#882276 (Rust) No.2351 Butterfly in Summer

• 問題: No.2351 Butterfly in Summer
• ユーザー: atcoder8
• 提出日時: 2023-06-17 00:43:28
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 1 ms / 2,000 ms
• コード長: 11,217 bytes
• コンパイル時間: 12,445 ms
• コンパイル使用メモリ: 387,188 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-06-24 17:45:10
• 合計ジャッジ時間: 13,531 ms
• ジャッジサーバーID （参考情報）: judge5 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,248 KB
testcase_02	AC	0 ms; 5,376 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	1 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	1 ms; 5,376 KB
testcase_09	AC	1 ms; 5,376 KB
testcase_10	AC	1 ms; 5,376 KB
testcase_11	AC	1 ms; 5,376 KB
testcase_12	AC	1 ms; 5,376 KB
testcase_13	AC	1 ms; 5,376 KB
testcase_14	AC	1 ms; 5,376 KB
testcase_15	AC	1 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB
testcase_17	AC	1 ms; 5,376 KB
testcase_18	AC	1 ms; 5,376 KB
testcase_19	AC	1 ms; 5,376 KB
testcase_20	AC	1 ms; 5,376 KB
testcase_21	AC	1 ms; 5,376 KB
testcase_22	AC	1 ms; 5,376 KB
testcase_23	AC	1 ms; 5,376 KB

ソースコード

use modint::Modint998244353;

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 {
    //! This module implements modular arithmetic.

    use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};

    type InnerType = u32;

    /// Return `x` such that `a * x` is equivalent to `1` with `m` as the modulus.
    fn modinv(a: u32, m: u32) -> u32 {
        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,
            "\
    There is no multiplicative inverse of `a` with `m` as the modulus, \
    because `a` and `m` are not prime to each other (gcd(a, m) = {}).",
            a.abs()
        );

        ((s % m as i64 + m as i64) % m as i64) as u32
    }

    pub trait Reminder {
        /// Return the remainder divided by `modulus`.
        fn reminder(self, modulus: InnerType) -> InnerType;
    }

    macro_rules! impl_reminder_for_small_unsigned_int {
        ($($unsigned_small_int: tt), *) => {
            $(
                impl Reminder for $unsigned_small_int {
                    fn reminder(self, modulus: InnerType) -> InnerType {
                        self as InnerType % modulus
                    }
                }
            )*
        };
    }

    // Implement `Reminder` trait for `u8`, `u16` and `u32`.
    impl_reminder_for_small_unsigned_int!(u8, u16, u32);

    macro_rules! impl_reminder_for_large_unsigned_int {
        ($($unsigned_large_int: tt), *) => {
            $(
                impl Reminder for $unsigned_large_int {
                    fn reminder(self, modulus: InnerType) -> InnerType {
                        (self % modulus as Self) as InnerType
                    }
                }
            )*
        };
    }

    // Implement `Reminder` trait for `usize`, `u64` and `u128`.
    impl_reminder_for_large_unsigned_int!(usize, u64, u128);

    macro_rules! impl_reminder_for_small_signed_int {
        ($($signed_small_int: tt), *) => {
            $(
                impl Reminder for $signed_small_int {
                    fn reminder(self, modulus: InnerType) -> InnerType {
                        (self as i32 % modulus as i32 + modulus as i32) as InnerType % modulus
                    }
                }
            )*
        };
    }

    // Implement `Reminder` trait for `i8`, `i16` and `i32`.
    impl_reminder_for_small_signed_int!(i8, i16, i32);

    macro_rules! impl_reminder_for_large_signed_int {
        ($($signed_large_int: tt), *) => {
            $(
                impl Reminder for $signed_large_int {
                    fn reminder(self, modulus: InnerType) -> InnerType {
                        (self % modulus as Self + modulus as Self) as InnerType % modulus
                    }
                }
            )*
        };
    }

    // Implement `Reminder` trait for `isize`, `i64` and `i128`.
    impl_reminder_for_large_signed_int!(isize, i64, i128);

