#include using namespace std; #define overload2(a, b, c, ...) c #define overload3(a, b, c, d, ...) d #define overload4(a, b, c, d, e ...) e #define overload5(a, b, c, d, e, f ...) f #define overload6(a, b, c, d, e, f, g ...) g #define fast_io ios::sync_with_stdio(false); cin.tie(nullptr); #pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math") typedef long long ll; typedef long double ld; #define chmin(a,b) a = min(a,b); #define chmax(a,b) a = max(a,b); #define bit_count(x) __builtin_popcountll(x) #define leading_zero_count(x) __builtin_clz(x) #define trailing_zero_count(x) __builtin_ctz(x) #define gcd(a,b) __gcd(a,b) #define lcm(a,b) a / gcd(a,b) * b #define rep(...) overload3(__VA_ARGS__, rrep, rep1)(__VA_ARGS__) #define rep1(i,n) for(int i = 0 ; i < n ; i++) #define rrep(i,a,b) for(int i = a ; i < b ; i++) #define repi(it,S) for(auto it = S.begin() ; it != S.end() ; it++) #define pt(a) cout << a << endl; #define print(...) printall(__VA_ARGS__); #define debug(a) cout << #a << " " << a << endl; #define all(a) a.begin(), a.end() #define endl "\n"; #define v1(T,n,a) vector(n,a) #define v2(T,n,m,a) vector>(n,v1(T,m,a)) #define v3(T,n,m,k,a) vector>>(n,v2(T,m,k,a)) #define v4(T,n,m,k,l,a) vector>>>(n,v3(T,m,k,l,a)) templateistream &operator>>(istream&is,pair&p){is>>p.first>>p.second;return is;} templateostream &operator<<(ostream&os,const pair&p){os<istream &operator>>(istream&is,vector&v){for(T &in:v){is>>in;}return is;} templateostream &operator<<(ostream&os,const vector&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?" ":"");}return os;} templateistream &operator>>(istream&is,vector>&v){for(T &in:v){is>>in;}return is;} templateostream &operator<<(ostream&os,const vector>&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?"\n":"");}return os;} templateostream &operator<<(ostream&os,const set&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?" ":"");}return os;} templateostream &operator<<(ostream&os,const multiset&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?" ":"");}return os;} template void printall(Args... args){for(auto i:initializer_list>{args...}) cout< struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt< mod >; const int MAX_N = 2010101 ; modint inv[MAX_N+1] ; // (n!)^(p-2) (mod p) を格納 modint fac[MAX_N+1] ; // (n!) (mod p) を格納 modint powmod(modint x , ll n){ modint res = 1 ; while(n > 0){ if(n & 1) res *= x; x *= x; n >>= 1 ; } return res ; } // 階乗の逆元(n!)^(-1)のmodを配列に格納 void f(){ inv[0] = 1 ; inv[1] = 1 ; for(ll i = 2 ; i <= MAX_N ; i++){ inv[i] = powmod(i,mod-2) * inv[i-1]; } } // 階乗のmodを配列に格納 void g(){ fac[0] = 1 ; fac[1] = 1 ; for(ll i = 2 ; i <= MAX_N ; i++){ fac[i] = fac[i-1] * i; } } //nCrの計算 modint combination(ll n , ll r){ if(n < 0 || r < 0 || n < r) return 0 ; return fac[n] * inv[n-r] * inv[r]; } modint permutation(ll n , ll r){ if(n < 0 || r < 0 || n < r) return 0 ; return fac[n] * inv[n-r]; } void init(){ f() ; g() ; } int n, q; void solve(){ cin >> n >> q; vector> X, Q; vector I(n+1); rep(i,q){ int l, r; cin >> l >> r; l--; I[l] += (ll)1 << i; I[r] -= (ll)1 << i; } rep(i,1,n) I[i] += I[i-1]; unordered_map mp; rep(i,n) mp[I[i]]++; modint res = 1; ll N = n; for(auto[k,x] : mp){ if(k == 0) continue; if(x % 2 == 1){ pt(0) return; } res *= combination(x,x/2) / (x/2 + 1); n -= x; } res *= combination((n+1)/2*2,(n+1)/2) / ((n+1)/2 + 1); res *= permutation(N/2,N/2) * permutation(N-N/2,N-N/2); pt(res) } int main(){ fast_io init(); int t = 1; // cin >> t; rep(i,t) solve(); }