#1026763 (Nim) No.1832 NAND Reversible

提出ソース
結果

問題	No.1832 NAND Reversible
コンテスト
ユーザー	hirayuu_yc
提出日時	2024-11-15 16:41:07
言語	Nim (2.2.0)
結果	AC
実行時間	202 ms / 2,000 ms
コード長	15,813 bytes
コンパイル時間	6,419 ms
コンパイル使用メモリ	89,784 KB
実行使用メモリ	6,880 KB
最終ジャッジ日時	2024-11-15 16:41:20
合計ジャッジ時間	10,484 ms
ジャッジサーバーID （参考情報）	judge1 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン	結果
sample	AC * 3
other	AC * 23
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

raw source code
import macros
macro Please(x): untyped = nnkStmtList.newTree()

Please use Nim-ACL
Please use Nim-ACL
Please use Nim-ACL



{.warning[UnusedImport]: off.}
import algorithm
import sequtils
import tables
import math
import sets
import strutils
import sugar
import heapqueue
import deques
import bitops
import re
import streams
import times
import strscans
let outstream=newFileStream(stdout)
proc input():string{.inline.}=stdin.readLine
proc print(args:varargs[string,`$`]):void{.inline.}=stdout.writeLine(args)
proc debug(args:varargs[string,`$`]):void{.inline.}=stderr.writeLine(args)
proc flush():void{.inline.}=flush(outstream)
proc `%`(x:int,y:int):int{.inline.}=((x mod y)+y) mod y
proc `//`(x:int,y:int):int{.inline.}=((x)-(x%y)) div y
proc `%=`(x:var int,y:int):void{.inline.}=x=x%y
proc `//=`(x:var int,y:int):void{.inline.}=x=x//y
proc `**`(x:int,y:int):int{.inline.}=x^y
proc `**`(x:float,y:int):float{.inline.}=x^y
proc `^`(x:int,y:int):int{.inline.}=x xor y
proc `&`(x:int,y:int):int{.inline.}=x and y
proc `|`(x:int,y:int):int{.inline.}=x or y
proc `<<`(x:int,y:int):int{.inline.}=x shl y
proc `>>`(x:int,y:int):int{.inline.}=x shr y
proc `~`(x:int):int{.inline.}=not x
proc `^=`(x:var int,y:int):void{.inline.}=x=x xor y
proc `&=`(x:var int,y:int):void{.inline.}=x=x and y
proc `|=`(x:var int,y:int):void{.inline.}=x=x or y
proc `<<=`(x:var int,y:int):void{.inline.}=x=x shl y
proc `>>=`(x:var int,y:int):void{.inline.}=x=x shr y
proc `max=`(x:var int,y:int):void{.inline.}=x=max(x,y)
proc `min=`(x:var int,y:int):void{.inline.}=x=min(x,y)
proc `max=`(x:var float,y:float):void{.inline.}=x=max(x,y)
proc `min=`(x:var float,y:float):void{.inline.}=x=min(x,y)

#[ import atcoder/modint ]#
when not declared ATCODER_MODINT_HPP:
  const ATCODER_MODINT_HPP* = 1
  import std/macros
  #[ import atcoder/generate_definitions ]#
  when not declared ATCODER_GENERATE_DEFINITIONS_NIM:
    const ATCODER_GENERATE_DEFINITIONS_NIM* = 1
    import std/macros
  
    type hasInv* = concept x
      x.inv()
  
    template generateDefinitions*(name, l, r, typeObj, typeBase, body: untyped): untyped {.dirty.} =
      proc name*(l, r: typeObj): auto {.inline.} =
        type T = l.type
        body
      proc name*(l: typeBase; r: typeObj): auto {.inline.} =
        type T = r.type
        body
      proc name*(l: typeObj; r: typeBase): auto {.inline.} =
        type T = l.type
        body
  
    template generatePow*(name) {.dirty.} =
      proc pow*(m: name; p: SomeInteger): name {.inline.} =
        when name is hasInv:
          if p < 0: return pow(m.inv(), -p)
        else:
          doAssert p >= 0
        if (p.type)(0) <= p:
          var
            p = p.uint
            m = m
          result = m.unit()
          while p > 0'u:
            if (p and 1'u) != 0'u: result *= m
            m *= m
            p = p shr 1'u
      proc `^`*[T:name](m: T; p: SomeInteger): T {.inline.} = m.pow(p)
  
    macro generateConverter*(name, from_type, to_type) =
      let fname = ident("to" & $`name` & "OfGenerateConverter")
      quote do:
        type `name`* = `to_type`
        converter `fname`*(a:`from_type`):`name` {.used.} =
          `name`.init(a)
    discard

  type
    StaticModInt*[M: static[int]] = object
      a:uint32
    DynamicModInt*[T: static[int]] = object
      a:uint32

  type ModInt* = StaticModInt or DynamicModInt
#  type ModInt* = concept x, type T
#    T is StaticModInt or T is DynamicModInt

  proc isStaticModInt*(T:typedesc[ModInt]):bool = T is StaticModInt
  proc isDynamicModInt*(T:typedesc[ModInt]):bool = T is DynamicModInt
  #proc isModInt*(T:typedesc):bool = T.isStaticModInt or T.isDynamicModInt
  proc isStatic*(T:typedesc[ModInt]):bool = T is StaticModInt
  proc getMod*[M:static[int]](t:typedesc[StaticModInt[M]]):int {.inline.} = M