    /// Structure for modular arithmetic.
    #[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
    pub struct Modint<const MODULUS: InnerType> {
        rem: InnerType,
    }

    impl<const MODULUS: InnerType> std::fmt::Display for Modint<MODULUS> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
            write!(f, "{}", self.rem)
        }
    }

    impl<const MODULUS: InnerType> Default for Modint<MODULUS> {
        /// Return a `Modint` instance equivalent to `0`.
        fn default() -> Self {
            Self::raw(0)
        }
    }

    impl<T, const MODULUS: InnerType> From<T> for Modint<MODULUS>
    where
        T: Reminder,
    {
        fn from(value: T) -> Self {
            Self::new(value)
        }
    }

    impl<const MODULUS: InnerType> Add<Modint<MODULUS>> for Modint<MODULUS> {
        type Output = Self;

        fn add(self, rhs: Modint<MODULUS>) -> Self::Output {
            Self::raw((self.rem + rhs.rem) % MODULUS)
        }
    }

    impl<const MODULUS: InnerType> Sub<Modint<MODULUS>> for Modint<MODULUS> {
        type Output = Self;

        fn sub(self, rhs: Modint<MODULUS>) -> Self::Output {
            Self::raw((self.rem + MODULUS - rhs.rem) % MODULUS)
        }
    }

    impl<const MODULUS: InnerType> Mul<Modint<MODULUS>> for Modint<MODULUS> {
        type Output = Self;

        fn mul(self, rhs: Modint<MODULUS>) -> Self::Output {
            Self::raw((self.rem as u64 * rhs.rem as u64 % MODULUS as u64) as InnerType)
        }
    }

    impl<const MODULUS: InnerType> Div<Modint<MODULUS>> for Modint<MODULUS> {
        type Output = Self;

        #[allow(clippy::suspicious_arithmetic_impl)]
        fn div(self, rhs: Modint<MODULUS>) -> Self::Output {
            self * rhs.inv()
        }
    }

    impl<const MODULUS: InnerType> Neg for Modint<MODULUS> {
        type Output = Self;

        fn neg(self) -> Self::Output {
            Self::raw((MODULUS - self.rem) % MODULUS)
        }
    }

    impl<const MODULUS: InnerType> AddAssign<Modint<MODULUS>> for Modint<MODULUS> {
        fn add_assign(&mut self, rhs: Modint<MODULUS>) {
            *self = *self + rhs;
        }
    }

    impl<const MODULUS: InnerType> SubAssign<Modint<MODULUS>> for Modint<MODULUS> {
        fn sub_assign(&mut self, rhs: Modint<MODULUS>) {
            *self = *self - rhs;
        }
    }

    impl<const MODULUS: InnerType> MulAssign<Modint<MODULUS>> for Modint<MODULUS> {
        fn mul_assign(&mut self, rhs: Modint<MODULUS>) {
            *self = *self * rhs;
        }
    }

    impl<const MODULUS: InnerType> DivAssign<Modint<MODULUS>> for Modint<MODULUS> {
        fn div_assign(&mut self, rhs: Modint<MODULUS>) {
            *self = *self / rhs;
        }
    }

    impl<const MODULUS: InnerType, T> Add<T> for Modint<MODULUS>
    where
        T: Reminder,
    {
        type Output = Modint<MODULUS>;

        fn add(self, rhs: T) -> Self::Output {
            self + Self::new(rhs)
        }
    }

    impl<const MODULUS: InnerType, T> Sub<T> for Modint<MODULUS>
    where
        T: Reminder,
    {
        type Output = Modint<MODULUS>;

        fn sub(self, rhs: T) -> Self::Output {
            self - Self::new(rhs)
        }
    }

    impl<const MODULUS: InnerType, T> Mul<T> for Modint<MODULUS>
    where
        T: Reminder,
    {
        type Output = Modint<MODULUS>;

        fn mul(self, rhs: T) -> Self::Output {
            self * Self::new(rhs)
        }
    }

    impl<const MODULUS: InnerType, T> Div<T> for Modint<MODULUS>
    where
        T: Reminder,
    {
        type Output = Modint<MODULUS>;

