using System; using System.Collections.Generic; using System.IO; using System.Linq; using static System.Math; using System.Text; using System.Threading; using System.Globalization; using System.Runtime.CompilerServices; using System.Runtime.InteropServices; using Library; namespace Program { public static class ProblemF { static bool SAIKI = false; static public int numberOfRandomCases = 0; static public void MakeTestCase(List _input, List _output, ref Func _outputChecker) { } static public void Solve() { var N = NN; var M = NN; var txy = Repeat(0, M).Select(_ => new { t = NN, x = NN, y = NN }).ToArray(); var all = LIB_Mod.Comb(N * 2, N) * 2 * N; foreach (var item in txy) { if (item.t == 1) { var thispat = LIB_Mod.Comb(item.x + item.y, item.x); var tox = N - item.x-1; var toy = N - item.y; all -= thispat * LIB_Mod.Comb(tox + toy, tox); } else { var thispat = LIB_Mod.Comb(item.x + item.y, item.x); var tox = N - item.x; var toy = N - item.y-1; all -= thispat * LIB_Mod.Comb(tox + toy, tox); } } Console.WriteLine(all); } class Printer : StreamWriter { public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; } public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; } } static LIB_FastIO fastio = new LIB_FastIODebug(); static public void Main(string[] args) { if (args.Length == 0) { fastio = new LIB_FastIO(); Console.SetOut(new Printer(Console.OpenStandardOutput())); } if (SAIKI) { var t = new Thread(Solve, 134217728); t.Start(); t.Join(); } else Solve(); Console.Out.Flush(); } static long NN => fastio.Long(); static double ND => fastio.Double(); static string NS => fastio.Scan(); static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray(); static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray(); static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray(); static long Count(this IEnumerable x, Func pred) => Enumerable.Count(x, pred); static IEnumerable Repeat(T v, long n) => Enumerable.Repeat(v, (int)n); static IEnumerable Range(long s, long c) => Enumerable.Range((int)s, (int)c); static IOrderedEnumerable OrderByRand(this IEnumerable x) => Enumerable.OrderBy(x, _ => xorshift); static IOrderedEnumerable OrderBy(this IEnumerable x) => Enumerable.OrderBy(x.OrderByRand(), e => e); static IOrderedEnumerable OrderBy(this IEnumerable x, Func selector) => Enumerable.OrderBy(x.OrderByRand(), selector); static IOrderedEnumerable OrderByDescending(this IEnumerable x) => Enumerable.OrderByDescending(x.OrderByRand(), e => e); static IOrderedEnumerable OrderByDescending(this IEnumerable x, Func selector) => Enumerable.OrderByDescending(x.OrderByRand(), selector); static IOrderedEnumerable OrderBy(this IEnumerable x) => x.OrderByRand().OrderBy(e => e, StringComparer.OrdinalIgnoreCase); static IOrderedEnumerable OrderBy(this IEnumerable x, Func selector) => x.OrderByRand().OrderBy(selector, StringComparer.OrdinalIgnoreCase); static IOrderedEnumerable OrderByDescending(this IEnumerable x) => x.OrderByRand().OrderByDescending(e => e, StringComparer.OrdinalIgnoreCase); static IOrderedEnumerable OrderByDescending(this IEnumerable x, Func selector) => x.OrderByRand().OrderByDescending(selector, StringComparer.OrdinalIgnoreCase); static string Join(this IEnumerable x, string separator = "") => string.Join(separator, x); static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } } static IEnumerator _xsi = _xsc(); static IEnumerator _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } } static bool Chmax(this ref T lhs, T rhs) where T : struct, IComparable { if (lhs.CompareTo(rhs) < 0) { lhs = rhs; return true; } return false; } static bool Chmin(this ref T lhs, T rhs) where T : struct, IComparable { if (lhs.CompareTo(rhs) > 0) { lhs = rhs; return true; } return false; } static void Fill(this T[] array, T value) => array.AsSpan().Fill(value); static void Fill(this