class comb():
  F = [1, 1]
  Fi = [1, 1]
  I = [0, 1]
  def __init__(self, num, mod):
    self.MOD = mod
    for i in range(2, num + 1):
      self.F.append((self.F[-1] * i) % mod)
      self.I.append(mod - self.I[mod % i] * (mod // i) % mod)
      self.Fi.append(self.Fi[-1] * self.I[i] % mod)
  def com(self, n, k):
    if n < k: return 0
    if n < 0 or k < 0: return 0
    return self.F[n] * (self.Fi[k] * self.Fi[n - k] % self.MOD) % self.MOD

N, M = list(map(int, input().split()))
A = list(map(int, input().split()))
B = list(map(int, input().split()))
MOD = 998244353

com = comb(N + M + 1, MOD)

No = 0
for i in range(1, N + 1, 2):
  No += com.com(N, i)
  No %= MOD

Nz = 0
for i in range(0, N + 1, 2):
  Nz += com.com(N, i)
  Nz %= MOD

ans = 1
for i in range(20):
  cnt = 0
  t = 1
  for j in range(M):
    b = B[j]
    if b >> i & 1:
      cnt += 1
      if j != M - 1:
        t *= No
    else:
      if j != M - 1:
        t *= Nz
    t %= MOD
  cnta = 0
  for a in A:
    if a >> i & 1:
      cnta += 1
  if cnt % 2 != cnta % 2:
    print(0)
    exit()
  ans *= t
  ans %= MOD
print(ans)