# require "/math/Mint" # require "../atcoder/src/Math" # ac-library.cr by hakatashi https://github.com/google/ac-library.cr # # Copyright 2021 Google LLC # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # https://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. module AtCoder # Implements [ACL's Math library](https://atcoder.github.io/ac-library/master/document_en/math.html) module Math def self.extended_gcd(a, b) last_remainder, remainder = a.abs, b.abs x, last_x, y, last_y = 0_i64, 1_i64, 1_i64, 0_i64 while remainder != 0 new_last_remainder = remainder quotient, remainder = last_remainder.divmod(remainder) last_remainder = new_last_remainder x, last_x = last_x - quotient * x, x y, last_y = last_y - quotient * y, y end return last_remainder, last_x * (a < 0 ? -1 : 1) end # Implements atcoder::inv_mod(value, modulo). def self.inv_mod(value, modulo) gcd, inv = extended_gcd(value, modulo) if gcd != 1 raise ArgumentError.new("#{value} and #{modulo} are not coprime") end inv % modulo end # Simplified AtCoder::Math.pow_mod with support of Int64 def self.pow_mod(base, exponent, modulo) if exponent == 0 return base.class.zero + 1 end if base == 0 return base end b = exponent > 0 ? base : inv_mod(base, modulo) e = exponent.abs ret = 1_i64 while e > 0 if e % 2 == 1 ret = mul_mod(ret, b, modulo) end b = mul_mod(b, b, modulo) e //= 2 end ret end # Caluculates a * b % mod without overflow detection @[AlwaysInline] def self.mul_mod(a : Int64, b : Int64, mod : Int64) if mod < Int32::MAX return a * b % mod end # 31-bit width a_high = (a >> 32).to_u64 # 32-bit width a_low = (a & 0xFFFFFFFF).to_u64 # 31-bit width b_high = (b >> 32).to_u64 # 32-bit width b_low = (b & 0xFFFFFFFF).to_u64 # 31-bit + 32-bit + 1-bit = 64-bit c = a_high * b_low + b_high * a_low c_high = c >> 32 c_low = c & 0xFFFFFFFF # 31-bit + 31-bit res_high = a_high * b_high + c_high # 32-bit + 32-bit res_low = a_low * b_low res_low_high = res_low >> 32 res_low_low = res_low & 0xFFFFFFFF # Overflow if res_low_high + c_low >= 0x100000000 res_high += 1 end res_low = (((res_low_high + c_low) & 0xFFFFFFFF) << 32) | res_low_low (((res_high.to_i128 << 64) | res_low) % mod).to_i64 end @[AlwaysInline] def self.mul_mod(a, b, mod) typeof(mod).new(a.to_i64 * b % mod) end # Implements atcoder::crt(remainders, modulos). def self.crt(remainders, modulos) raise ArgumentError.new unless remainders.size == modulos.size total_modulo = 1_i64 answer = 0_i64 remainders.zip(modulos).each do |(remainder, modulo)| gcd, p = extended_gcd(total_modulo, modulo) if (remainder - answer) % gcd != 0 return 0_i64, 0_i64 end tmp = (remainder - answer) // gcd * p % (modulo // gcd) answer += total_modulo * tmp total_modulo *= modulo // gcd end return answer % total_modulo, total_modulo end # Implements atcoder::floor_sum(n, m, a, b). def self.floor_sum(n, m, a, b) n, m, a, b = n.to_i64, m.to_i64, a.to_i64, b.to_i64 res = 0_i64 if a < 0 a2 = a % m res -= n * (n - 1) // 2 * ((a2 - a) // m) a = a2 end if b < 0 b2 = b % m res -= n * ((b2 - b) // m) b = b2 end res + floor_sum_unsigned(n, m, a, b) end private def self.floor_sum_unsigned(n, m, a, b) res = 0_i64 loop do if a >= m res += n * (n - 1) // 2 * (a // m) a = a % m end if b >= m res += n * (b // m) b = b % m end y_max = a * n + b break if y_max < m n = y_max // m b = y_max % m m, a = a, m end res end end end macro static_modint(name, mod) struct {{name}} MOD = {{mod}}i64 def self.zero new end def self.raw(value : Int64) result = new