#1116528 (Rust) No.2857 Div Array

• 問題: No.2857 Div Array
• ユーザー: urectanc
• 提出日時: 2025-09-01 19:40:34
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 44 ms / 2,000 ms
• コード長: 8,767 bytes
• コンパイル時間: 14,627 ms
• コンパイル使用メモリ: 400,376 KB
• 実行使用メモリ: 7,716 KB
• 最終ジャッジ日時: 2025-09-01 19:40:51
• 合計ジャッジ時間: 16,462 ms
• ジャッジサーバーID （参考情報）: judge2 / judge1

ファイルパターン	結果
other	AC * 30

ソースコード

use std::collections::HashMap;

use modint::ModInt998244353;
use proconio::input;

type Mint = ModInt998244353;
type Mat = Vec<Vec<Mint>>;

fn main() {
    input! {
        n: usize, m: usize, k: usize
    }

    if n == 1 {
        println!("{m}");
        return;
    }

    let mut count = HashMap::new();
    for i in 1..=m {
        let div = m / i;
        *count.entry(div).or_insert(0) += 1;
    }

    let s = count.len();
    let (div, way): (Vec<_>, Vec<_>) = count.into_iter().unzip();

    let mut a = vec![vec![Mint::new(0); s]; s];
    for i in 0..s {
        for j in 0..s {
            if div[i].abs_diff(div[j]) <= k {
                a[j][i] = way[j].into();
            }
        }
    }

    let trans = mat_pow(&a, n - 1);
    let ans = trans
        .iter()
        .map(|row| row.iter().zip(&way).map(|(a, &x)| a * x).sum::<Mint>())
        .sum::<Mint>();
    println!("{ans}")
}

fn mat_mul(a: &Mat, b: &Mat) -> Mat {
    let n = a.len();
    let mut res = vec![vec![Mint::new(0); n]; n];
    for i in 0..n {
        for j in 0..n {
            for k in 0..n {
                res[i][j] += a[i][k] * b[k][j];
            }
        }
    }
    res
}

fn mat_pow(a: &Mat, mut k: usize) -> Mat {
    assert!(k > 0);
    k -= 1;
    let mut res = a.clone();
    let mut pow = a.clone();
    while k > 0 {
        if k & 1 == 1 {
            res = mat_mul(&res, &pow);
        }
        pow = mat_mul(&pow, &pow);
        k >>= 1;
    }
    res
}

#[allow(dead_code)]
mod modint {
    use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};

    pub type ModInt998244353 = ModInt<998244353>;
    pub type ModInt1000000007 = ModInt<1000000007>;

    type ModIntInner = u64;

    #[derive(Clone, Copy, PartialEq, Eq)]
    pub struct ModInt<const M: ModIntInner> {
        val: ModIntInner,
    }

    impl<const M: ModIntInner> ModInt<M> {
        const IS_PRIME: bool = is_prime(M as u32);

        pub const fn modulus() -> ModIntInner {
            M
        }

        pub const fn new(val: ModIntInner) -> Self {
            assert!(M < (1 << 31));
            Self {
                val: val.rem_euclid(M),
            }
        }

        pub const fn new_unchecked(val: ModIntInner) -> Self {
            Self { val }
        }

        pub const fn val(&self) -> ModIntInner {
            self.val
        }

        pub fn pow(self, mut exp: u64) -> Self {
            let mut result = Self::new(1);
            let mut base = self;
            while exp > 0 {
                if exp & 1 == 1 {
                    result *= base;
                }
                base *= base;
                exp >>= 1;
            }
            result
        }

        pub fn inv(self) -> Self {
            assert!(Self::IS_PRIME);
            self.pow(M as u64 - 2).into()
        }
    }

    impl<const M: ModIntInner> std::fmt::Display for ModInt<M> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
            write!(f, "{}", self.val)
        }
    }

    impl<const M: ModIntInner> std::fmt::Debug for ModInt<M> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
            write!(f, "{}", self.val)
        }
    }

    impl<const M: ModIntInner> std::str::FromStr for ModInt<M> {
        type Err = std::num::ParseIntError;
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            let value = s.parse::<ModIntInner>()?;
            Ok(ModInt::new(value))
        }
    }

    impl<const M: ModIntInner> Neg for ModInt<M> {
        type Output = Self;
        fn neg(mut self) -> Self::Output {
            if self.val > 0 {
                self.val = M - self.val;
            }
            self
        }
    }

    impl<const M: ModIntInner, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
        fn add_assign(&mut self, rhs: T) {
            self.val += rhs.into().val;
            if self.val >= M {
                self.val -= M;
            }
        }
    }

