#include #include #include #include #include #include #include #include #include #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; constexpr int mod = 998244353; long long fac[200005], finv[200005], inv[200005]; void COMinit() { fac[0] = fac[1] = finv[0] = finv[1] = inv[1] = 1; for (int i = 2; i < 200005; i++) { fac[i] = fac[i - 1] * i % mod; inv[i] = mod - inv[mod % i] * (mod / i) % mod; finv[i] = finv[i - 1] * inv[i] % mod; } } long long COM(int n, int k){ if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % mod) % mod; } long long choose(int n,int k) { if(n < 0 || k < 0) return 0; if(n == 0) return 1; return COM(n+k-1,k-1); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int N,M; cin >> N >> M; if(N%2) { cout << 0 << "\n"; return 0; } COMinit(); vector,vector>>tmp; for(int i = 0; i < M; i++) { int L,R; cin >> L >> R; L--; if((R-L)%2) continue; vectora(R-L+1),b(R-L+1); a[0] = 1; b[R-L] = (COM(R-L,(R-L)/2)+mod-COM(R-L,(R-L)/2+1))%mod; tmp.push_back({a,b}); } while(tmp.size() > 1) { vector,vector>>nxt; for(int i = 0; i < tmp.size(); i += 2) { if(i+1 == tmp.size()) { nxt.push_back(tmp[i]); } else { auto a1 = convolution(tmp[i].first,tmp[i+1].first); auto a2 = convolution(tmp[i].second,tmp[i+1].second); auto b1 = convolution(tmp[i].first,tmp[i+1].second); auto b2 = convolution(tmp[i].second,tmp[i+1].first); for(int i = 0; i < a1.size(); i++) { a1[i] += a2[i]; if(a1[i] >= mod) a1[i] -= mod; b1[i] += b2[i]; if(b1[i] >= mod) b1[i] -= mod; } nxt.push_back({a1,b1}); } } tmp = nxt; } if(tmp.empty()) { cout << (COM(N,N/2)+mod-COM(N,N/2+1))%mod << "\n"; return 0; } int ans = 0; for(int i = 0; i < tmp[0].first.size(); i += 2) { ans += (COM(N-i,(N-i)/2)+mod-COM(N-i,(N-i)/2+1))%mod*tmp[0].first[i]%mod; if(ans >= mod) ans -= mod; ans += mod-(COM(N-i,(N-i)/2)+mod-COM(N-i,(N-i)/2+1))%mod*tmp[0].second[i]%mod; if(ans >= mod) ans -= mod; } cout << ans << "\n"; }