結果

問題 No.1321 塗るめた
ユーザー cotton_fn_
提出日時 2020-12-18 03:39:16
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 11 ms / 2,000 ms
コード長 13,560 bytes
コンパイル時間 14,460 ms
コンパイル使用メモリ 400,056 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-09-21 08:50:50
合計ジャッジ時間 15,250 ms
ジャッジサーバーID
(参考情報)
judge1 / judge4
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 * 2
other AC * 45
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

#![allow(unused_imports, unused_macros)]
use kyoproio::*;
use std::{
collections::*,
io::{self, prelude::*},
iter,
mem::{replace, swap},
};
fn run<I: Input, O: Write>(mut kin: I, mut out: O) {
let (n, m, k): (usize, usize, usize) = kin.input();
let f = Fact::new(n);
let mut ans = mint(0);
let mut sign = mint(1);
let m_inv = mint(m as u32).inv();
for i in (1..=k).rev() {
let x = m_inv * mint(i as u32);
ans += sign * f.binom(k, i) * (mint(1) + x).pow(n);
sign = -sign;
}
ans += (-mint(1)).pow(k);
ans *= f.binom(m, k) * mint(m as u32).pow(n);
outln!(out, "{}", ans);
}
pub struct Fact<M> {
f: Vec<ModInt<M>>,
finv: Vec<ModInt<M>>,
}
impl<M: Modulo> Fact<M> {
pub fn new(n: usize) -> Self {
let mut f = vec![ModInt::new(0); n + 1];
f[0] = ModInt::new(1);
f[1] = ModInt::new(1);
for i in 2..=n {
f[i] = ModInt::new(i as u32) * f[i - 1];
}
let mut finv = vec![ModInt::new(0); n + 1];
finv[n] = f[n].inv();
for i in (0..n).rev() {
finv[i] = finv[i + 1] * ModInt::new(i as u32 + 1);
}
Self { f, finv }
}
pub fn fact(&self, x: usize) -> ModInt<M> {
self.f[x]
}
pub fn fact_inv(&self, x: usize) -> ModInt<M> {
self.finv[x]
}
pub fn binom(&self, n: usize, k: usize) -> ModInt<M> {
if n >= k {
self.fact(n) * self.fact_inv(n - k) * self.fact_inv(k)
} else {
ModInt::new(0)
}
}
pub fn perm(&self, n: usize, k: usize) -> ModInt<M> {
if n >= k {
self.fact(n) * self.fact_inv(n - k)
} else {
ModInt::new(0)
}
}
}
use std::{cmp, fmt, marker::PhantomData, ops};
pub type Mint = ModInt<Mod998244353>;
pub fn mint(x: u32) -> Mint {
ModInt::new(x)
}
pub trait Modulo {
fn modulo() -> u32;
}
macro_rules! modulo_impl {
($($Type:ident $val:tt)*) => {
$(pub struct $Type;
impl Modulo for $Type {
fn modulo() -> u32 {
$val
}
})*
};
}
modulo_impl!(Mod998244353 998244353 Mod1e9p7 1000000007);
use std::sync::atomic;
pub struct VarMod;
static VAR_MOD: atomic::AtomicU32 = atomic::AtomicU32::new(0);
pub fn set_var_mod(m: u32) {
VAR_MOD.store(m, atomic::Ordering::Relaxed);
}
impl Modulo for VarMod {
fn modulo() -> u32 {
VAR_MOD.load(atomic::Ordering::Relaxed)
}
}
pub struct ModInt<M>(u32, PhantomData<M>);
impl<M: Modulo> ModInt<M> {
pub fn new(x: u32) -> Self {
debug_assert!(x < M::modulo());
Self(x, PhantomData)
}
pub fn normalize(self) -> Self {
if self.0 < M::modulo() {
self
} else {
Self::new(self.0 % M::modulo())
}
}
pub fn get(self) -> u32 {
self.0
}
pub fn inv(self) -> Self {
self.pow(M::modulo() - 2)
}
pub fn half(self) -> Self {
Self::new(self.0 / 2 + self.0 % 2 * ((M::modulo() + 1) / 2))
}
pub fn modulo() -> u32 {
M::modulo()
}
}
impl<M: Modulo> ops::Neg for ModInt<M> {
type Output = Self;
fn neg(self) -> Self {
Self::new(if self.0 == 0 { 0 } else { M::modulo() - self.0 })
}
}
impl<M: Modulo> ops::Add for ModInt<M> {
type Output = Self;
fn add(self, rhs: Self) -> Self {
let s = self.0 + rhs.0;
Self::new(if s < M::modulo() { s } else { s - M::modulo() })
}
}
impl<M: Modulo> ops::Sub for ModInt<M> {
type Output = Self;
fn sub(self, rhs: Self) -> Self {
Self::new(if self.0 >= rhs.0 {
self.0 - rhs.0
} else {
M::modulo() + self.0 - rhs.0
})
}
}
impl<M: Modulo> ops::Mul for ModInt<M> {
