Buggy python submission (verdict: Time Limit Exceeded):
k,n =map(int,input().split())
mod = 998244353
fact=[1]*5000
for i in range(1,len(fact)):
  fact[i] = fact[i-1]*i%mod
def comb(n,k,p):
  if com[n][k] != -1:
    return com[n][k]
  if n<0 or k<0 or n<k: return 0
  if n==0 or k==0: return 1
  a=fact[n]
  b=fact[k]
  c=fact[n-k]
  yey = (a*power_func(b,p-2,p)*power_func(c,p-2,p))%p
  com[n][k] = yey
  return yey
def power_func(a,b,p):
  if b==0: return 1
  if b%2==0:
    d=power_func(a,b//2,p)
    return d*d %p
  if b%2==1:
    return (a*power_func(a,b-1,p ))%p
com = [[-1] *4050 for i in range(4050)]
for i in range(2,2*k+1):
  ans = 0
  if i %2 == 1:
    pp = (i+1)//2
    pm = i - pp
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*power_func(2,q,mod)%mod
      if n - q<0:
        continue
      r = k-p*2
      if r <0:
        r = 0
      ans += sen* comb(n+r-1,n-q,mod)%mod
    print(ans%mod)
  else:
    pp = i//2 +1
    pm = i//2 -1
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*power_func(2,q,mod)%mod
      if n - q<0:
        continue
      r = k-p*2-1
      if r <0:
        r = 0
      ans += sen* comb(n+r-1,n-q,mod)%mod
    for q in range(p+1):
      sen = comb(p,q,mod)*power_func(2,q,mod)%mod
      if n - q-1<0:
        continue
      r = k-p*2-1
      if r <0:
        r = 0
      ans += sen* comb(n+r-2,n-q-1,mod)%mod
    print(ans%mod)

Fixed submission:
k,n =map(int,input().split())
mod = 998244353
fact = [1]*(n+k+1)
rfact = [1]*(n+k+1)
for i in range(n+k):
    fact[i+1] = rr = ((i+1) * fact[i]) % mod
    rfact[i+1] = pow(rr, mod-2, mod)
def comb(N, K,mod):
    return fact[N] * rfact[K] * rfact[N-K] % mod
kota = []
for i in range(2,k+2):
  ans = 0
  if i %2 == 1:
    pp = (i+1)//2
    pm = i - pp
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*pow(2,q,mod)%mod
      if n - q<0:
        break
      r = k-p*2
      if r <0:
        r = 0
      if n+r-1 < n-q:
        continue
      ans += sen* comb(n+r-1,n-q,mod)%mod
    kota.append(ans%mod)
  else:
    pp = i//2 +1
    pm = i//2 -1
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*pow(2,q,mod)%mod
      if n - q<0:
        break
      r = k-p*2-1
      if r <0:
        r = 0
      if n+r-1 < n-q:
        continue
      ans += sen* comb(n+r-1,n-q,mod)%mod
    for q in range(p+1):
      sen = comb(p,q,mod)*pow(2,q,mod)%mod
      if n - q-1<0:
        break
      r = k-p*2-1
      if r <0:
        r = 0
      if n+r-2 < n-q-1:
        continue
      ans += sen* comb(n+r-2,n-q-1,mod)%mod
    kota.append(ans%mod)
for i in kota:
  print(i)
for i in range(len(kota)-2,-1,-1):
  print(kota[i])

Buggy python submission (verdict: Time Limit Exceeded):
k,n =map(int,input().split())
mod = 998244353
fact=[1]*5000
for i in range(1,len(fact)):
  fact[i] = fact[i-1]*i%mod
def comb(n,k,p):
  if n<0 or k<0 or n<k: return 0
  if n==0 or k==0: return 1
  a=fact[n]
  b=fact[k]
  c=fact[n-k]
  return (a*power_func(b,p-2,p)*power_func(c,p-2,p))%p
def power_func(a,b,p):
  if b==0: return 1
  if b%2==0:
    d=power_func(a,b//2,p)
    return d*d %p
  if b%2==1:
    return (a*power_func(a,b-1,p ))%p
for i in range(2,2*k+1):
  ans = 0
  if i %2 == 1:
    pp = (i+1)//2
    pm = i - pp
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*2**q
      if n - q<0:
        continue
      r = k-p*2
      if r <0:
        r = 0
      ans += sen* comb(n+r-1,n-q,mod)
    print(ans%mod)
  else:
    pp = i//2 +1
    pm = i//2 -1
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*2**q
      if n - q<0:
        continue
      r = k-p*2-1
      if r <0:
        r = 0
      ans += sen* comb(n+r-1,n-q,mod)
    for q in range(p+1):
      sen = comb(p,q,mod)*2**q
      if n - q-1<0:
        continue
      r = k-p*2-1
      if r <0:
        r = 0
      ans += sen* comb(n+r-2,n-q-1,mod)
    print(ans%mod)

