結果
| 問題 | No.2351 Butterfly in Summer |
| ユーザー |
 atcoder8
|
| 提出日時 | 2023-06-16 21:35:11 |
| 言語 | Rust (1.77.0) |
| 結果 |
AC
|
| 実行時間 | 1 ms / 2,000 ms |
| コード長 | 16,172 bytes |
| コンパイル時間 | 2,755 ms |
| コンパイル使用メモリ | 147,192 KB |
| 実行使用メモリ | 4,384 KB |
| 最終ジャッジ日時 | 2023-09-06 18:52:46 |
| 合計ジャッジ時間 | 3,957 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge12 |
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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 | 1 ms
4,380 KB |
| testcase_01 | AC | 1 ms
4,380 KB |
| testcase_02 | AC | 1 ms
4,384 KB |
| testcase_03 | AC | 1 ms
4,380 KB |
| testcase_04 | AC | 1 ms
4,380 KB |
| testcase_05 | AC | 1 ms
4,384 KB |
| testcase_06 | AC | 1 ms
4,384 KB |
| testcase_07 | AC | 1 ms
4,384 KB |
| testcase_08 | AC | 1 ms
4,384 KB |
| testcase_09 | AC | 1 ms
4,384 KB |
| testcase_10 | AC | 1 ms
4,380 KB |
| testcase_11 | AC | 1 ms
4,384 KB |
| testcase_12 | AC | 1 ms
4,384 KB |
| testcase_13 | AC | 1 ms
4,380 KB |
| testcase_14 | AC | 1 ms
4,380 KB |
| testcase_15 | AC | 1 ms
4,384 KB |
| testcase_16 | AC | 1 ms
4,384 KB |
| testcase_17 | AC | 1 ms
4,380 KB |
| testcase_18 | AC | 1 ms
4,380 KB |
| testcase_19 | AC | 1 ms
4,380 KB |
| testcase_20 | AC | 1 ms
4,380 KB |
| testcase_21 | AC | 1 ms
4,384 KB |
| testcase_22 | AC | 1 ms
4,384 KB |
| testcase_23 | AC | 1 ms
4,384 KB |
ソースコード
use modint::Modint998244353;
use crate::modint::Pow;
type Mint = Modint998244353;
fn main() {
let (n, k) = {
let mut line = String::new();
std::io::stdin().read_line(&mut line).unwrap();
let mut iter = line.split_whitespace();
(
iter.next().unwrap().parse::<usize>().unwrap(),
iter.next().unwrap().parse::<usize>().unwrap(),
)
};
let ans = Mint::new(n) * Mint::new(k - 1) / Mint::new(k).pow(n - 1);
println!("{}", ans);
}
pub mod modint {
use std::ops::{
Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, ShrAssign, Sub, SubAssign,
};
pub trait RemEuclidU32 {
fn rem_euclid_u32(self, modulus: u32) -> u32;
}
/// Calculate the modular multiplicative inverse of `a` with `m` as modulus.
pub fn modinv(a: u32, m: u32) -> u32 {
assert!(m >= 2);
let (mut a, mut b, mut s, mut t) = (a as i64, m as i64, 1, 0);
while b != 0 {
let q = a / b;
a -= q * b;
std::mem::swap(&mut a, &mut b);
s -= q * t;
std::mem::swap(&mut s, &mut t);
}
assert_eq!(
a.abs(),
1,
"Because `a` and `m` are not prime to each other, \
there is no multiplicative inverse of `a` with `m` as the modulus.
gcd(a, m) = {}",
a.abs()
);
s %= m as i64;
if s < 0 {
s += m as i64;
}
s as u32
}
/// This macro implements rem_euclid_u32 for signed integer types of 32 bits or less.
macro_rules! impl_rem_euclid_u32_for_small_signed {
($($small_signed_type:tt),*) => {
$(
impl RemEuclidU32 for $small_signed_type {
fn rem_euclid_u32(self, modulus: u32) -> u32 {
let ret = (self as i32) % (modulus as i32);
if ret >= 0 {
ret as u32
} else {
(ret + modulus as i32) as u32
}
}
}
)*
};
}
/// This macro implements rem_euclid_u32 for 64-bit signed integer types (including isize).
macro_rules! impl_rem_euclid_u32_for_large_signed {
($($large_signed_type:tt),*) => {
$(
impl RemEuclidU32 for $large_signed_type {
fn rem_euclid_u32(self, modulus: u32) -> u32 {
let ret = (self as i64) % (modulus as i64);
if ret >= 0 {
ret as u32
} else {
(ret + modulus as i64) as u32
}
}
}
)*
};
}
/// This macro implements rem_euclid_u32 for unsigned integer types greater than 32 bits.
