#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::io::{self, BufRead};

#[allow(unused)]
macro_rules! input_at_once {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner_for_input_at_once!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner_for_input_at_once!{iter, $($r)*}
    };
}

#[allow(unused)]
macro_rules! input_inner_for_input_at_once {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value_for_input_at_once!($iter, $t);
        input_inner_for_input_at_once!{$iter $($r)*}
    };
}

#[allow(unused)]
macro_rules! read_value_for_input_at_once {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value_for_input_at_once!($iter, $t)),* )
    };

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

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

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

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

#[allow(unused)]
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)]
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)]
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>>()
    };

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

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

const P: i64 = 998244353;

fn pow(n: i64, k: i64) -> i64 {
  if k == 0 {
    1
  } else if k % 2 == 0 {
    pow((n * n) % P, k / 2)
  } else {
    (pow((n * n) % P, k / 2) * n) % P
  }
}

fn inv(n: i64) -> i64 {
  pow(n, P - 2)
}

fn main() {
  // pray for AC
  let mut c_ = vec![vec![-1; 4001]; 4001];
  input!{
    k: i64,
    n: i64,
  };
  for i in 0..4001 {
    c_[i][0] = 1;
  }

  fn c_f(c_: &mut Vec<Vec<i64>>, n: i64, k: i64) -> i64 {
    if n < k {
      0
    } else {
      let n_ = n as usize;
      let k_ = k as usize;
      if c_[n_][k_] < 0 {
        c_[n_][k_] = (((n - (k - 1)) * inv(k)) % P * c_f(c_, n, k - 1)) % P;
      }
      c_[n_][k_]
    }
  }
  let mut c = |n: i64, k: i64| -> i64 { c_f(&mut c_, n, k) };
  /*
  for i in 0..4001 {
    for j in 0..i {
      c[i][j + 1] =
        ((((i - j) as i64 * inv((j + 1) as i64)) % P) * c[i][j]) % P;
    }
  }
  */
  for i in 2..2 * k + 1 {
    let m = k - (k + 1 - i).abs();
    let mut ans = 0;
    for l in 0..(m / 2 + 1) {
      if l == 0 && k == m {
        continue;
      }
      ans +=
        ((pow(2, l) * c(n + k - m - 1, l + k - m - 1) % P) * c(m / 2, l)) % P;
      ans %= P;
      if m % 2 == 1 {
        ans +=
          ((pow(2, l) * c(n + k - m - 2, l + k - m - 1) % P) * c(m / 2, l)) % P;
        ans %= P;
      }
    }
    println!("{}", ans);
  }
}


Measured memory_bytes: 152060