#1153186 (Crystal) No.3478 XOR-Folding Primes

• 問題: No.3478 XOR-Folding Primes
• ユーザー: tomerun
• 提出日時: 2026-03-20 22:34:07
• 言語: Crystal (1.19.1)
• 結果: AC
• 実行時間: 1,323 ms / 4,000 ms
• コード長: 2,797 bytes
• コンパイル時間: 10,103 ms
• コンパイル使用メモリ: 342,088 KB
• 実行使用メモリ: 23,132 KB
• 最終ジャッジ日時: 2026-03-20 22:34:28
• 合計ジャッジ時間: 15,597 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge1_0

ファイルパターン	結果
sample	AC * 1
other	AC * 8

ソースコード

MOD      = 998244353i64
IS_PRIME = Array.new(10_001_001, true)
2.upto(IS_PRIME.size - 1) do |i|
  if IS_PRIME[i]
    (i * 2).step(to: IS_PRIME.size - 1, by: i) do |j|
      IS_PRIME[j] = false
    end
  end
end
PRIMES = (2...IS_PRIME.size).select { |i| IS_PRIME[i] }
TWINS  = [] of Int32
7.step(to: IS_PRIME.size - 1, by: 4) do |i|
  if IS_PRIME[i] && IS_PRIME[i - 2]
    TWINS << i
  end
end

read_line.to_i.times do
  puts solve()
end

def solve
  n, m = read_line.split.map(&.to_i)
  if n == 1
    return PRIMES.bsearch_index { |v, _| v > m }.not_nil!
  end
  mat = Matrix(Int64).new(3, 3)
  cnt = TWINS.bsearch_index { |v, _| v > m } || TWINS.size
  mat.a[1][0] = cnt
  mat.a[2][0] = cnt
  mat.a[0][1] = 1
  mat.a[0][2] = 1
  mat.a[1][2] = 1
  mat.a[2][1] = 1
  mat = mat.pow(n - 1)
  ans = 0i64
  v = [1, cnt, cnt]
  3.times do |i|
    3.times do |j|
      ans += mat.a[i][j] * v[j]
    end
  end
  ans % MOD
end

class Matrix(T)
  @a : Array(Array(T))
  getter :a, :d1, :d2

  def initialize(n : Int32, m : Int32)
    @a = Array.new(n) { Array.new(m, T.zero) }
    @d1 = n
    @d2 = m
  end

  def clone
    ret = Matrix(T).new(@d1, @d2)
    @d1.times do |i|
      @d2.times do |j|
        ret.a[i][j] = @a[i][j]
      end
    end
    return ret
  end

  def [](idx : Int32)
    return @a[idx]
  end

  def mul(other : Matrix(T))
    if @d2 != other.d1
      raise ArgumentError.new
    end
    d3 = other.d2
    tmp = Array.new(d3) { Array.new(@d2, T.zero) }
    d3.times do |i|
      tr1 = tmp[i]
      @d2.times do |j|
        tr1[j] = other[j][i]
      end
    end
    ret = Array.new(@d1) { Array.new(d3, T.zero) }
    @d1.times do |i|
      row1 = @a[i]
      ret1 = ret[i]
      d3.times do |j|
        sum = T.zero
        row2 = tmp[j]
        @d2.times do |k|
          sum += row1[k] * row2[k]
          sum %= MOD
        end
        ret1[j] = sum
      end
    end
    @a = ret
  end

  def mul_l(other : Matrix(T))
    # in-place
    if other.d2 != @d1
      raise ArgumentError.new
    end
    d3 = @d2
    tmp = Array.new(d3) { Array.new(@d1, T.zero) }
    d3.times do |i|
      tr1 = tmp[i]
      @d1.times do |j|
        tr1[j] = @a[j][i]
      end
    end
    other.d1.times do |i|
      row1 = other.a[i]
      ret1 = @a[i]
      d3.times do |j|
        sum = T.zero
        row2 = tmp[j]
        other.d2.times do |k|
          sum += row1[k] * row2[k]
          sum %= MOD
        end
        ret1[j] = sum
      end
    end
  end

  def pow(p : Int64)
    b = Matrix(T).new(@d1, @d2)
    ret = Matrix(T).new(@d1, @d2)
    @d1.times do |i|
      @d2.times do |j|
        b.a[i][j] = @a[i][j] % MOD
      end
      ret.a[i][i] = 1
    end
    while p > 0
      if (p & 1) != 0
        ret.mul_l(b)
      end
      b.mul(b)
      p >>= 1
    end
    return ret
  end
end