    impl<const M: ModIntInner, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
        fn sub_assign(&mut self, rhs: T) {
            self.val = self.val.wrapping_sub(rhs.into().val);
            if self.val > M {
                self.val = self.val.wrapping_add(M);
            }
        }
    }

    impl<const M: ModIntInner, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
        fn mul_assign(&mut self, rhs: T) {
            self.val = self.val * rhs.into().val % M;
        }
    }

    impl<const M: ModIntInner, T: Into<ModInt<M>>> DivAssign<T> for ModInt<M> {
        fn div_assign(&mut self, rhs: T) {
            *self *= rhs.into().inv();
        }
    }

    macro_rules! impl_binnary_operators {
    ($({ $op: ident, $op_assign: ident, $fn: ident, $fn_assign: ident}),*) => {$(
        impl<const M: ModIntInner, T: Into<ModInt<M>>> $op<T> for ModInt<M> {
            type Output = ModInt<M>;
            fn $fn(mut self, rhs: T) -> ModInt<M> {
                self.$fn_assign(rhs.into());
                self
            }
        }

        impl<const M: ModIntInner> $op<&ModInt<M>> for ModInt<M> {
            type Output = ModInt<M>;
            fn $fn(self, rhs: &ModInt<M>) -> ModInt<M> {
                self.$fn(*rhs)
            }
        }

        impl<const M: ModIntInner, T: Into<ModInt<M>>> $op<T> for &ModInt<M> {
            type Output = ModInt<M>;
            fn $fn(self, rhs: T) -> ModInt<M> {
                (*self).$fn(rhs.into())
            }
        }

        impl<const M: ModIntInner> $op<&ModInt<M>> for &ModInt<M> {
            type Output = ModInt<M>;
            fn $fn(self, rhs: &ModInt<M>) -> ModInt<M> {
                (*self).$fn(*rhs)
            }
        }

        impl<const M: ModIntInner> $op_assign<&ModInt<M>> for ModInt<M> {
            fn $fn_assign(&mut self, rhs: &ModInt<M>) {
                *self = self.$fn(*rhs);
            }
        }
    )*};
}

    impl_binnary_operators!(
        {Add, AddAssign, add, add_assign},
        {Sub, SubAssign, sub, sub_assign},
        {Mul, MulAssign, mul, mul_assign},
        {Div, DivAssign, div, div_assign}
    );

    impl<const M: ModIntInner> std::iter::Sum for ModInt<M> {
        fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::new(0), Add::add)
        }
    }

    impl<'a, const M: ModIntInner> std::iter::Sum<&'a Self> for ModInt<M> {
        fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::new(0), Add::add)
        }
    }

    impl<const M: ModIntInner> std::iter::Product for ModInt<M> {
        fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::new(1), Mul::mul)
        }
    }

    impl<'a, const M: ModIntInner> std::iter::Product<&'a Self> for ModInt<M> {
        fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::new(1), Mul::mul)
        }
    }

    macro_rules! impl_rem_euclid_signed {
    ($($ty:tt),*) => {
        $(
            impl<const M: ModIntInner> From<$ty> for ModInt<M> {
                fn from(value: $ty) -> ModInt<M> {
                    Self::new_unchecked((value as i64).rem_euclid(M as i64) as ModIntInner)
                }
            }
        )*
    };
}
    impl_rem_euclid_signed!(i8, i16, i32, i64, isize);

    macro_rules! impl_rem_euclid_unsigned {
    ($($ty:tt),*) => {
        $(
            impl<const M: ModIntInner> From<$ty> for ModInt<M> {
                fn from(value: $ty) -> ModInt<M> {
                    Self::new_unchecked((value as u64).rem_euclid(M as u64) as ModIntInner)
                }
            }
        )*
    };
}
    impl_rem_euclid_unsigned!(u8, u16, u32, u64, usize);

    const fn is_prime(n: u32) -> bool {
        const fn miller_rabin(n: u32, witness: u32) -> bool {
            let (n, witness) = (n as u64, witness as u64);
            let mut d = n >> (n - 1).trailing_zeros();
            let mut y = {
                let (mut res, mut pow, mut e) = (1, witness, d);
                while e > 0 {
                    if e & 1 == 1 {
                        res = res * pow % n;
                    }
                    pow = pow * pow % n;
                    e >>= 1;
                }
                res
            };
            while d != n - 1 && y != 1 && y != n - 1 {
                y = y * y % n;
                d <<= 1;
            }
            y == n - 1 || d & 1 == 1
        }

        const WITNESS: [u32; 3] = [2, 7, 61];

        if n == 1 || n % 2 == 0 {
            return n == 2;
        }

        let mut i = 0;
        while i < WITNESS.len() {
            if !miller_rabin(n, WITNESS[i]) {
                return false;
            }
            i += 1;
        }

        true
    }
}