type Output = Self;
fn mul(self, rhs: Self) -> Self {
Self::new((self.0 as u64 * rhs.0 as u64 % M::modulo() as u64) as u32)
}
}
impl<M: Modulo> ops::Div for ModInt<M> {
type Output = Self;
fn div(self, rhs: Self) -> Self {
assert_ne!(rhs.get(), 0);
self * rhs.inv()
}
}
macro_rules! op_impl {
($($Op:ident $op:ident $OpAssign:ident $op_assign:ident)*) => {
$(impl<M: Modulo> ops::$Op<&Self> for ModInt<M> {
type Output = Self;
fn $op(self, rhs: &Self) -> Self {
self.$op(*rhs)
}
}
impl<M: Modulo> ops::$Op<ModInt<M>> for &ModInt<M> {
type Output = ModInt<M>;
fn $op(self, rhs: ModInt<M>) -> ModInt<M> {
(*self).$op(rhs)
}
}
impl<M: Modulo> ops::$Op<&ModInt<M>> for &ModInt<M> {
type Output = ModInt<M>;
fn $op(self, rhs: &ModInt<M>) -> ModInt<M> {
(*self).$op(*rhs)
}
}
impl<M: Modulo> ops::$OpAssign for ModInt<M> {
fn $op_assign(&mut self, rhs: Self) {
*self = ops::$Op::$op(*self, rhs);
}
}
impl<M: Modulo> ops::$OpAssign<&ModInt<M>> for ModInt<M> {
fn $op_assign(&mut self, rhs: &ModInt<M>) {
self.$op_assign(*rhs);
}
})*
};
}
op_impl! {
Add add AddAssign add_assign
Sub sub SubAssign sub_assign
Mul mul MulAssign mul_assign
Div div DivAssign div_assign
}
impl<M: Modulo> std::iter::Sum for ModInt<M> {
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(ModInt::new(0), |x, y| x + y)
}
}
impl<M: Modulo> std::iter::Product for ModInt<M> {
fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(ModInt::new(1), |x, y| x * y)
}
}
pub trait Pow<T> {
fn pow(self, n: T) -> Self;
}
impl<M: Modulo> Pow<u32> for ModInt<M> {
fn pow(mut self, mut n: u32) -> Self {
let mut y = Self::new(1);
while n > 0 {
if n % 2 == 1 {
y *= self;
}
self *= self;
n /= 2;
}
y
}
}
macro_rules! mod_int_pow_impl {
($($T:ident)*) => {
$(impl<M: Modulo> Pow<$T> for ModInt<M> {
fn pow(self, n: $T) -> Self {
self.pow(n.rem_euclid(M::modulo() as $T - 1) as u32)
}
})*
};
}
mod_int_pow_impl!(isize i32 i64 usize u64);
macro_rules! mod_int_from_impl {
($($T:ident)*) => {
$(impl<M: Modulo> From<$T> for ModInt<M> {
#[allow(unused_comparisons)]
fn from(x: $T) -> Self {
if M::modulo() <= $T::max_value() as u32 {
Self::new(x.rem_euclid(M::modulo() as $T) as u32)
} else if x < 0 {
Self::new((M::modulo() as i32 + x as i32) as u32)
} else {
Self::new(x as u32)
}
}
})*
}
}
mod_int_from_impl!(isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128);
impl<M> Copy for ModInt<M> {}
impl<M> Clone for ModInt<M> {
fn clone(&self) -> Self {
*self
}
}
impl<M: Modulo> Default for ModInt<M> {
fn default() -> Self {
Self::new(0)
}
}
impl<M> cmp::PartialEq for ModInt<M> {
fn eq(&self, other: &Self) -> bool {
self.0 == other.0
}
}
impl<M> cmp::Eq for ModInt<M> {}
impl<M> cmp::PartialOrd for ModInt<M> {
fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering> {
self.0.partial_cmp(&other.0)
}
}
impl<M> cmp::Ord for ModInt<M> {
fn cmp(&self, other: &Self) -> cmp::Ordering {
self.0.cmp(&other.0)
}
}
impl<M> std::hash::Hash for ModInt<M> {
fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
self.0.hash(state);
}
}
impl<M> fmt::Display for ModInt<M> {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
self.0.fmt(f)
}
}
impl<M> fmt::Debug for ModInt<M> {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
f.pad("ModInt(")?;
self.0.fmt(f)?;
f.pad(")")
}
}
// -----------------------------------------------------------------------------
fn main() -> io::Result<()> {
std::thread::Builder::new()
.stack_size(64 * 1024 * 1024)
.spawn(|| {
run(
KInput::new(io::stdin().lock()),
io::BufWriter::new(io::stdout().lock()),
)
})?