Fixed submission:
k,n =map(int,input().split())
mod = 998244353
fact = [1]*(n+k+1)
rfact = [1]*(n+k+1)
for i in range(n+k):
    fact[i+1] = rr = ((i+1) * fact[i]) % mod
    rfact[i+1] = pow(rr, mod-2, mod)
def comb(N, K,mod):
    return fact[N] * rfact[K] * rfact[N-K] % mod
kota = []
for i in range(2,k+2):
  ans = 0
  if i %2 == 1:
    pp = (i+1)//2
    pm = i - pp
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*pow(2,q,mod)%mod
      if n - q<0:
        break
      r = k-p*2
      if r <0:
        r = 0
      if n+r-1 < n-q:
        continue
      ans += sen* comb(n+r-1,n-q,mod)%mod
    kota.append(ans%mod)
  else:
    pp = i//2 +1
    pm = i//2 -1
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*pow(2,q,mod)%mod
      if n - q<0:
        break
      r = k-p*2-1
      if r <0:
        r = 0
      if n+r-1 < n-q:
        continue
      ans += sen* comb(n+r-1,n-q,mod)%mod
    for q in range(p+1):
      sen = comb(p,q,mod)*pow(2,q,mod)%mod
      if n - q-1<0:
        break
      r = k-p*2-1
      if r <0:
        r = 0
      if n+r-2 < n-q-1:
        continue
      ans += sen* comb(n+r-2,n-q-1,mod)%mod
    kota.append(ans%mod)
for i in kota:
  print(i)
for i in range(len(kota)-2,-1,-1):
  print(kota[i])

Buggy python submission (verdict: Time Limit Exceeded):
k,n =map(int,input().split())
mod = 998244353
fact=[1]*4010
for i in range(1,len(fact)):
  fact[i] = fact[i-1]*i%mod
def comb(n,k,p):
  if n<0 or k<0 or n<k: return 0
  if n==0 or k==0: return 1
  a=fact[n]
  b=fact[k]
  c=fact[n-k]
  return (a*power_func(b,p-2,p)*power_func(c,p-2,p))%p
def power_func(a,b,p):
  if b==0: return 1
  if b%2==0:
    d=power_func(a,b//2,p)
    return d*d %p
  if b%2==1:
    return (a*power_func(a,b-1,p ))%p
for i in range(2,2*k+1):
  ans = 0
  if i %2 == 1:
    pp = (i+1)//2
    pm = i - pp
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*2**q
      if n - q<0:
        continue
      r = k-p*2
      if r <0:
        r = 0
      ans += sen* comb(n+r-1,n-q,mod)
    print(ans%mod)
  else:
    pp = i//2 +1
    pm = i//2 -1
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*2**q
      if n - q<0:
        continue
      r = k-p*2-1
      if r <0:
        r = 0
      ans += sen* comb(n+r-1,n-q,mod)
    for q in range(p+1):
      sen = comb(p,q,mod)*2**q
      if n - q-1<0:
        continue
      r = k-p*2-1
      if r <0:
        r = 0
      ans += sen* comb(n+r-2,n-q-1,mod)
    print(ans%mod)

Fixed submission:
k,n =map(int,input().split())
mod = 998244353
fact = [1]*(n+k+1)
rfact = [1]*(n+k+1)
for i in range(n+k):
    fact[i+1] = rr = ((i+1) * fact[i]) % mod
    rfact[i+1] = pow(rr, mod-2, mod)
def comb(N, K,mod):
    return fact[N] * rfact[K] * rfact[N-K] % mod
kota = []
for i in range(2,k+2):
  ans = 0
  if i %2 == 1:
    pp = (i+1)//2
    pm = i - pp
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*pow(2,q,mod)%mod
      if n - q<0:
        break
      r = k-p*2
      if r <0:
        r = 0
      if n+r-1 < n-q:
        continue
      ans += sen* comb(n+r-1,n-q,mod)%mod
    kota.append(ans%mod)
  else:
    pp = i//2 +1
    pm = i//2 -1
    p = min(k-pp+1,pm)
    for q in range(p+1):
      sen = comb(p,q,mod)*pow(2,q,mod)%mod
      if n - q<0:
        break
      r = k-p*2-1
      if r <0:
        r = 0
      if n+r-1 < n-q:
        continue
      ans += sen* comb(n+r-1,n-q,mod)%mod
    for q in range(p+1):
      sen = comb(p,q,mod)*pow(2,q,mod)%mod
      if n - q-1<0:
        break
      r = k-p*2-1
      if r <0:
        r = 0
      if n+r-2 < n-q-1:
        continue
      ans += sen* comb(n+r-2,n-q-1,mod)%mod
    kota.append(ans%mod)
for i in kota:
  print(i)
for i in range(len(kota)-2,-1,-1):
  print(kota[i])