#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; constexpr int mod = 998244353; template< int mod > struct NumberTheoreticTransform { vector< int > rev, rts; int base, max_base, root; NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} { assert(mod >= 3 && mod % 2 == 1); auto tmp = mod - 1; max_base = 0; while(tmp % 2 == 0) tmp >>= 1, max_base++; root = 2; while(mod_pow(root, (mod - 1) >> 1) == 1) ++root; assert(mod_pow(root, mod - 1) == 1); root = mod_pow(root, (mod - 1) >> max_base); } inline int mod_pow(int x, int n) { int ret = 1; while(n > 0) { if(n & 1) ret = mul(ret, x); x = mul(x, x); n >>= 1; } return ret; } inline int inverse(int x) { return mod_pow(x, mod - 2); } inline unsigned add(unsigned x, unsigned y) { x += y; if(x >= mod) x -= mod; return x; } inline unsigned mul(unsigned a, unsigned b) { return 1ull * a * b % (unsigned long long) mod; } void ensure_base(int nbase) { if(nbase <= base) return; rev.resize(1 << nbase); rts.resize(1 << nbase); for(int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } assert(nbase <= max_base); while(base < nbase) { int z = mod_pow(root, 1 << (max_base - 1 - base)); for(int i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; rts[(i << 1) + 1] = mul(rts[i], z); } ++base; } } void ntt(vector< int > &a) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for(int i = 0; i < n; i++) { if(i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for(int k = 1; k < n; k <<= 1) { for(int i = 0; i < n; i += 2 * k) { for(int j = 0; j < k; j++) { int z = mul(a[i + j + k], rts[j + k]); a[i + j + k] = add(a[i + j], mod - z); a[i + j] = add(a[i + j], z); } } } } vector< int > multiply(vector< int > a, vector< int > b) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; a.resize(sz, 0); b.resize(sz, 0); ntt(a); ntt(b); int inv_sz = inverse(sz); for(int i = 0; i < sz; i++) { a[i] = mul(a[i], mul(b[i], inv_sz)); } reverse(a.begin() + 1, a.end()); ntt(a); a.resize(need); return a; } }; 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}); } NumberTheoreticTransformntt; 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 = ntt.multiply(tmp[i].first,tmp[i+1].first); auto a2 = ntt.multiply(tmp[i].second,tmp[i+1].second); auto b1 = ntt.multiply(tmp[i].first,tmp[i+1].second); auto b2 = ntt.multiply(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"; }