#include using namespace std; typedef long long ll; #define all(x) (x).begin(),(x).end() template bool chmin(T1 &a,T2 b){if(a<=b)return 0; a=b; return 1;} template bool chmax(T1 &a,T2 b){if(a>=b)return 0; a=b; return 1;} int dx[4]={0,1,0,-1}, dy[4]={1,0,-1,0}; long double eps = 1e-9; long double pi = acos(-1); template< int mod = 1000000007 > 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; } }; const int mod = 1000000007; // const int mod = 998244353; using mint = ModInt< mod >; const int MAX = 5100005; mint fac[MAX], finv[MAX], inv[MAX]; // テーブルを作る前処理 void COMinit() { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < MAX; i++){ fac[i] = fac[i - 1] * i; } finv[MAX-1] = fac[MAX-1].inverse(); for(int i=MAX-2;i>=1;i--){ finv[i] = finv[i+1]*(i+1); inv[i+1] = fac[i]*finv[i+1]; } } // 二項係数計算 mint 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]); } // n次多項式f(x)に対して、f(0),f(1),...f(n)が分かっているなら任意のtに対してf(t)が復元できる // return f(t) mint LagrangePolynomial(vector y,ll T){ int n=y.size()-1; if (T<=n) return y[T]; vector dp(n+1,1),pd(n+1,1),fac(n+1,1),finv(n+1,1); for (int i=0;i0;--i) pd[i-1]=pd[i]*(T-i); for (int i=1;i0;--i) finv[i-1]=finv[i]*i; mint res=0; for (int i=0;i<=n;++i){ mint x=y[i]*dp[i]*pd[i]*finv[i]*finv[n-i]; if ((n-i)&1) res-=x; else res+=x; } return res; } signed main(){ ios::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20); COMinit(); int n,m; cin>>n>>m; mint ans = COM(n+n,n) * (n+n); for(int i=0;i>t>>x>>y; if(t == 1){ ans -= COM(x+y,x) * COM(n+n-x-y-1,n-x-1); } else{ ans -= COM(x+y,x)* COM(n+n-x-y-1,n-y-1); } } cout << ans << endl; }