  #[ import atcoder/internal_math ]#
  when not declared ATCODER_INTERNAL_MATH_HPP:
    const ATCODER_INTERNAL_MATH_HPP* = 1
    import std/math
  
    # Fast moduler by barrett reduction
    # Reference: https:#en.wikipedia.org/wiki/Barrett_reduction
    # NOTE: reconsider after Ice Lake
    type Barrett* = object
      m*, im*:uint
  
    # @param m `1 <= m`
    proc initBarrett*(m:uint):auto = Barrett(m:m, im:cast[uint](-1) div m + 1)
  
    # @return m
    proc umod*(self: Barrett):uint =
      self.m
  
    {.emit: """
  #include<cstdio>
  inline unsigned long long calc_mul(const unsigned long long &a, const unsigned long long &b){
    return (unsigned long long)(((unsigned __int128)(a)*b) >> 64);
  }
  """.}
    proc calc_mul*(a,b:culonglong):culonglong {.importcpp: "calc_mul(#,#)", nodecl, inline.}
    # @param a `0 <= a < m`
    # @param b `0 <= b < m`
    # @return `a * b % m`
    proc quo*(self: Barrett, n:int | uint):int =
      let n = n.uint
      let x = calc_mul(n.culonglong, self.im.culonglong).uint
      let r = n - x * self.m
      return int(if self.m <= r: x - 1 else: x)
    proc rem*(self: Barrett, n:int | uint):int =
      let n = n.uint
      let x = calc_mul(n.culonglong, self.im.culonglong).uint
      let r = n - x * self.m
      return int(if self.m <= r: r + self.m else: r)
    proc quorem*(self: Barrett, n:int | uint):(int, int) =
      let n = n.uint
      let x = calc_mul(n.culonglong, self.im.culonglong).uint
      let r = n - x * self.m
      return if self.m <= r: (int(x - 1), int(r + self.m)) else: (int(x), int(r))
  
    proc pow*(self: Barrett, n:uint | int, p:int):int =
      var
        a = self.rem(n)
        r:uint = if self.m == 1: 0 else: 1
        p = p
      while p > 0:
        if (p and 1) != 0: r = self.mul(r, a.uint)
        a = self.mul(a.uint, a.uint).int
        p = p shr 1
      return int(r)
  
    proc mul*(self: Barrett, a:uint, b:uint):uint {.inline.} =
      # [1] m = 1
      # a = b = im = 0, so okay
  
      # [2] m >= 2
      # im = ceil(2^64 / m)
      # -> im * m = 2^64 + r (0 <= r < m)
      # let z = a*b = c*m + d (0 <= c, d < m)
      # a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
      # c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
      # ((ab * im) >> 64) == c or c + 1
      let z = a * b
      #  #ifdef _MSC_VER
      #      unsigned long long x;
      #      _umul128(z, im, &x);
      #  #else
      ##TODO
      #      unsigned long long x =
      #        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
      #  #endif
      #let x = calc_mul(z.culonglong, self.im.culonglong).uint
      #result = z - x * self.m
      #if self.m <= result: result += self.m
      return self.rem(z).uint
  
    # @param n `0 <= n`
    # @param m `1 <= m`
    # @return `(x ** n) % m`
    proc pow_mod_constexpr*(x, n, m:int):int =
      if m == 1: return 0
      var
        r = 1
        y = floorMod(x, m)
        n = n
      while n != 0:
        if (n and 1) != 0: r = (r * y) mod m
        y = (y * y) mod m
        n = n shr 1
      return r.int
    
    # Reference:
    # M. Forisek and J. Jancina,
    # Fast Primality Testing for Integers That Fit into a Machine Word
    # @param n `0 <= n`
    proc is_prime_constexpr*(n:int):bool =
      if n <= 1: return false
      if n == 2 or n == 7 or n == 61: return true
      if n mod 2 == 0: return false
      var d = n - 1
      while d mod 2 == 0: d = d div 2
      for a in [2, 7, 61]:
        var
          t = d
          y = pow_mod_constexpr(a, t, n)
        while t != n - 1 and y != 1 and y != n - 1:
          y = y * y mod n
          t =  t shl 1
        if y != n - 1 and t mod 2 == 0:
          return false
      return true
    proc is_prime*[n:static[int]]():bool = is_prime_constexpr(n)
  #  
  #  # @param b `1 <= b`
  #  # @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
    proc inv_gcd*(a, b:int):(int,int) =
      var a = floorMod(a, b)
      if a == 0: return (b, 0)
    