.join()
.unwrap();
Ok(())
}
#[macro_export]
macro_rules! out {
($($arg:tt)*) => { write!($($arg)*).unwrap(); }
}
#[macro_export]
macro_rules! outln {
($dst:expr $(, $($arg:tt)*)?) => {{
writeln!($dst $(, $($arg)*)?).unwrap();
if cfg!(debug_assertions) { $dst.flush().unwrap(); }
}}
}
#[macro_export]
macro_rules! eout {
($($arg:tt)*) => { if cfg!(debug_assertions) { eprintln!($($arg)*); } }
}
#[macro_export]
macro_rules! kdbg {
($($v:expr),*) => { if cfg!(debug_assertions) { dbg!($($v),*) } else { ($($v),*) } }
}
pub mod kyoproio {
use std::{
io::prelude::*,
iter::FromIterator,
marker::PhantomData,
mem::{self, MaybeUninit},
str,
};
pub trait Input {
fn bytes(&mut self) -> &[u8];
fn str(&mut self) -> &str {
str::from_utf8(self.bytes()).unwrap()
}
fn input<T: InputItem>(&mut self) -> T {
T::input(self)
}
fn iter<T: InputItem>(&mut self) -> Iter<T, Self> {
Iter(self, PhantomData)
}
fn seq<T: InputItem, B: FromIterator<T>>(&mut self, n: usize) -> B {
self.iter().take(n).collect()
}
}
pub struct KInput<R> {
src: R,
buf: Vec<u8>,
pos: usize,
len: usize,
}
impl<R: Read> KInput<R> {
pub fn new(src: R) -> Self {
Self {
src,
buf: vec![0; 1 << 16],
pos: 0,
len: 0,
}
}
fn read(&mut self) -> usize {
if self.pos > 0 {
self.buf.copy_within(self.pos..self.len, 0);
self.len -= self.pos;
self.pos = 0;
} else if self.len >= self.buf.len() {
self.buf.resize(2 * self.buf.len(), 0);
}
let n = self.src.read(&mut self.buf[self.len..]).unwrap();
self.len += n;
n
}
}
impl<R: Read> Input for KInput<R> {
fn bytes(&mut self) -> &[u8] {
loop {
while let Some(d) = self.buf[self.pos..self.len]
.iter()
.position(u8::is_ascii_whitespace)
{
let p = self.pos;
self.pos += d + 1;
if d > 0 {
return &self.buf[p..p + d];
}
}
if self.read() == 0 {
return &self.buf[mem::replace(&mut self.pos, self.len)..self.len];
}
}
}
}
pub struct Iter<'a, T, I: ?Sized>(&'a mut I, PhantomData<*const T>);
impl<'a, T: InputItem, I: Input + ?Sized> Iterator for Iter<'a, T, I> {
type Item = T;
fn next(&mut self) -> Option<T> {
Some(self.0.input())
}
fn size_hint(&self) -> (usize, Option<usize>) {
(!0, None)
}
}
pub trait InputItem: Sized {
fn input<I: Input + ?Sized>(src: &mut I) -> Self;
}
impl InputItem for Vec<u8> {
fn input<I: Input + ?Sized>(src: &mut I) -> Self {
src.bytes().to_owned()
}
}
macro_rules! from_str {
($($T:ty)*) => {
$(impl InputItem for $T {
fn input<I: Input + ?Sized>(src: &mut I) -> Self {
src.str().parse::<$T>().unwrap()
}
})*
}
}
from_str!(String char bool f32 f64);
macro_rules! parse_int {
($($I:ty: $U:ty)*) => {
$(impl InputItem for $I {
fn input<I: Input + ?Sized>(src: &mut I) -> Self {
let f = |s: &[u8]| s.iter().fold(0, |x, b| 10 * x + (b & 0xf) as $I);
let s = src.bytes();
if let Some((&b'-', t)) = s.split_first() { -f(t) } else { f(s) }
}
}
impl InputItem for $U {
fn input<I: Input + ?Sized>(src: &mut I) -> Self {
src.bytes().iter().fold(0, |x, b| 10 * x + (b & 0xf) as $U)
}
})*
}
}
parse_int!(isize:usize i8:u8 i16:u16 i32:u32 i64:u64 i128:u128);
macro_rules! tuple {
($H:ident $($T:ident)*) => {
impl<$H: InputItem, $($T: InputItem),*> InputItem for ($H, $($T),*) {
fn input<I: Input + ?Sized>(src: &mut I) -> Self {
($H::input(src), $($T::input(src)),*)
}
}
tuple!($($T)*);
};
() => {}
}
tuple!(A B C D E F G);
macro_rules! array {
($($N:literal)*) => {
$(impl<T: InputItem> InputItem for [T; $N] {
fn input<I: Input + ?Sized>(src: &mut I) -> Self {
let mut arr = MaybeUninit::uninit();
let ptr = arr.as_mut_ptr() as *mut T;
unsafe {
for i in 0..$N {
ptr.add(i).write(src.input());
}
arr.assume_init()
}
}
})*
}
}
array!(1 2 3 4 5 6 7 8);
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0