macro_rules! impl_rem_euclid_u32_for_small_unsigned {
($($small_unsigned_type:tt),*) => {
$(
impl RemEuclidU32 for $small_unsigned_type {
fn rem_euclid_u32(self, modulus: u32) -> u32 {
self as u32 % modulus
}
}
)*
};
}
/// This macro implements rem_euclid_u32 for 64-bit and larger unsigned integer types (including usize).
macro_rules! impl_rem_euclid_u32_for_large_unsigned {
($($large_unsigned_type:tt),*) => {
$(
impl RemEuclidU32 for $large_unsigned_type {
fn rem_euclid_u32(self, modulus: u32) -> u32 {
(self % modulus as $large_unsigned_type) as u32
}
}
)*
};
}
// Implement rem_euclid_u32 for signed integer types of 32 bits or less.
impl_rem_euclid_u32_for_small_signed!(i8, i16, i32);
// Implement rem_euclid_u32 for 64-bit signed integer types (including isize).
impl_rem_euclid_u32_for_large_signed!(i64, isize);
// Implement rem_euclid_u32 for unsigned integer types of 32 bits or more.
impl_rem_euclid_u32_for_small_unsigned!(u8, u16, u32);
// Implement rem_euclid_u32 for unsigned integer types (including usize) of 64 bits or more.
impl_rem_euclid_u32_for_large_unsigned!(u64, u128, usize);
// Implement rem_euclid_u32 for i128.
impl RemEuclidU32 for i128 {
fn rem_euclid_u32(self, modulus: u32) -> u32 {
let ret = self % (modulus as i128);
if ret >= 0 {
ret as u32
} else {
(ret + modulus as i128) as u32
}
}
}
pub trait Pow<T: Copy + ShrAssign> {
/// Calculate the power of `n` using the iterative squaring method.
fn pow(self, n: T) -> Self;
}
/// Macro to overload binary operation with `$modint_type` for each integer type
macro_rules! impl_ops {
($modint_type:tt, $($other_type:tt),*) => {
$(
impl Add<$other_type> for $modint_type {
type Output = Self;
fn add(self, rhs: $other_type) -> Self::Output {
self + Self::new(rhs)
}
}
impl Add<$modint_type> for $other_type {
type Output = $modint_type;
fn add(self, rhs: $modint_type) -> Self::Output {
$modint_type::new(self) + rhs
}
}
impl Sub<$other_type> for $modint_type {
type Output = Self;
fn sub(self, rhs: $other_type) -> Self::Output {
self - Self::new(rhs)
}
}
impl Sub<$modint_type> for $other_type {
type Output = $modint_type;
fn sub(self, rhs: $modint_type) -> Self::Output {
$modint_type::new(self) - rhs
}
}
impl Mul<$other_type> for $modint_type {
type Output = Self;
fn mul(self, rhs: $other_type) -> Self::Output {
self * Self::new(rhs)
}
}
impl Mul<$modint_type> for $other_type {
type Output = $modint_type;
fn mul(self, rhs: $modint_type) -> Self::Output {
$modint_type::new(self) * rhs
}
}
impl Div<$other_type> for $modint_type {
type Output = Self;
fn div(self, rhs: $other_type) -> Self::Output {
self / Self::new(rhs)
}
}
impl Div<$modint_type> for $other_type {
type Output = $modint_type;
fn div(self, rhs: $modint_type) -> Self::Output {
$modint_type::new(self) / rhs
}
}
impl AddAssign<$other_type> for $modint_type {
fn add_assign(&mut self, other: $other_type) {
*self = *self + Self::new(other);
}
}
impl SubAssign<$other_type> for $modint_type {
fn sub_assign(&mut self, other: $other_type) {
*self = *self - Self::new(other);
}
}
impl MulAssign<$other_type> for $modint_type {
fn mul_assign(&mut self, other: $other_type) {
*self = *self * Self::new(other);
}
}
impl DivAssign<$other_type> for $modint_type {
fn div_assign(&mut self, other: $other_type) {
*self = *self / Self::new(other);
}
}
)*
};
}
/// This macro defines powers of Modint for unsigned integer types.
macro_rules! impl_power_for_unsigned {
($modint_type:tt, $($unsigned_type:tt),*) => {
$(
impl Pow<$unsigned_type> for $modint_type {
fn pow(self, mut n: $unsigned_type) -> Self {
let mut ret = Self::new(1);
let mut mul = self;
while n != 0 {
if n & 1 == 1 {
ret *= mul;
}
mul *= mul;
n >>= 1;
}
ret
}
}
)*
};
}
/// This macro defines powers of Modint for signed integer types of 32 bits or less.
macro_rules! impl_power_for_small_signed {
($modint_type:tt, $($small_signed_type:tt),*) => {
$(
impl Pow<$small_signed_type> for $modint_type {
fn pow(self, n: $small_signed_type) -> Self {
if n >= 0 {
self.pow(n as u32)
} else {
self.pow(-n as u32).inv()
}
}
}
)*
};
}
/// This macro defines the power of Modint for 64-bit signed integer types (including isize).