      # Contracts:
      # [1] s - m0 * a = 0 (mod b)
      # [2] t - m1 * a = 0 (mod b)
      # [3] s * |m1| + t * |m0| <= b
      var
        s = b
        t = a
        m0 = 0
        m1 = 1
    
      while t != 0:
        var u = s div t
        s -= t * u;
        m0 -= m1 * u;  # |m1 * u| <= |m1| * s <= b
    
        # [3]:
        # (s - t * u) * |m1| + t * |m0 - m1 * u|
        # <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        # = s * |m1| + t * |m0| <= b
    
        var tmp = s
        s = t;t = tmp;
        tmp = m0;m0 = m1;m1 = tmp;
      # by [3]: |m0| <= b/g
      # by g != b: |m0| < b/g
      if m0 < 0: m0 += b div s
      return (s, m0)
  
    # Compile time primitive root
    # @param m must be prime
    # @return primitive root (and minimum in now)
    proc primitive_root_constexpr*(m:int):int =
      if m == 2: return 1
      if m == 167772161: return 3
      if m == 469762049: return 3
      if m == 754974721: return 11
      if m == 998244353: return 3
      var divs:array[20, int]
      divs[0] = 2
      var cnt = 1
      var x = (m - 1) div 2
      while x mod 2 == 0: x = x div 2
      var i = 3
      while i * i <= x:
        if x mod i == 0:
          divs[cnt] = i
          cnt.inc
          while x mod i == 0:
            x = x div i
        i += 2
      if x > 1:
        divs[cnt] = x
        cnt.inc
      var g = 2
      while true:
        var ok = true
        for i in 0..<cnt:
          if pow_mod_constexpr(g, (m - 1) div divs[i], m) == 1:
            ok = false
            break
        if ok: return g
        g.inc
    proc primitive_root*[m:static[int]]():auto =
      primitive_root_constexpr(m)
  
    # @param n `n < 2^32`
    # @param m `1 <= m < 2^32`
    # @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
    proc floor_sum_unsigned*(n, m, a, b:uint):uint =
      result = 0
      var (n, m, a, b) = (n, m, a, b)
      while true:
        if a >= m:
          result += n * (n - 1) div 2 * (a div m)
          a = a mod m
        if b >= m:
          result += n * (b div m)
          b = b mod m
  
        let y_max = a * n + b
        if y_max < m: break
        # y_max < m * (n + 1)
        # floor(y_max / m) <= n
        n = y_max div m
        b = y_max mod m
        swap(m, a)
    discard

  proc getBarrett*[T:static[int]](t:typedesc[DynamicModInt[T]]):ptr Barrett =
    {.cast(noSideEffect).}:
      var Barrett_of_DynamicModInt {.global.} = initBarrett(998244353.uint)
      return Barrett_of_DynamicModInt.addr
  
  proc getMod*[T:static[int]](t:typedesc[DynamicModInt[T]]):uint32 {.inline.} =
    (t.getBarrett)[].m.uint32
  proc setMod*[T:static[int]](t:typedesc[DynamicModInt[T]], M:SomeInteger){.inline.} =
    (t.getBarrett)[] = initBarrett(M.uint)

  proc val*(m: ModInt): int {.inline.} = int(m.a)

  proc `$`*(m: StaticModInt or DynamicModInt): string {.inline.} = $(m.val())

  template umod*[T:ModInt](self: typedesc[T] or T):uint32 =
    when T is typedesc:
      when T is StaticModInt:
        T.M.uint32
      elif T is DynamicModInt:
        T.getMod()
      else:
        static: assert false
    else: T.umod

  template `mod`*[T:ModInt](self:typedesc[T] or T):int = T.umod.int

  proc init*[T:ModInt](t:typedesc[T], v: SomeInteger or T): auto {.inline.} =
    when v is T: return v
    else:
      when v is SomeUnsignedInt:
        if v.uint < T.umod:
          return T(a:v.uint32)
        else:
          return T(a:(v.uint mod T.umod.uint).uint32)
      else:
        var v = v.int
        if 0 <= v:
          if v < T.mod: return T(a:v.uint32)
          else: return T(a:(v mod T.mod).uint32)
        else:
          v = v mod T.mod
          if v < 0: v += T.mod
          return T(a:v.uint32)
  proc unit*[T:ModInt](t:typedesc[T] or T):T = T.init(1)

  template initModInt*(v: SomeInteger or ModInt; M: static[int] = 1_000_000_007): auto =
    StaticModInt[M].init(v)

