#define ATCODER #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ld = long double; using pll = pair; using pdd = pair; //template using pq = priority_queue, greater>; #define FOR(i, a, b) for(ll i=(a); i<(b);i++) #define REP(i, n) for(ll i=0; i<(n);i++) #define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--) #define PER(i, n) for(ll i=n-1; i>=0;i--) #define REPREP(i,j,a,b) for(ll i=0;i > #define VV2(type,n,m,val) vector< vector > val;val.resize(n);for(ll i;i #define VEC(type,n,val) vector val;val.resize(n) #define VL vector #define VVL vector< vector > #define VP vector< pair > #define SZ size() #define all(i) begin(i),end(i) #define SORT(i) sort(all(i)) #define BITI(i) (1<>i) & 1) != 0) #define ALLBIT(n) (ll(1)<v?v:n #define MP(a,b) make_pair(a,b) #define DET2(x1,y1,x2,y2) x1*y2-x2*y1 #define DET3(x1,y1,z1,x2,y2,z2,x3,y3,z3) x1*y2*z3+x2*y3*z1+x3*y1*z2-z1*y2*x3-z2*y3*x1-z3*y1*x2 #define INC(a) for(auto& v:a)v++; #define DEC(a) for(auto& v:a)v--; #define SQU(x) (x)*(x) #define L0 ll(0) #ifdef ATCODER #include using namespace atcoder; using mint = modint1000000007; using mint2 = modint998244353; #endif template vector read(size_t n) { vector ts(n); for (size_t i = 0; i < n; i++) cin >> ts[i]; return ts; } template void read_tuple_impl(TV&) {} template void read_tuple_impl(TV& ts) { get(ts).emplace_back(*(istream_iterator(cin))); read_tuple_impl(ts); } template decltype(auto) read_tuple(size_t n) { tuple...> ts; for (size_t i = 0; i < n; i++) read_tuple_impl(ts); return ts; } using val = pair; using func = ll; val op(val a, val b) { return MP(a.first + b.first, a.second + b.second); } val e() { return MP(0, 0); } val mp(func f, val a) { return MP(a.first + f * a.second, a.second); } func comp(func f, func g) { return f + g; } func id() { return 0; } ll di[4] = { 1,0,-1,0 }; ll dj[4] = { 0,1,0,-1 }; ll si[4] = { 0,3,3,0 }; ll sj[4] = { 0,0,3,3 }; //ll di[4] = { -1,-1,1,1 }; //ll dj[4] = { -1,1,-1,1 }; ll di8[8] = { 0,-1,-1,-1,0,1,1,1 }; ll dj8[8] = { -1,-1,0,1,1,1,0,-1 }; template T Combi(ll a, ll b, vector& fact) { if (a < 0 || b < 0 || a < b) return 0; return fact[a] / (fact[b] * fact[a - b]); } vector pow(vector& f, ll k) { if (k == 1) return f; vector ff = convolution(f, f); vector res = pow(ff, k / 2); if (k % 2) res = convolution(res, f); return res; } void solve() { ll n, m; cin >> n >> m; auto [l, r] = read_tuple(m); DEC(l); if (n % 2) { cout << 0; return; } unordered_map cnt; REP(i, m) cnt[r[i] - l[i]]++; vector f(n + 1, 1); REP(i, n) f[i + 1] = f[i] * (i + 1); vector p(n/2+1); p[0] = 1; ll sum = 1; for (auto& [k, v] : cnt) { if (k % 2 || v == 0) continue; mint2 minus = -Combi(k, k / 2, f) / (k / 2 + 1); REP(t, v) { PER(i, sum) { p[i + k / 2] += p[i] * minus; } sum += k / 2; } } mint2 ans = 0; REP(i, n/2+1) { ans += p[i] * Combi(n - i * 2, n / 2 - i, f) / (n / 2 - i + 1); } cout << ans.val(); } int main() { ll t = 1; //cin >> t; while (t--) { solve(); } return 0; }