#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define rep(x, s, t) for(ll x = (s); (x) <= (t); (x)++) #define per(x, s, t) for(ll x = (s); (x) >= (t); (x)--) #define reps(x, s) for(ll x = 0; (x) < (ll)(s).size(); (x)++) #define pers(x, s) for(ll x = (ll)(s).size()-1; (x) >= 0; (x)--) #define chmin(x, y) (x) = min((x), (y)) #define chmax(x, y) (x) = max((x), (y)) #define sz(x) ((ll)(x).size()) #define all(x) (x).begin(),(x).end() #define rall(x) (x).rbegin(),(x).rend() #define outl(...) dump_func(__VA_ARGS__) #define outf(x) cout << fixed << setprecision(16) << (x) << endl #define pb push_back #define fi first #define se second #define inf 2e18 #define eps 1e-9 const double PI = 3.1415926535897932384626433; using namespace std; typedef long long ll; typedef unsigned long long ull; typedef pair P; struct edge{ ll to, cost; edge(){} edge(ll a, ll b){ to = a, cost = b;} }; const int dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1}; const int dx8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dy8[] = {0, -1, -1, -1, 0, 1, 1, 1}; const int mod = 998244353; //const int mod = 1000000007; struct mint{ int x; mint(ll y = 0){if(y < 0 || y >= mod) y = (y%mod+mod)%mod; x = y;} mint(const mint &ope) {x = ope.x;} mint operator-(){return mint(-x);} mint operator+(const mint &ope){return mint(x) += ope;} mint operator-(const mint &ope){return mint(x) -= ope;} mint operator*(const mint &ope){return mint(x) *= ope;} mint operator/(const mint &ope){return mint(x) /= ope;} mint& operator+=(const mint &ope){x += ope.x; if(x >= mod) x -= mod; return *this;} mint& operator-=(const mint &ope){x += mod - ope.x; if(x >= mod) x -= mod; return *this;} mint& operator*=(const mint &ope){ll tp = x; tp *= ope.x, tp %= mod; x = tp; return *this;} mint& operator/=(const mint &ope){ ll n = mod-2; mint mul = ope; while(n){if(n & 1) *this *= mul; mul *= mul; n >>= 1;} return *this; } mint inverse(){return mint(1) / *this;} bool operator ==(const mint &ope){return x == ope.x;} bool operator !=(const mint &ope){return x != ope.x;} bool operator <(const mint &ope)const{return x < ope.x;} }; mint modpow(mint a, ll n){ if(n == 0) return mint(1); if(n % 2) return a * modpow(a, n-1); else return modpow(a*a, n/2); } istream& operator >>(istream &is, mint &ope){ll t; is >> t, ope = mint(t); return is;} ostream& operator <<(ostream &os, mint &ope){return os << ope.x;} ostream& operator <<(ostream &os, const mint &ope){return os << ope.x;} ll modpow(ll a, ll n, ll mod){ if(n == 0) return 1; if(n % 2) return ((a%mod) * (modpow(a, n-1, mod)%mod)) % mod; else return modpow((a*a)%mod, n/2, mod) % mod; } vector fact, fact_inv; void make_fact(int n){ fact.resize(n+1), fact_inv.resize(n+1); fact[0] = mint(1); rep(i, 1, n) fact[i] = fact[i-1] * mint(i); fact_inv[n] = fact[n].inverse(); per(i, n-1, 0) fact_inv[i] = fact_inv[i+1] * mint(i+1); } mint comb(int n, int k){ if(n < 0 || k < 0 || n < k) return mint(0); return fact[n] * fact_inv[k] * fact_inv[n-k];} mint perm(int n, int k){ return comb(n, k) * fact[k]; } mint divide(int n, int k){ if(n == 0 && k == 0) return 1; return comb(n+k-1, k-1); } template T comb2(ll n, ll k){ if(n < 0 || k < 0 || n < k) return T(0); T ret = 1; rep(i, 1, k) ret *= n-k+i, ret /= i; return ret;} vector prime, pvec, qrime; void make_prime(int n){ prime.resize(n+1); rep(i, 2, n){ if(prime[i] == 0) pvec.push_back(i), prime[i] = i; for(auto p : pvec){ if(i*p > n || p > prime[i]) break; prime[i*p] = p;} } } void make_qrime(int n){ qrime.resize(n+1); rep(i, 2, n){int ni = i / prime[i]; if(prime[i] == prime[ni]) qrime[i] = qrime[ni] * prime[i]; else qrime[i] = prime[i];} } void factorize(ll n, map &mp){ mp.clear(); for(auto p : pvec) while(n % p == 0) mp[p]++, n /= p; if(n > 1) mp[n]++; } bool exceed(ll x, ll y, ll m){return y > 0 && x >= m / y + 1;} void mark(){ cout << "*" << endl; } void yes(){ cout << "Yes" << endl; } void no(){ cout << "No" << endl; } ll floor(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return a/b; else return -((-a+b-1)/b); } ll ceil(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return (a+b-1)/b; else return -((-a)/b); } ll modulo(ll a, ll b){ b = abs(b); return a - floor(a, b) * b;} ll sgn(ll x){ if(x > 0) return 1; if(x < 0) return -1; return 0;} ll gcd(ll a, ll b){if(b == 0) return a; return gcd(b, a%b);} ll lcm(ll a, ll b){return a/gcd(a, b)*b;} template T arith(T x){return x*(x+1)/2;} template T arith2(T x){return x*(x+1)*(x*2+1)/6;} ll digitnum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret++; return ret;} ll digitsum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret += x % b; return ret;} string lltos(ll x, ll b = 10){if(x == 0) return "0"; string ret; for(;x;x/=b) ret += x % b + '0'; reverse(all(ret)); return ret;} ll stoll(string &s, ll b = 10){ll ret = 0; for(auto c : s) ret *= b, ret += c - '0'; return ret;} template void uniq(T &vec){sort(all(vec)); vec.erase(unique(all(vec)), vec.end());} int popcount(ull x){ x -= ((x>>1)&0x5555555555555555ULL), x = (x & 0x3333333333333333ULL) + ((x>>2) & 0x3333333333333333ULL); return (((x + (x>>4)) & 0x0F0F0F0F0F0F0F0FULL) * 0x0101010101010101ULL) >> 56; } template vector> rle(vector vec){ vector> ret; for(auto x : vec){if(sz(ret) == 0 || ret.back().first != x) ret.push_back(P(x, 1)); else ret.back().second++;} return ret; } vector> rle(string s){ vector vec; for(auto c : s) vec.push_back(c); return rle(vec);} template pair& operator+=(pair &s, const pair &t){s.first += t.first, s.second += t.second; return s;} template pair& operator-=(pair &s, const pair &t){s.first -= t.first, s.second -= t.second; return s;} template pair operator+(const pair &s, const pair &t){return pair(s.first+t.first, s.second+t.second);} template pair operator-(const pair &s, const pair &t){return pair(s.first-t.first, s.second-t.second);} template T dot(const pair &s, const pair &t){return s.first*t.first + s.second*t.second;} template T cross(const pair &s, const pair &t){return s.first*t.second - s.second*t.first;} template T mdist(pair s, pair t){return abs(s.first-t.first) + abs(s.second-t.second);} template T cdist(pair s, pair t){return max(abs(s.first-t.first), abs(s.second-t.second));} template T edist2(pair s, pair t){return (s.first-t.first)*(s.first-t.first) + (s.second-t.second)*(s.second-t.second);} template ostream& operator << (ostream& os, vector& vec){reps(i, vec) os << vec[i] << " "; return os;} template ostream& operator << (ostream& os, const vector& vec){reps(i, vec) os << vec[i] << " "; return os;} template ostream& operator << (ostream& os, list& ls){for(auto x : ls) os << x << " "; return os;} template ostream& operator << (ostream& os, const list& ls){for(auto x : ls) os << x << " "; return os;} template ostream& operator << (ostream& os, deque& deq){reps(i, deq) os << deq[i] << " "; return os;} template ostream& operator << (ostream& os, pair& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;} template ostream& operator << (ostream& os, const pair& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;} template ostream& operator << (ostream& os, map& ope){ for(auto p : ope) os << "(" << p.first << ", " << p.second << "),";return os;} template ostream& operator << (ostream& os, set& ope){for(auto x : ope) os << x << " "; return os;} template ostream& operator << (ostream& os, multiset& ope){for(auto x : ope) os << x << " "; return os;} template void outa(T a[], ll s, ll t){rep(i, s, t){ cout << a[i]; if(i < t) cout << " ";} cout << endl;} template ostream& operator << (ostream& os, array& arr){reps(i, arr) os << arr[i] << " "; return os;} template ostream& operator << (ostream& os, const array& arr){reps(i, arr) os << arr[i] << " "; return os;} void dump_func(){cout << endl;} template void dump_func(Head &&head, Tail &&... tail){cout << head; if(sizeof...(Tail) > 0) cout << " "; dump_func(std::move(tail)...);} template void bssert(bool b, T t){ if(!b) cout << t << endl, exit(0); } struct NTT_Convolution{ NTT_Convolution(){}; static int rev(int x, int n){ int ret = 0; for(int i = 0; i < n; i++) ret <<= 1, ret |= (x>>i) & 1; return ret; } static void DFT(vector &f, vector &F, int n, mint root, bool inv = false) { int N = 1< f, vector g, vector &dest) { ll logf = 0, logg = 0, len = f.size() + g.size(); for(int i = f.size(); i; i /= 2) logf++; for(int i = g.size(); i; i /= 2) logg++; ll n = max(logf, logg)+1, N = 1< F, G; DFT(f, F, n, root), DFT(g, G, n, root); for(int i = 0; i < N; i++) F[i] *= G[i]; DFT(F, f, n, root, true); f.resize(len-1); dest = f; } }; ll h, w; ll a[1005], b[1005]; vector dp[1005]; mint inv[5005]; int main(void) { ios::sync_with_stdio(0); cin.tie(0); make_fact(5005); rep(i, 1, 5000) inv[i] = mint(i).inverse(); cin >> h >> w; rep(i, 1, h) cin >> a[i] >> b[i]; dp[0] = {1}; rep(i, 0, h-1){ reps(j, dp[i]) dp[i][j] *= fact_inv[j]; vector vec; mint A = 1, B = 1; rep(j, 0, w-1) A *= w+b[i+1]-j, B *= w+a[i+1]-1-j; rep(j, 1, w) A *= inv[j], B *= inv[j]; rep(k, 0, w){ mint tmp = A - B; vec.pb(tmp * fact_inv[k]); A *= b[i+1]-k, A *= inv[w+k+1], B *= a[i+1]-1-k, B *= inv[w+k+1]; } NTT_Convolution::conv(dp[i], vec, dp[i+1]); dp[i].resize(w+1); reps(j, dp[i+1]) dp[i+1][j] *= fact[j]; //outl(dp[i+1]); } outl(dp[h][w]); return 0; }