#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

pub mod modular {
    const M: i64 = 998244353;

    #[derive(Debug, Clone, Copy, Default, PartialOrd, Ord, PartialEq, Eq)]
    pub struct Modular(i64);

    impl ::std::fmt::Display for Modular {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }

    impl Modular {
        pub fn new(v: i64) -> Modular {
            Modular(v % M)
        }

        pub fn pow(self, mut r: i64) -> Modular {
            let mut k = self;
            let mut ret = 1.into();

            while r > 0 {
                if r % 2 != 0 {
                    ret = ret * k;
                }
                r /= 2;
                k = k * k;
            }

            ret
        }

        // This requires M is prime
        pub fn recip(self) -> Modular {
            self.pow(M - 2)
        }
    }

    use std::ops::*;

    impl<T: Into<Modular>> Add<T> for Modular {
        type Output = Modular;
        fn add(self, rhs: T) -> Self::Output {
            Modular::new(self.0 + rhs.into().0)
        }
    }
    impl<T: Into<Modular>> AddAssign<T> for Modular {
        fn add_assign(&mut self, rhs: T) {
            *self = *self + rhs;
        }
    }

    impl<T: Into<Modular>> Sub<T> for Modular {
        type Output = Modular;
        fn sub(self, rhs: T) -> Self::Output {
            Modular::new(self.0 - rhs.into().0 + M)
        }
    }
    impl<T: Into<Modular>> SubAssign<T> for Modular {
        fn sub_assign(&mut self, rhs: T) {
            *self = *self - rhs;
        }
    }

    impl<T: Into<Modular>> Mul<T> for Modular {
        type Output = Modular;
        fn mul(self, rhs: T) -> Self::Output {
            Modular::new(self.0 * rhs.into().0)
        }
    }
    impl<T: Into<Modular>> MulAssign<T> for Modular {
        fn mul_assign(&mut self, rhs: T) {
            *self = *self * rhs;
        }
    }

    impl<T: Into<Modular>> Div<T> for Modular {
        type Output = Modular;
        fn div(self, rhs: T) -> Self::Output {
            self * rhs.into().recip()
        }
    }
    impl<T: Into<Modular>> DivAssign<T> for Modular {
        fn div_assign(&mut self, rhs: T) {
            *self = *self / rhs;
        }
    }

    impl Neg for Modular {
        type Output = Modular;
        fn neg(self) -> Self::Output {
            Modular(0) - self
        }
    }

    impl<T: ::std::convert::Into<i64>> ::std::convert::From<T> for Modular {
        fn from(v: T) -> Self {
            Modular::new(v.into())
        }
    }
}

use modular::Modular;

fn main() {
    input!{
        k: i64,
        n: i64,
    }

    let mut fact_tbl = vec![Modular::new(1); 4001];
    let mut ifact_tbl = vec![Modular::new(1); 4001];

    for i in 1..fact_tbl.len() {
        fact_tbl[i] = fact_tbl[i - 1] * Modular::new(i as i64);
        ifact_tbl[i] = fact_tbl[i].recip();
    }

    let comb = |n: i64, k: i64| -> Modular {
        // println!("{} {} {}", n, k, n - k);

        // fact(n) * fact(k).recip() * fact(n - k).recip()
        fact_tbl[n as usize] * ifact_tbl[k as usize] * ifact_tbl[(n - k) as usize]
    };

    let h = |n: i64, r: i64| -> Modular {
        // println!("{} {}", n, r);
        if r == 0 {
            1.into()
        } else if n == 0 || r < 0 {
            0.into()
        } else {
            comb(n + r - 1, r)
        }
    };

    // fn fact(n: i64) -> Modular {
    //     if n == 0 {
    //         1.into()
    //     } else {
    //         Modular::new(n) * fact(n - 1)
    //     }
    // }

    let mut ans: Vec<Modular> = vec![];
    for i in 2..k + 2 {
        let one = if i % 2 == 0 { 1 } else { 0 };
        let pair = (i - 1) / 2;
        let solo = k - one - pair * 2;

        // println!("* {} {} {}", one, pair, solo);

        let mut mul = Modular::new(1);
        let mut acc = Modular::new(0);
        for j in 0..pair + 1 {
            let c = comb(pair, j);
            acc += h(j + solo, n - j) * c * mul;
            if one == 1 {
                acc += h(j + solo, n - 1 - j) * c * mul;
            }
            mul *= 2;
        }
        ans.push(acc);
    }

    for &v in ans.iter() {
        println!("{}", v);
    }
    for &v in ans.iter().rev().skip(1) {
        println!("{}", v);
    }
}


Measured memory_bytes: 4352