macro_rules! impl_power_for_large_signed {
($modint_type:tt, $($large_signed_type:tt),*) => {
$(
impl Pow<$large_signed_type> for $modint_type {
fn pow(self, n: $large_signed_type) -> Self {
if n >= 0 {
self.pow(n as u64)
} else {
self.pow(-n as u64).inv()
}
}
}
)*
};
}
/// This macro generates Modint by specifying the type name and modulus.
macro_rules! generate_modint {
($modint_type:tt, $modulus:literal) => {
#[derive(Debug, Default, Hash, Clone, Copy, PartialEq, Eq)]
pub struct $modint_type {
val: u32,
}
impl $modint_type {
const MOD: u32 = $modulus;
}
impl $modint_type {
/// Create a `Modint` instance that is equivalent to `val`.
pub fn new<T: RemEuclidU32>(val: T) -> Self {
Self {
val: val.rem_euclid_u32($modulus),
}
}
/// Create `x` such that `x * denom` is equivalent to `numer`.
pub fn frac<T: RemEuclidU32>(numer: T, denom: T) -> Self {
Self::new(numer) / Self::new(denom)
}
/// Create a `Modint` instance from a value of type `u32`
/// without any internal modulo operation.
/// The `val` must be less than the modulus.
pub fn raw(val: u32) -> Self {
Self { val }
}
/// Return the remainder as a value of type `u32`.
/// The value is a non-negative integer less than the modulus.
pub fn val(&self) -> u32 {
self.val
}
/// Return the multiplicative inverse.
pub fn inv(&self) -> Self {
Self::new(modinv(self.val, $modulus))
}
/// Return a modint instance that is equivalent to 0.
pub fn zero() -> Self {
Self::new(0)
}
/// Return `true` only if it is equivalent to 0.
pub fn equiv_zero(&self) -> bool {
self.val == 0
}
/// Return `Modint` instance that is equivalent to 1.
pub fn one() -> Self {
Self::new(1)
}
/// Return `Modint` instance that is equivalent to 2.
pub fn two() -> Self {
Self::new(2)
}
}
impl<T: RemEuclidU32> From<T> for $modint_type {
/// Create a `Modint` instance that is equivalent to `val`.
fn from(val: T) -> Self {
Self::new(val)
}
}
impl std::fmt::Display for $modint_type {
fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
write!(f, "{}", self.val)
}
}
impl Add for $modint_type {
type Output = Self;
fn add(self, rhs: Self) -> Self::Output {
Self::new(self.val + rhs.val)
}
}
impl Sub for $modint_type {
type Output = Self;
fn sub(self, rhs: Self) -> Self::Output {
Self::new(self.val + $modulus - rhs.val)
}
}
impl Mul for $modint_type {
type Output = Self;
fn mul(self, rhs: Self) -> Self::Output {
Self::new(self.val as u64 * rhs.val as u64)
}
}
impl Div for $modint_type {
type Output = Self;
#[allow(clippy::suspicious_arithmetic_impl)]
fn div(self, rhs: Self) -> Self::Output {
self * rhs.inv()
}
}
impl AddAssign for $modint_type {
fn add_assign(&mut self, other: Self) {
*self = *self + other;
}
}
impl SubAssign for $modint_type {
fn sub_assign(&mut self, other: Self) {
*self = *self - other;
}
}
impl MulAssign for $modint_type {
fn mul_assign(&mut self, other: Self) {
*self = *self * other;
}
}
impl DivAssign for $modint_type {
fn div_assign(&mut self, other: Self) {
*self = *self / other;
}
}
impl Neg for $modint_type {
type Output = Self;
fn neg(self) -> Self::Output {
Self::new(Self::MOD - self.val)
}
}
// Define a binary operation between each integer type and $modint_type.
impl_ops!(
$modint_type,
i8,
i16,
i32,
i64,
i128,
isize,
u8,
u16,
u32,
u64,
u128,
usize
);
// Define powers of Modint for unsigned integer types.
impl_power_for_unsigned!($modint_type, u8, u16, u32, u64, u128, usize);
// Define powers of Modint for signed integer types of 32 bits or less.
impl_power_for_small_signed!($modint_type, i8, i16, i32);
// Define Modint powers for 64-bit signed integer types (including isize).
impl_power_for_large_signed!($modint_type, i64, isize);
// Define the power of Modint for 128-bit signed integer types.
impl Pow<i128> for $modint_type {
fn pow(self, n: i128) -> Self {
if n >= 0 {
self.pow(n as u128)
} else {
self.pow(-n as u128).inv()
}
}
}
};
}
// Define Modint with 998244353 as modulus
generate_modint!(Modint998244353, 998244353);
// Define Modint with 1000000007 as modulus
generate_modint!(Modint1000000007, 1000000007);
}