count() { return cnt; }; bool same(int x, int y) { return root(x) == root(y); } void clear() { cnt = n; fill(begin(data), end(data), -1); } }; template struct Mod_Int { int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} static int get_mod() { return mod; } Mod_Int& operator+=(const Mod_Int& p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int& operator-=(const Mod_Int& p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int& operator*=(const Mod_Int& p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int& operator/=(const Mod_Int& p) { *this *= p.inverse(); return *this; } Mod_Int& operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int& operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int& p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int& p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int& p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int& p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int& p) const { return x == p.x; } bool operator!=(const Mod_Int& p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream& operator<<(ostream& os, const Mod_Int& p) { return os << p.x; } friend istream& operator>>(istream& is, Mod_Int& p) { long long a; is >> a; p = Mod_Int(a); return is; } }; ll mpow2(ll x, ll n, ll mod) { ll ans = 1; x %= mod; while (n != 0) { if (n & 1) ans = ans * x % mod; x = x * x % mod; n = n >> 1; } ans %= mod; return ans; } template T modinv(T a, const T& m) { T b = m, u = 1, v = 0; while (b > 0) { T t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return u >= 0 ? u % m : (m - (-u) % m) % m; } ll divide_int(ll a, ll b) { if (b < 0) a = -a, b = -b; return (a >= 0 ? a / b : (a - b + 1) / b); } // const int MOD = 1000000007; const int MOD = 998244353; using mint = Mod_Int; // ----- library ------- template struct Combination { static vector _fac, _ifac; Combination() {} static void init(int n) { _fac.resize(n + 1), _ifac.resize(n + 1); _fac[0] = 1; for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i; _ifac[n] = _fac[n].inverse(); for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i; } static T fac(int k) { return _fac[k]; } static T ifac(int k) { return _ifac[k]; } static T inv(int k) { return fac(k - 1) * ifac(k); } static T P(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k); } static T C(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k) * ifac(k); } // n 個の区別できる箱に、k 個の区別できない玉を入れる場合の数 static T H(int n, int k) { if (n < 0 || k < 0) return 0; return k == 0 ? 1 : C(n + k - 1, k); } // n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数 static T second_stirling_number(int n, int k) { T ret = 0; for (int i = 0; i <= k; i++) { T tmp = C(k, i) * T(i).pow(n); ret += ((k - i) & 1) ? -tmp : tmp; } return ret * ifac(k); } // n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数 static T bell_number(int n, int k) { if (n == 0) return 1; k = min(k, n); vector pref(k + 1); pref[0] = 1; for (int i = 1; i <= k; i++) { if (i & 1) { pref[i] = pref[i - 1] - ifac(i); } else { pref[i] = pref[i - 1] + ifac(i); } } T ret = 0; for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i]; return ret; } }; template vector Combination::_fac = vector(); template vector Combination::_ifac = vector(); // ----- library ------- int main() { ios::sync_with_stdio(false); std::cin.tie(nullptr); cout << fixed << setprecision(15); using comb = Combination; comb::init(2e6); int n, m, k; cin >> n >> m >> k; vector ls; vector x(k), y(k); rep(i, k) { cin >> x[i] >> y[i]; x[i]--, y[i]--; ls.eb(x[i]), ls.eb(y[i]); } rearrange(ls); int cm = n - m, cs = m; each(e, ls) (e < m ? cs : cm)--; rep(i, k) x[i] = lb(ls, x[i]), y[i] = lb(ls, y[i]); int c = sz(ls); if (!c) { cout << comb::C(cm - 1 + cs, cs) * comb::fac(cm) * comb::fac(cs) << endl; return 0; } vector> dp(2, vector(1 << c, 0)); vector ng(c, 0); rep(i, k) ng[x[i]] |= 1 << y[i]; rep(i, c) ng[i] |= 1 << i; rep(i, c) dp[ls[i] < m][1 << i] = 1; rep(f, 2) rep(i, 1 << c) rep(j, c) { if (!(ng[j] & i)) dp[f][i | (1 << j)] += dp[f][i]; } int tar = (1 << c) - 1; mint val = comb::C(cm + c, cm) * (dp[0][tar] + dp[1][tar]) - comb::C(cm + c - 1, cm) * (dp[1][tar]); val *= comb::C(n - 1, cs) * comb::fac(cm) * comb::fac(cs); cout << val << endl; }