T[,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0], array.Length).Fill(value); static void Fill(this T[,,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0, 0], array.Length).Fill(value); static void Fill(this T[,,,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0, 0, 0], array.Length).Fill(value); } } namespace Library { class LIB_Math { [MethodImpl(MethodImplOptions.AggressiveInlining)] static public IEnumerable Primes(long x) { if (x < 2) yield break; yield return 2; var halfx = x / 2; var table = new bool[halfx + 1]; var max = (long)(Math.Sqrt(x) / 2); for (long i = 1; i <= max; ++i) { if (table[i]) continue; var add = 2 * i + 1; yield return add; for (long j = 2 * i * (i + 1); j <= halfx; j += add) table[j] = true; } for (long i = max + 1; i <= halfx; ++i) if (!table[i] && 2 * i + 1 <= x) yield return 2 * i + 1; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public IEnumerable Factors(long x) { if (x < 2) yield break; while (x % 2 == 0) { x /= 2; yield return 2; } var max = (long)Math.Sqrt(x); for (long i = 3; i <= max; i += 2) { while (x % i == 0) { x /= i; yield return i; } } if (x != 1) yield return x; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public IEnumerable Divisor(long x) { if (x < 1) yield break; var max = (long)Math.Sqrt(x); for (long i = 1; i <= max; ++i) { if (x % i != 0) continue; yield return i; if (i != x / i) yield return x / i; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public long GCD(long a, long b) { while (b > 0) { var tmp = b; b = a % b; a = tmp; } return a; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public long LCM(long a, long b) => a / GCD(a, b) * b; [MethodImpl(MethodImplOptions.AggressiveInlining)] static public long Pow(long x, long y) { long a = 1; while (y != 0) { if ((y & 1) == 1) a *= x; if (x < long.MaxValue / x) x *= x; y >>= 1; } return a; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public decimal Sqrt(decimal x) { decimal prev, cur = (decimal)Math.Sqrt((double)x); do { prev = cur; if (prev == 0) return 0; cur = (prev + x / prev) / 2; } while (cur != prev); return cur; } static List _fact = new List() { 1 }; [MethodImpl(MethodImplOptions.AggressiveInlining)] static void Build(long n) { if (n >= _fact.Count) for (int i = _fact.Count; i <= n; ++i) _fact.Add(_fact[i - 1] * i); } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public long Comb(long n, long k) { Build(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k]; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public long Perm(long n, long k) { Build(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)]; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public IEnumerable> MakePermutation(long n, bool zeroIndexed = true) { if (n <= 0) throw new Exception(); var c = new int[n]; var a = new int[n]; if (!zeroIndexed) a[0] = 1; for (var i = 1; i < n; i++) a[i] = a[i - 1] + 1; yield return new List(a); for (var i = 0; i < n;) { if (c[i] < i) { if (i % 2 == 0) { var t = a[0]; a[0] = a[i]; a[i] = t; } else { var t = a[c[i]]; a[c[i]] = a[i]; a[i] = t; } yield return new List(a); ++c[i]; i = 0; } else { c[i] = 0; ++i; } } } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public bool NextPermutation(long[] ary) { var n = ary.Length; var i = n - 1; while (i - 1 >= 0 && ary[i - 1] > ary[i]) --i; if (i == 0) return false; var j = i; while (j + 1 < n && ary[i - 1] < ary[j + 1]) ++j; var tmp = ary[i - 1]; ary[i - 1] = ary[j]; ary[j] = tmp; var s = i; var t = n - 1; while (t - s > 0) { tmp = ary[t]; ary[t] = ary[s]; ary[s] = tmp; ++s; --t; } return true; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public (long, long) InvGCD(long a, long b) { a = (a + b) % b; if (a == 0) return (b, 0); var s = b; var t = a; var m0 = 0L; var m1 = 1L; while (t > 0) { var u = s / t; s -= t * u; m0 -= m1 * u; var tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return (s, m0); } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public (long, long) CRT(long[] r, long[] m) { var r0 = 0L; var m0 = 1L; for (var i = 0; i < m.Length; i++) { var m1 = m[i]; var r1 = (r[i] + m1) % m1; if (m0 < m1) { r0 ^= r1; r1 ^= r0; r0 ^= r1; m0 ^= m1; m1 ^= m0; m0 ^= m1; } if (m0 % m1 == 0) { if (r0 % m1 != r1) return (0, 0); continue; } var gim = InvGCD(m0, m1); var u1 = m1 / gim.Item1; if ((r1 - r0) % gim.Item1 != 0) return (0, 0); var x = (r1 - r0) / gim.Item1 % u1 * gim.Item2 % u1; r0 += x * m0; m0 *= u1; if (r0 < 0) r0 += m0; } return (r0, m0); } [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)] /// /// a*i + b /// i=0...n-1 /// 格子高さm /// static public long FloorSum(long n, long m, long a, long b) { unchecked { var ans = 0UL; var un = (ulong)n; var um = (ulong)m; var ua = (ulong)a; var ub = (ulong)b; if (a < 0) { var am = a % m; if (am < 0) am += m; var a2 = (ulong)am; ans -= un * (un - 1) / 2 * ((a2 + (ulong)(-a)) / um); ua = a2; } if (b < 0) { var bm = b % m; if (bm < 0) bm += m; var b2 = (ulong)bm; ans -= un * ((b2 + (ulong)(-b)) / um); ub = b2; } while (true) { if (ua >= um) { ans += (un - 1) * un / 2 * (ua / um); ua %= um; } if (ub >= um) { ans += un * (ub / um); ub %= um; } var ymax = ua * un + ub; if (ymax < um) return (long)ans; un = ymax / um; ub = ymax % um; um ^= ua; ua ^= um; um ^= ua; } } } } partial struct LIB_Mod : IEquatable, IEquatable { static public long _mod = 1000000007; long v; [MethodImpl(MethodImplOptions.AggressiveInlining)] public LIB_Mod(long x) { if (x < _mod && x >= 0) v = x; else if ((v = x % _mod) < 0) v += _mod; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public implicit operator LIB_Mod(long x) => new LIB_Mod(x); [MethodImpl(MethodImplOptions.AggressiveInlining)] static public implicit operator long(LIB_Mod x) => x.v; [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Add(LIB_Mod x) { if ((v += x.v) >= _mod) v -= _mod; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Sub(LIB_Mod x) { if ((v -= x.v) < 0) v += _mod; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Mul(LIB_Mod x) => v = (v * x.v) % _mod; [MethodImpl(MethodImplOptions.AggressiveInlining)] public void Div(LIB_Mod x) => v = (v * Inverse(x.v)) % _mod; [MethodImpl(MethodImplOptions.AggressiveInlining)] static public LIB_Mod operator +(LIB_Mod x, LIB_Mod y) { var t = x.v + y.v; return t >= _mod ? new LIB_Mod { v = t - _mod } : new LIB_Mod { v = t }; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public LIB_Mod operator -(LIB_Mod x, LIB_Mod y) { var t = x.v - y.v; return t < 0 ? new LIB_Mod { v = t + _mod } : new LIB_Mod { v = t }; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public LIB_Mod operator *(LIB_Mod x, LIB_Mod y) => x.v * y.v; [MethodImpl(MethodImplOptions.AggressiveInlining)] static public LIB_Mod operator /(LIB_Mod x, LIB_Mod y) => x.v * Inverse(y.v); [MethodImpl(MethodImplOptions.AggressiveInlining)] static public bool operator ==(LIB_Mod x, LIB_Mod y) => x.v == y.v; [MethodImpl(MethodImplOptions.AggressiveInlining)] static public bool operator !=(LIB_Mod x, LIB_Mod y) => x.v != y.v; [MethodImpl(MethodImplOptions.AggressiveInlining)] static public long Inverse(long x) { long b = _mod, r = 1, u = 0, t = 0; while (b > 0) { var q = x / b; t = u; u = r - q * u; r = t; t = b; b = x - q * b; x = t; } return r < 0 ? r + _mod : r; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public bool Equals(LIB_Mod x) => v == x.v; [MethodImpl(MethodImplOptions.AggressiveInlining)] public bool Equals(long x) => v == x; [MethodImpl(MethodImplOptions.AggressiveInlining)] public override bool Equals(object x) => x == null ? false : Equals((LIB_Mod)x); [MethodImpl(MethodImplOptions.AggressiveInlining)] public override int GetHashCode() => v.GetHashCode(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public override string ToString() => v.ToString(); static List _fact = new List() { 1, 1 }; static List _inv = new List() { 0, 1 }; static List _factinv = new List() { 1, 1 }; static long _factm = _mod; [MethodImpl(MethodImplOptions.AggressiveInlining)] static void B(long n) { if (_factm != _mod) { _fact = new List() { 1, 1 }; _inv = new List() { 0, 1 }; _factinv = new List() { 1, 1 }; } if (n >= _fact.Count) { for (int i = _fact.Count; i <= n; ++i) { _fact.Add(_fact[i - 1] * i); _inv.Add(_mod - _inv[(int)(_mod % i)] * (_mod / i)); _factinv.Add(_factinv[i - 1] * _inv[i]); } } _factm = _mod; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public LIB_Mod Comb(long n, long k) { B(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] * _factinv[(int)(n - k)] * _factinv[(int)k]; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public LIB_Mod CombOK(long n, long k) { LIB_Mod ret = 1; for (var i = 0; i < k; i++) ret *= n - i; for (var i = 1; i <= k; i++) ret /= i; return ret; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public LIB_Mod Perm(long n, long k) { B(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] * _factinv[(int)(n - k)]; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public LIB_Mod KanzenPerm(long n, long k) => Enumerable.Range(0, (int)k + 1).Aggregate((LIB_Mod)0, (a, e) => a + (1 - ((e & 1) << 1)) * LIB_Mod.Comb(k, e) * LIB_Mod.Perm(n - e, k - e)); [MethodImpl(MethodImplOptions.AggressiveInlining)] static public LIB_Mod Pow(LIB_Mod x, long y) { LIB_Mod a = 1; while (y != 0) { if ((y & 1) == 1) a.Mul(x); x.Mul(x); y >>= 1; } return a; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public long[] LogBuild(long a) { var ret = new long[_mod]; ret[1] = 0; for (var i = 1; i < _mod; i++) { ret[a] = i; a *= 2; a %= _mod; } return ret; } [MethodImpl(MethodImplOptions.AggressiveInlining)] static public long Log(long a, long b) { var g = 1L; for (var i = _mod; i != 0; i >>= 1) { g *= a; g %= _mod; } g = LIB_Math.GCD(g, _mod); var t = 1L; var c = 0L; for (; t % g != 0; ++c) { if (t == b) return c; t *= a; t %= _mod; } if (b % g != 0) return -1; t /= g; b /= g; var n = _mod / g; var h = 0L; var gs = 1L; for (; h * h < n; ++h) { gs *= a; gs %= n; } var bs = new Dictionary(); for (long s = 0L, e = b; s < h; bs[e] = ++s) { e *= a; e %= n; } for (long s = 0L, e = t; s < n;) { e *= gs; e %= n; s += h; if (bs.ContainsKey(e) && bs[e] > 0) return c + s - bs[e]; } return -1; } } class LIB_FastIO { [MethodImpl(MethodImplOptions.AggressiveInlining)] public LIB_FastIO() { str = Console.OpenStandardInput(); } readonly Stream str; readonly byte[] buf = new byte[2048]; int len, ptr; [MethodImpl(MethodImplOptions.AggressiveInlining)] byte read() { if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 2048)) <= 0) { return 0; } } return buf[ptr++]; } [MethodImpl(MethodImplOptions.AggressiveInlining)] char Char() { byte b = 0; do b = read(); while (b < 33 || 126 < b); return (char)b; } [MethodImpl(MethodImplOptions.AggressiveInlining)] virtual public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] virtual public long Long() { long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != '-' && (b < '0' || '9' < b)); if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = (ret << 3) + (ret << 1) + b - '0'; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] virtual public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); } } class LIB_FastIODebug : LIB_FastIO { Queue param = new Queue(); [MethodImpl(MethodImplOptions.AggressiveInlining)] string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public LIB_FastIODebug() { } [MethodImpl(MethodImplOptions.AggressiveInlining)] public override string Scan() => NextString(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public override long Long() => long.Parse(NextString()); [MethodImpl(MethodImplOptions.AggressiveInlining)] public override double Double() => double.Parse(NextString()); } }