        fn div(self, rhs: T) -> Self::Output {
            self / Self::new(rhs)
        }
    }

    impl<const MODULUS: InnerType, T> AddAssign<T> for Modint<MODULUS>
    where
        T: Reminder,
    {
        fn add_assign(&mut self, rhs: T) {
            *self += Modint::new(rhs);
        }
    }

    impl<const MODULUS: InnerType, T> SubAssign<T> for Modint<MODULUS>
    where
        T: Reminder,
    {
        fn sub_assign(&mut self, rhs: T) {
            *self -= Modint::new(rhs);
        }
    }

    impl<const MODULUS: InnerType, T> MulAssign<T> for Modint<MODULUS>
    where
        T: Reminder,
    {
        fn mul_assign(&mut self, rhs: T) {
            *self *= Modint::new(rhs);
        }
    }

    impl<const MODULUS: InnerType, T> DivAssign<T> for Modint<MODULUS>
    where
        T: Reminder,
    {
        fn div_assign(&mut self, rhs: T) {
            *self /= Modint::new(rhs);
        }
    }

    impl<const MODULUS: InnerType> Modint<MODULUS> {
        /// Return the modulus.
        pub fn modulus() -> InnerType {
            MODULUS
        }

        /// Return a `Modint` instance equivalent to `a`.
        pub fn new<T>(a: T) -> Self
        where
            T: Reminder,
        {
            Self {
                rem: a.reminder(MODULUS),
            }
        }

        /// Create a `Modint` instance from a non-negative integer less than `MODULUS`.
        pub fn raw(a: InnerType) -> Self {
            Self { rem: a }
        }

        /// Return `x` such that `x * q` is equivalent to `p`.
        pub fn frac<T>(p: T, q: T) -> Self
        where
            T: Reminder,
        {
            Self::new(p) / Self::new(q)
        }

        /// Return the remainder divided by `MODULUS`.
        /// The returned value is a non-negative integer less than `MODULUS`.
        pub fn rem(self) -> InnerType {
            self.rem
        }

        /// Return the modular multiplicative inverse.
        pub fn inv(self) -> Self {
            Self {
                rem: modinv(self.rem, MODULUS),
            }
        }

        /// Calculate the power of `exp` using the iterative squaring method.
        pub fn pow<T>(self, exp: T) -> Self
        where
            T: ToExponent,
        {
            let mut ret = Self::new(1);
            let mut mul = self;
            let exp = exp.to_exponent();
            let mut t = exp.abs;

            while t != 0 {
                if t & 1 == 1 {
                    ret *= mul;
                }

                mul *= mul;
                t >>= 1;
            }

            if exp.neg {
                ret = ret.inv();
            }

            ret
        }
    }

    pub struct Exponent {
        neg: bool,
        abs: u128,
    }

    pub trait ToExponent {
        fn to_exponent(self) -> Exponent;
    }

    macro_rules! impl_to_exponent_for_unsigned_int {
        ($($ty: tt), *) => {
            $(
                impl ToExponent for $ty {
                    fn to_exponent(self) -> Exponent {
                        Exponent {
                            neg: false,
                            abs: self as u128,
                        }
                    }
                }
            )*
        };
    }

    impl_to_exponent_for_unsigned_int!(usize, u8, u16, u32, u64, u128);

    macro_rules! impl_to_exponent_for_signed_int {
        ($($ty: tt), *) => {
            $(
                impl ToExponent for $ty {
                    fn to_exponent(self) -> Exponent {
                        Exponent {
                            neg: self.is_negative(),
                            abs: self.abs() as u128,
                        }
                    }
                }
            )*
        };
    }

    impl_to_exponent_for_signed_int!(isize, i8, i16, i32, i64, i128);

    /// The type `Modint` with 1000000007 as the modulus.
    pub type Modint1000000007 = Modint<1000000007>;

    /// The type `Modint` with 998244353 as the modulus.
    pub type Modint998244353 = Modint<998244353>;
}