#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--) #define repk(i, k, n) for (int i = k; i < (int)(n); i++) #define all(v) v.begin(), v.end() #define mod1 1000000007 #define mod2 998244353 #define mod3 100000007 #define vi vector #define vs vector #define vc vector #define vl vector #define vb vector #define vvi vector> #define vvc vector> #define vvl vector> #define vvb vector> #define vvvi vector>> #define vvvl vector>> #define pii pair #define pil pair #define pli pair #define pll pair #define vpii vector> #define vpll vector> #define vvpii vector>> #define vvpll vector>> using mint = modint998244353; template void debug(T e) { cerr << e << endl; } void debug(vector &v) { rep(i, v.size()) { cerr << v[i].val() << " "; } cerr << endl; } template void debug(vector &v) { rep(i, v.size()) { cerr << v[i] << " "; } cerr << endl; } template void debug(vector> &v) { rep(i, v.size()) { rep(j, v[i].size()) { cerr << v[i][j] << " "; } cerr << endl; } } template void debug(vector> &v) { rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; } } template void debug(set &st) { for (auto itr = st.begin(); itr != st.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(multiset &ms) { for (auto itr = ms.begin(); itr != ms.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(map &mp) { for (auto itr = mp.begin(); itr != mp.end(); itr++) { cerr << itr->first << " " << itr->second << endl; } } void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << H << " "; debug_out(T...); } mint comb(ll n, ll r, vector &fact, vector &fact_inv) { mint ret = 0; if (r < 0) { return ret.val(); } else if (n < r) { return ret.val(); } ret = 1; ret *= fact[n]; ret *= fact_inv[n - r]; ret *= fact_inv[r]; return ret.val(); } int main() { ll N, M, K; cin >> N >> M >> K; vector X(K); vector Y(K); for (ll i = 0; i < K; i++) { cin >> X[i] >> Y[i]; } map mp; for (ll i = 0; i < K; i++) { mp[X[i]]++; mp[Y[i]]++; } ll subh = M; ll mainh = N - M; vector vecs(0); ll now = 0; for (auto itr = mp.begin(); itr != mp.end(); itr++) { itr->second = now; if (itr->first <= M) { subh--; } else { mainh--; } vecs.push_back(itr->first); now++; } vector bitdp1(1 << now, 0); vector bitdp2(1 << now, 0); for (ll i = 0; i < now; i++) { if (vecs[i] <= M) { bitdp1[1 << i] += 1; } else { bitdp2[1 << i] += 1; } } vector> allowed(now, vector(now, true)); for (ll i = 0; i < K; i++) { allowed[mp[Y[i]]][mp[X[i]]] = false; } for (ll i = 0; i < (1 << now); i++) { for (ll j = 0; j < now; j++) { if ((i >> j) & 1) { continue; } bool pos = true; for (ll k = 0; k < now; k++) { if ((i >> k) & 1) { if (!allowed[k][j]) { pos = false; } } } if (pos) { bitdp1[i + (1 << j)] += bitdp1[i]; bitdp2[i + (1 << j)] += bitdp2[i]; } } } if (now == 0) { bitdp2[0] = 1; } vector fact(1050001); fact[0] = 1; for (ll i = 0; i < 1050000; i++) { fact[i + 1] = fact[i] * (i + 1); } vector fact_inv(1050001); for (ll i = 0; i < 1050001; i++) { fact_inv[i] = 1 / fact[i]; } mint ans = 0; // 最初が K 個の中に入らない場合 // 最初は絶対メインなので mainh 通り // 残りの並び順で (subh + mainh - 1)! 通り // 残りの挿入場所の選択で comb(N - 1, now) 通り ans += mainh * fact[subh + mainh - 1] * (bitdp1[(1 << now) - 1] + bitdp2[(1 << now) - 1]) * comb(N - 1, now, fact, fact_inv); // 最初が K 個の中に入る場合 // 最初は絶対メインなので bitdp2 のみ使用する // 残りの並び順は (subh + mainh)! 通り // 残りの挿入場所の選択で comb(N - 1, now - 1) 通り ans += fact[subh + mainh] * bitdp2[(1 << now) - 1] * comb(N - 1, now - 1, fact, fact_inv); cout << ans.val() << endl; }