#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 #ifdef LOCAL # include "debug_print.hpp" # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using namespace std; #define rep(i,n) for(int i=0; i<(n); i++) #define rrep(i,n) for(int i=(n)-1; i>=0; i--) #define FOR(i,a,b) for(int i=(a); i<(b); i++) #define RFOR(i,a,b) for(int i=(b-1); i>=(a); i--) #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ); #define pb push_back using ll = long long; using D = double; using LD = long double; using P = pair; template using PQ = priority_queue>; template using minPQ = priority_queue, greater>; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } #include "atcoder/modint.hpp" #include "atcoder/convolution.hpp" using mint = atcoder::modint998244353; constexpr int mod = 998244353; constexpr int mx = 200005; mint fact[mx]; mint inv[mx]; mint finv[mx]; mint comb(int n, int m){ if(n < 0 or m < 0 or n < m) return 0; return fact[n] * finv[m] * finv[n-m]; } int main(){ ios_base::sync_with_stdio(false); cin.tie(nullptr); int n,m; in(n,m); rep(i,mx) fact[i] = inv[i] = finv[i] = 1; for(int i = 2; i < mx; i++){ fact[i] = fact[i-1] * i; inv[i] = -inv[mod%i] * (mod/i); finv[i] = finv[i-1] * inv[i]; } vector l(m),r(m); rep(i,m) in(l[i],r[i]); vector cat(n+1); rep(i,n+1) if(i%2==0) cat[i] = comb(i,i/2) * inv[i/2+1]; queue> q; rep(i,m){ vector f(r[i]-l[i]+2); f[0] = 1; f[r[i]-l[i]+1] = -cat[r[i]-l[i]+1]; q.push(f); } if(m == 0){ out(cat[n].val()); return 0; } while(q.size() > 1){ auto f = q.front(); q.pop(); auto g = q.front(); q.pop(); q.push(atcoder::convolution(f,g)); } int md = q.front().size(); mint ans = 0; rep(i,md){ ans += q.front()[i] * cat[n-i]; } out(ans.val()); }