結果

問題 No.802 だいたい等差数列
ユーザー te-sh
提出日時 2021-07-08 12:57:28
言語 Crystal
(1.14.0)
結果
AC  
実行時間 64 ms / 2,000 ms
コード長 6,755 bytes
コンパイル時間 13,447 ms
コンパイル使用メモリ 304,020 KB
実行使用メモリ 23,164 KB
最終ジャッジ日時 2024-07-01 12:29:44
合計ジャッジ時間 14,131 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

def solve(io)
  n, m, d1, d2 = io.get4(Int64)
  d = d2-d1
  m = m-(n-1)*d1-1
  io.put_e 0 if m < 0
  f = Fact(Mint).new((n+m).to_i32)
  r = f.homo(n+1, m)
  (1..n-1).each do |i|
    next if m-(d+1)*i < 0
    r -= f.combi(n-1, i) * f.homo(n+1, m-i*(d+1)) * (-1)**(i-1)
  end
  io.put r
end
class Array
  macro new_md(*args, &block)
    {% if !block %}
      {% for arg, i in args[0...-2] %}
        Array.new({{arg}}) {
      {% end %}
      Array.new({{args[-2]}}, {{args[-1]}})
      {% for arg in args[0...-2] %}
        }
      {% end %}
    {% else %}
      {% for arg, i in args %}
        Array.new({{arg}}) { |_i{{i}}|
      {% end %}
      {% for block_arg, i in block.args %}
        {{block_arg}} = _i{{i}}
      {% end %}
      {{block.body}}
      {% for arg in args %}
        }
      {% end %}
    {% end %}
  end
end
struct Int
  def cdiv(b : Int)
    (self + b - 1) // b
  end
  def bit?(i : Int)
    bit(i) == 1
  end
  def set_bit(i : Int)
    self | (self.class.new(1) << i)
  end
  def reset_bit(i : Int)
    self & ~(self.class.new(1) << i)
  end
  {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.34.0") < 0 %}
    def bit_length : Int32
      x = self < 0 ? ~self : self
      if x.is_a?(Int::Primitive)
        Int32.new(sizeof(self) * 8 - x.leading_zeros_count)
      else
        to_s(2).size
      end
    end
  {% end %}
end
struct Int32
  SQRT_MAX = 46_340_i32
  def isqrt
    m = SQRT_MAX
    r = (1_i32..SQRT_MAX).bsearch { |i| i**2 > self }
    r.nil? ? SQRT_MAX : r - 1
  end
end
struct Int64
  SQRT_MAX = 3_037_000_499_i64
  def isqrt
    r = (1_i64..SQRT_MAX).bsearch { |i| i**2 > self }
    r.nil? ? SQRT_MAX : r - 1
  end
end
struct Number
  {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.36.0") < 0 %}
    def self.additive_identity
      zero
    end
    def self.multiplicative_identity
      new(1)
    end
  {% end %}
end
class ProconIO
  def initialize(@ins : IO = STDIN, @outs : IO = STDOUT)
    @buf = [] of String
    @index = 0
  end
  def get(k : T.class = Int32) forall T
    get_v(k)
  end
  macro define_get
    {% for i in (2..9) %}
      def get(
           {% for j in (1..i) %}
             k{{j}}{% if j < i %},{% end %}
           {% end %}
         )
        {
          {% for j in (1..i) %}
            get(k{{j}}){% if j < i %},{% end %}
          {% end %}
        }
      end
    {% end %}
  end
  define_get
  macro define_getn
    {% for i in (2..9) %}
      def get{{i}}(k : T.class = Int32) forall T
        get(
          {% for j in (1..i) %}
            k{% if j < i %}, {% end %}
          {% end %}
        )
      end
    {% end %}
  end
  define_getn
  def get_a(n : Int, k : T.class = Int32) forall T
    Array.new(n) { get_v(k) }
  end
  def get_c(n : Int, k : T.class = Int32) forall T
    get_a(n, k)
  end
  macro define_get_c
    {% for i in (2..9) %}
      def get_c(
           n : Int,
           {% for j in (1..i) %}
             k{{j}}{% if j < i %},{% end %}
           {% end %}
         )
        a = Array.new(n) do
          get(
            {% for j in (1..i) %}
              k{{j}}{% if j < i %},{% end %}
            {% end %}
          )
        end
        {
          {% for j in (1..i) %}