# TODO
#  converter toModInt[M:static[int]](n:SomeInteger):StaticModInt[M] {.inline.} = initModInt(n, M)

#  proc initModIntRaw*(v: SomeInteger; M: static[int] = 1_000_000_007): auto {.inline.} =
#    ModInt[M](v.uint32)
  proc raw*[T:ModInt](t:typedesc[T], v:SomeInteger):auto = T(a:v)

  proc inv*[T:ModInt](v:T):T {.inline.} =
    var
      a = v.a.int
      b = T.mod
      u = 1
      v = 0
    while b > 0:
      let t = a div b
      a -= t * b;swap(a, b)
      u -= t * v;swap(u, v)
    return T.init(u)


  proc `-`*[T:ModInt](m: T): T {.inline.} =
    if int(m.a) == 0: return m
    else: return T(a:m.umod() - m.a)

  proc `+=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =
    m.a += T.init(n).a
    if m.a >= T.umod: m.a -= T.umod
    return m

  proc `-=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =
    m.a -= T.init(n).a
    if m.a >= T.umod: m.a += T.umod
    return m

  proc `*=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =
    when T is StaticModInt:
      m.a = (m.a.uint * T.init(n).a.uint mod T.umod).uint32
    elif T is DynamicModInt:
      m.a = T.getBarrett[].mul(m.a.uint, T.init(n).a.uint).uint32
    else:
      static: assert false
    return m

  proc `/=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =
    m.a = (m.a.uint * T.init(n).inv().a.uint mod T.umod).uint32
    return m

  generateDefinitions(`+`, m, n, ModInt, SomeInteger):
    result = T.init(m)
    result += n

  generateDefinitions(`-`, m, n, ModInt, SomeInteger):
    result = T.init(m)
    result -= n

  generateDefinitions(`*`, m, n, ModInt, SomeInteger):
    result = T.init(m)
    result *= n

  generateDefinitions(`/`, m, n, ModInt, SomeInteger):
    result = T.init(m)
    result /= n

  generateDefinitions(`==`, m, n, ModInt, SomeInteger):
    result = (T.init(m).val() == T.init(n).val())

  proc inc*(m: var ModInt):ModInt {.inline discardable.} =
    m.a.inc
    if m.a == m.umod.uint32:
      m.a = 0
    return m
  proc `++`*(m: var ModInt):ModInt {.inline discardable.} = m.inc

  proc dec*(m: var ModInt):ModInt {.inline discardable.} =
    if m.a == 0.uint32:
      m.a = m.umod - 1
    else:
      m.a.dec
    return m
  proc `--`*(m: var ModInt):ModInt {.inline discardable.} = m.dec

  generatePow(ModInt)
  
  # TODO: intのところはSomeIntegerに拡張したいがそうするとSystem.nimのuintのconverterとバッティングする。。。
  template useStaticModint*(name, M) =
    generateConverter(name, int, StaticModInt[M])
  template useDynamicModInt*(name, M) =
    generateConverter(name, int, DynamicModInt[M])

  # TODO: Nimのstatic[int]を使うconverterがバグっていて個々に宣言しないとconverterが使えない
  # したがって、下記以外のmodintを使う場合はuseStaticModIntあるいはuseDynamicModIntで宣言が必要
  useStaticModInt(modint998244353, 998244353)
  useStaticModInt(modint1000000007, 1000000007)
  useDynamicModInt(modint, -1)

  import std/math as math_lib_modint
  proc estimateRational*(a:ModInt, ub:int = int(sqrt(float(ModInt.mod))), output_stderr:static[bool] = false):string =
    var v:seq[tuple[s, n, d: int]]
    for d in 1 .. ub:
      var n = (a * d).val
      # n or mod - n
      if n * 2 > a.mod:
        n = - (a.mod - n)
      if gcd(n, d) > 1: continue
      v.add((n.abs + d, n, d))
    v.sort
    when output_stderr:
      stderr.write "estimation result: ", v
    return $v[0].n & "/" & $v[0].d

  # TODO:
  # Modint -> intのconverterあるとmint(2) * 3みたいなのがintになっちゃう
  # converter toInt*(m: ModInt):int {.inline.} = m.val


  discard
type mint=modint998244353
var fact,rev:array[500000,mint]
fact[0]=1
rev[0]=1
for i in 1..<500000:
    fact[i]=fact[i-1]*i
    rev[i]=fact[i].inv()
var N,K:int
discard input().scanf("$i $i",N,K)
if K==0:
    print 1
    quit()
if K==1:
    if N%2==0:print 2
    else:print N-2
    quit()
var ans:mint=0
for i in 0..N-K:
    if i%2==1:
        continue
    let use=N-i
    ans+=(i+1)*fact[use-2]*rev[K-2]*rev[use-K]
print ans
yukicoder

結果

ソースコード
