Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(10000000)

m = [[0] * 2005 for i in range(4005)]

def f():
    K, N = map(int, raw_input().split())
    MOD = 998244353

    for i in range(4001):
        m[i][0] = 1
    for i in range(2001):
        m[i][i] = 1
    for i in range(1, 4001):
        for j in range(1, 2001):
            m[i][j] = (m[i - 1][j] + m[i - 1][j - 1]) % MOD

    m2 = [1] * 4005
    for i in range(1, 4001):
        m2[i] = (m2[i - 1] * 2) % MOD

    ls = []
    for i in range(2, K + 2):
        ans = 0
        if i % 2 == 0:
            rem = i / 2 - 1
            for j in range(rem + 1):
                ans += m[N + K - 2 - rem * 2][K - 2 - rem * 2 + j] \
                * m[rem][j] * m2[j]
                ans += m[N + K - 3 - rem * 2][K - 2 - rem * 2 + j] \
                * m[rem][j] * m2[j]
                ans %= MOD
        else:
            rem = i / 2
            for j in range(rem + 1):
                ans += m[N + K - 1 - rem * 2][K - 1 - rem * 2 + j] \
                * m[rem][j] * m2[j]
                ans %= MOD
        ls.append(ans % MOD)

    ls += ls[:-1][::-1]

    for num in ls:
        print num

f()


Fixed submission:
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(10000000)

m = [[0] * 2005 for i in range(4005)]

def f():
    K, N = map(int, raw_input().split())
    MOD = 998244353

    for i in range(4001):
        m[i][0] = 1
    for i in range(2001):
        m[i][i] = 1
    for i in range(1, 4001):
        for j in range(1, 2001):
            m[i][j] = (m[i - 1][j] + m[i - 1][j - 1]) % MOD

    m2 = [1] * 4005
    for i in range(1, 4001):
        m2[i] = (m2[i - 1] * 2) % MOD

    ls = []
    for i in range(2, K + 2):
        ans = 0
        if i % 2 == 0:
            rem = i / 2 - 1
            for j in range(rem + 1):
                ans += m[N + K - 2 - rem * 2][K - 2 - rem * 2 + j] \
                * m[rem][j] * m2[j]
                ans += m[N + K - 3 - rem * 2][K - 2 - rem * 2 + j] \
                * m[rem][j] * m2[j]
                ans %= MOD
        else:
            rem = i / 2
            for j in range(rem + 1):
                ans += m[N + K - 1 - rem * 2][K - 1 - rem * 2 + j] \
                * m[rem][j] * m2[j]
                ans %= MOD
        ls.append(ans % MOD)

    ls += ls[:-1][::-1]

    for num in ls:
        print num

f()

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(10000000)

m = [[-1] * 2001 for i in range(4001)]

def f():
    K, N = map(int, raw_input().split())
    MOD = 998244353

    def comb(n, k):
        if n < 0 or k < 0:
            return 0
        if n == k or k == 0:
            return 1
        if m[n][k] < 0:
            m[n][k] = (comb(n - 1, k) + comb(n - 1, k - 1)) % MOD
        return m[n][k]

    m2 = {}
    def p2(n):
        if n == 0:
            return 1
        if not n in m2:
            m2[n] = (p2(n - 1) * 2) % MOD
        return m2[n]

    ls = []
    for i in range(2, K + 2):
        ans = 0
        if i % 2 == 0:
            rem = i / 2 - 1
            for j in range(rem + 1):
                ans += comb(N + K - 2 - rem * 2, K - 2 - rem * 2 + j) \
                * comb(rem, j) * p2(j)
                ans += comb(N + K - 3 - rem * 2, K - 2 - rem * 2 + j) \
                * comb(rem, j) * p2(j)
                ans %= MOD
        else:
            rem = i / 2
            for j in range(rem + 1):
                ans += comb(N + K - 1 - rem * 2, K - 1 - rem * 2 + j) \
                * comb(rem, j) * p2(j)
                ans %= MOD
        ls.append(ans % MOD)

    ls += ls[:-1][::-1]

    for num in ls:
        print num

f()


Fixed submission:
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(10000000)

m = [[0] * 2005 for i in range(4005)]

def f():
    K, N = map(int, raw_input().split())
    MOD = 998244353

    for i in range(4001):
        m[i][0] = 1
    for i in range(2001):
        m[i][i] = 1
    for i in range(1, 4001):
        for j in range(1, 2001):
            m[i][j] = (m[i - 1][j] + m[i - 1][j - 1]) % MOD

    m2 = [1] * 4005
    for i in range(1, 4001):
        m2[i] = (m2[i - 1] * 2) % MOD

    ls = []
    for i in range(2, K + 2):
        ans = 0
        if i % 2 == 0:
            rem = i / 2 - 1
            for j in range(rem + 1):
                ans += m[N + K - 2 - rem * 2][K - 2 - rem * 2 + j] \
                * m[rem][j] * m2[j]
                ans += m[N + K - 3 - rem * 2][K - 2 - rem * 2 + j] \
                * m[rem][j] * m2[j]
                ans %= MOD
        else:
            rem = i / 2
            for j in range(rem + 1):
                ans += m[N + K - 1 - rem * 2][K - 1 - rem * 2 + j] \
                * m[rem][j] * m2[j]
                ans %= MOD
        ls.append(ans % MOD)

    ls += ls[:-1][::-1]

    for num in ls:
        print num

f()