            a.map { |e| e[{{j-1}}] }{% if j < i %},{% end %}
          {% end %}
        }
      end
    {% end %}
  end
  define_get_c
  macro define_getn_c
    {% for i in (2..9) %}
      def get{{i}}_c(n : Int, k : T.class = Int32) forall T
        get_c(
          n,
          {% for j in (1..i) %}
            k{% if j < i %}, {% end %}
          {% end %}
        )
      end
    {% end %}
  end
  define_getn_c
  def get_m(r : Int, c : Int, k : T.class = Int32) forall T
    Array.new(r) { get_a(c, k) }
  end
  def put(*vs)
    vs.each.with_index do |v, i|
      put_v(v)
      @outs.print i < vs.size - 1 ? " " : "\n"
    end
  end
  def put_e(*vs)
    put(*vs)
    exit
  end
  private def get_v(k : Int32.class); get_token.to_i32; end
  private def get_v(k : Int64.class); get_token.to_i64; end
  private def get_v(k : String.class); get_token; end
  private def get_token
    if @buf.size == @index
      str = @ins.read_line
      @buf = str.split
      @index = 0
    end
    v = @buf[@index]
    @index += 1
    v
  end
  private def put_v(vs : Enumerable)
    vs.each_with_index do |v, i|
      @outs.print v
      @outs.print " " if i < vs.size - 1
    end
  end
  private def put_v(v)
    @outs.print v
  end
end
macro min_u(a, b)
  {{a}} = Math.min({{a}}, {{b}})
end
macro max_u(a, b)
  {{a}} = Math.max({{a}}, {{b}})
end
class Fact(T)
  def initialize(@n : Int32)
    @table = Array.new(@n+1, T.multiplicative_identity)
    (1..@n).each do |i|
      @table[i] = @table[i-1] * i
    end
    @inv_table = Array.new(@n+1, T.multiplicative_identity)
    @inv_table[@n] //= @table[@n]
    (1..@n).reverse_each do |i|
      @inv_table[i-1] = @inv_table[i] * i
    end
  end
  getter table : Array(T)
  getter inv_table : Array(T)
  def fact(n : Int)
    @table[n]
  end
  def perm(n : Int, r : Int)
    @table[n] * @inv_table[n-r]
  end
  def combi(n : Int, r : Int)
    @table[n] * @inv_table[r] * @inv_table[n-r]
  end
  def homo(n : Int, r : Int)
    combi(n+r-1, r)
  end
  @table : Array(T)
  @inv_table : Array(T)
end
def powr(a : T, n : Int, i : T = T.multiplicative_identity) forall T
  powr(a, n, i) { |a, b| a * b }
end
def powr(a : T, n : Int, i : T = T.multiplicative_identity, &block) forall T
  return i if n == 0
  r, b = i, a
  while n > 0
    r = yield r, b if n.bit(0) == 1
    b = yield b, b
    n >>= 1
  end
  r
end
def ext_gcd(a : T, b : T) forall T
  if a == 0
    {b, T.new(0), T.new(1)}
  else
    g, x, y = ext_gcd(b%a, a)
    {g, y-(b//a)*x, x}
  end
end
abstract struct ModInt < Number
  macro new_type(name, mod)
    struct {{name}} < ModInt
      @@mod : Int32 = {{mod}}
    end
  end
  def initialize(v : Int)
    @v = (v % @@mod).to_i64
  end
  def_hash @@mod, @v
  def to_s
    @v.to_s
  end
  def to_s(io : IO) : Nil
    @v.to_s(io)
  end
  getter v : Int64
  delegate to_i, to: @v
  def ==(r : self)
    @v == r.v
  end
  def ==(r : Int)
    @v == (r % @@mod)
  end
  def - : self
    m(-@v)
  end
  def +(r : self)
    m(@v + r.v)
  end
  def +(r : Int)
    self + m(r)
  end
  def -(r : self)
    m(@v - r.v)
  end
  def -(r : Int)
    self - m(r)
  end
  def *(r : self)
    m(@v * r.v)
  end
  def *(r : Int)
    self * m(r)
  end
  def //(r : self)
    self * r.inv
  end
  def //(r : Int)
    self // m(r)
  end
  def **(n : Int)
    powr(self, n)
  end
  def inv
    m(ext_gcd(@v.to_i32, @@mod)[1])
  end
  private def m(v : Int)
    self.class.new(v)
  end
end
ModInt.new_type(Mint, 10**9+7)
solve(ProconIO.new)
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