結果
| 問題 | No.1832 NAND Reversible |
| ユーザー |
 hirayuu_yc
|
| 提出日時 | 2024-11-15 16:11:05 |
| 言語 | Nim (2.0.2) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 19,314 bytes |
| コンパイル時間 | 5,983 ms |
| コンパイル使用メモリ | 94,684 KB |
| 実行使用メモリ | 813,500 KB |
| 最終ジャッジ日時 | 2024-11-15 16:11:40 |
| 合計ジャッジ時間 | 34,391 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 1 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | TLE | - |
| testcase_04 | AC | 36 ms
6,816 KB |
| testcase_05 | AC | 2 ms
6,820 KB |
| testcase_06 | WA | - |
| testcase_07 | TLE | - |
| testcase_08 | TLE | - |
| testcase_09 | AC | 13 ms
6,688 KB |
| testcase_10 | WA | - |
| testcase_11 | AC | 2 ms
6,692 KB |
| testcase_12 | AC | 1 ms
6,692 KB |
| testcase_13 | WA | - |
| testcase_14 | WA | - |
| testcase_15 | TLE | - |
| testcase_16 | TLE | - |
| testcase_17 | TLE | - |
| testcase_18 | TLE | - |
| testcase_19 | TLE | - |
| testcase_20 | AC | 23 ms
6,692 KB |
| testcase_21 | TLE | - |
| testcase_22 | TLE | - |
| testcase_23 | AC | 9 ms
6,688 KB |
| testcase_24 | WA | - |
| testcase_25 | MLE | - |
ソースコード
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
#[ import atcoder/extra/math/combination ]#
when not defined ATCODER_COMBINATION_HPP:
const ATCODER_COMBINATION_HPP* = 1
#[ import atcoder/element_concepts ]#
when not declared ATCODER_ELEMENT_CONCEPTS_HPP:
const ATCODER_ELEMENT_CONCEPTS_HPP* = 1
proc inv*[T:SomeFloat](a:T):auto = T(1) / a
proc init*(self:typedesc[SomeFloat], a:SomeNumber):auto = self(a)
type AdditiveGroupElem* = concept x, y, type T
x + y
x - y
-x
T(0)
type MultiplicativeGroupElem* = concept x, y, type T
x * y
x / y
# x.inv()
T(1)
type RingElem* = concept x, y, type T
x + y
x - y
-x
x * y
T(0)
T(1)
type FieldElem* = concept x, y, type T
x + y
x - y
x * y
x / y
-x
# x.inv()
T(0)
T(1)
type FiniteFieldElem* = concept x, type T
T is FieldElem
T.mod
T.mod() is int
x.pow(1000000)
type hasInf* = concept x, type T
T(Inf)
discard
type Combination*[T] = object
fact_a, rfact_a: seq[T]
type CombinationC* = concept x
x is typedesc[FieldElem] or x is var Combination
proc enhance[T:FieldElem](cmb: var Combination[T], k:int):auto =
if k >= cmb.fact_a.len:
if cmb.fact_a.len == 0:
cmb.fact_a = @[T(1)]
cmb.rfact_a = @[T(1)]
let sz_old = cmb.fact_a.len - 1
let sz = min(max(sz_old * 2, k), T.mod - 1)
cmb.fact_a.setlen(sz + 1)
cmb.rfact_a.setlen(sz + 1)
for i in sz_old + 1..sz: cmb.fact_a[i] = cmb.fact_a[i-1] * T(i)
cmb.rfact_a[sz] = T(1) / cmb.fact_a[sz]
for i in countdown(sz - 1, sz_old + 1): cmb.rfact_a[i] = cmb.rfact_a[i + 1] * T(i + 1)
return cmb.addr
proc enhance(T:typedesc[FieldElem], k:int):auto {.discardable.} =
var cmb{.global.} = Combination[T]()
return cmb.enhance(k)
template zero*(T:typedesc[FieldElem]):T = T(0)
template zero*[T:FieldElem](cmb:Combination[T]):T = T(0)
template fact*(T:CombinationC, k:int):auto = T.enhance(k)[].fact_a[k]
template rfact*(T:CombinationC, k:int):auto = T.enhance(k)[].rfact_a[k]
template invfact*(T:CombinationC, k:int):auto = T.enhance(k)[].rfact_a[k]
template inv*(T:CombinationC, k:int):auto = T.fact(k - 1) * T.rfact(k)
template resetCombination*(T:typedesc[FieldElem] or var Combination) =
var p = T.enhance(-1)
p[].fact_a.setLen(0)
p[].rfact_a.setLen(0)
template P*(T:CombinationC, n,r:int):auto =
if r < 0 or n < r: T.zero()
else: T.fact(n) * T.rfact(n - r)
template C_impl*(T:CombinationC, n, r:int):auto =
if r < 0 or n < r: T.zero()
else: T.fact(n) * T.rfact(r) * T.rfact(n - r)
template C*(T:CombinationC, n,r:int):auto =
if n >= 0:
T.C_impl(n, r)
else:
let N = -n
var a = T.C_impl(N + r - 1, N - 1)
if r mod 2 != 0: a *= -1
a
template H*(T:CombinationC, n,r:int):auto =
if n < 0 or r < 0: T.zero()
elif r == 0: T.zero() + 1
else: T.C(n + r - 1, r)
template P_large*(T:CombinationC, n,r:int):auto =
if r < 0 or n < r: T.zero()
else:
var a = T(1)
for i in 0..<r:a *= n - i
a
template C_large_impl*(T:CombinationC, n,r:int):auto =
if r < 0 or n < r: T.zero()
else: T.P_large(n, r) * T.rfact(r)
template C_large*(T:CombinationC, n,r:int):auto =
if n >= 0:
T.C_large_impl(n, r)
else:
let N = -n
var a = T.C_large_impl(N + r - 1, N - 1)
if r mod 2 != 0: a *= -1
a
template H_large*(T:CombinationC, n,r:int):auto =
if n < 0 or r < 0: T.zero()
elif r == 0: T.zero() + 1
else: T.C_large(n + r - 1, r)
discard
type mint=modint998244353
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)*mint.C(use-2,K-2)
print ans