//各辺について引く. スタートから何通り?とゴールから何通り?の積 #include #include #include #include #include #include #include #include #include #include #include #include #define int long long #define rep(i, n) for(i = 0; i < n; i++) using namespace std; const int mod = 1000000007; int powmod(int a, int n, int mod) { if (n == 0) return 1; if (n % 2 == 0) return powmod((a * a) % mod, n / 2, mod); return a * powmod(a, n - 1, mod) % mod; } int fact[500000]; int finv[500000]; int n, m; int t[200000], x[200000], y[200000]; int comb(int n, int k) { return fact[n] * finv[k] % mod * finv[n - k] % mod; } signed main() { int i; fact[0] = 1; finv[0] = 1; for (i = 1; i < 500000; i++) { fact[i] = i * fact[i - 1] % mod; finv[i] = powmod(fact[i], mod - 2, mod); } cin >> n >> m; int diff = 0; rep(i, m) { cin >> t[i] >> x[i] >> y[i]; //(0, 0) -> (x[i], y[i]) int cnt1 = comb(x[i] + y[i], x[i]); int dx, dy; if (t[i] == 1) { //(x[i] + 1, y[i]) -> (n, n) dx = n - x[i] - 1; dy = n - y[i]; } else { dx = n - x[i]; dy = n - y[i] - 1; } int cnt2 = comb(dx + dy, dx); int e8kun = cnt1 * cnt2 % mod; //cout << "i = " << i << ", cnt1 = " << cnt1 << ", cnt2 = " << cnt2 << endl; diff += e8kun; diff %= mod; } //全ての辺のコストが1のとき、経路長はちょうど2N. int allOne = 2 * n * comb(2 * n , n) % mod; int ans = (allOne + mod - diff) % mod; cout << ans << endl; return 0; }