result.value = value result end getter value : Int64 def initialize @value = 0i64 end def initialize(value) @value = value.to_i64 % MOD end def initialize(m : self) @value = m.value end protected def value=(value : Int64) @value = value end def ==(m : self) value == m.value end def ==(m) value == m end def + : self self end def - : self self.class.raw(value != 0 ? MOD &- value : 0i64) end def +(v) self + self.class.new(v) end def +(m : self) x = value &+ m.value x &-= MOD if x >= MOD self.class.raw(x) end def -(v) self - self.class.new(v) end def -(m : self) x = value &- m.value x &+= MOD if x < 0 self.class.raw(x) end def *(v) self * self.class.new(v) end def *(m : self) self.class.new(value &* m.value) end def /(v) self / self.class.new(v) end def /(m : self) raise DivisionByZeroError.new if m.value == 0 a, b, u, v = m.value, MOD, 1i64, 0i64 while b != 0 t = a // b a &-= t &* b a, b = b, a u &-= t &* v u, v = v, u end self.class.new(value &* u) end def //(v) self / v end def **(exponent : Int) t, res = self, self.class.raw(1i64) while exponent > 0 res *= t if exponent & 1 == 1 t *= t exponent >>= 1 end res end {% for op in %w[< <= > >=] %} def {{op.id}}(other) raise NotImplementedError.new({{op}}) end {% end %} def inv self.class.raw AtCoder::Math.inv_mod(value, MOD) end def succ self.class.raw(value != MOD &- 1 ? value &+ 1 : 0i64) end def pred self.class.raw(value != 0 ? value &- 1 : MOD &- 1) end def abs self end def abs2 self * self end def to_i64 : Int64 value end delegate to_s, to: @value delegate inspect, to: @value end {% to = ("to_" + name.stringify.downcase.gsub(/mint|modint/, "m")).id %} struct Int {% for op in %w[+ - * / //] %} def {{op.id}}(value : {{name}}) {{to}} {{op.id}} value end {% end %} {% for op in %w[< <= > >=] %} def {{op.id}}(m : {{name}}) raise NotImplementedError.new({{op}}) end {% end %} def {{to}} : {{name}} {{name}}.new(self) end end class String def {{to}} : {{name}} {{name}}.new(self) end end end static_modint(Mint, 1000000007) static_modint(Mint2, 998244353) # require "/math/Combination" class Combination(T) def initialize(initial_capacity : Int = 2) initial_capacity += 1 @size = 2 @factorial = Array(T).new(initial_capacity) @factorial << T.new(1) << T.new(1) @inv = Array(T).new(initial_capacity) @inv << T.zero << T.new(1) @finv = Array(T).new(initial_capacity) @finv << T.new(1) << T.new(1) expand_until(initial_capacity) end private def expand_until(n : Int) while @size <= n @factorial << @factorial[-1] * @size @inv << -@inv[T::MOD % @size] * (T::MOD // @size) @finv << @finv[-1] * @inv[@size] @size += 1 end end def factorial(n : Int) expand_until(n) @factorial.unsafe_fetch(n) end def inv(n : Int) expand_until(n) @inv.unsafe_fetch(n) end def finv(n : Int) expand_until(n) @finv.unsafe_fetch(n) end def permutation(n : Int, r : Int) (n < r || n < 0 || r < 0) ? T.zero : factorial(n) * finv(n - r) end def combination(n : Int, r : Int) (n < r || n < 0 || r < 0) ? T.zero : factorial(n) * finv(r) * finv(n - r) end def repeated_combination(n : Int, r : Int) (n < 0 || r < 0) ? T.zero : r == 0 ? T.new(1) : combination(n + r - 1, r) end end C = Combination(Mint).new n, m = read_line.split.map(&.to_i) ans = C.combination(n * 2, n) * n * 2 m.times do t, x, y = read_line.split.map(&.to_i) if t == 1 x1, y1 = n - x.succ, n - y ans -= C.combination(x + y, y) * C.combination(x1 + y1, x1) else x1, y1 = n - x, n - y.succ ans -= C.combination(x + y, y) * C.combination(x1 + y1, x1) end end puts ans