典型057

typical90_be.rb

# 提出: https://atcoder.jp/contests/typical90/submissions/23159483

# 入力
N, M = gets.split.map(&:to_i)
A = Array.new(N) { gets; gets.split.map(&:to_i) }
S = gets.split.map(&:to_i)

# 行ベクトルの配列
xs = A.map { |indices|
  x = 0
  indices.each do |index|
    x |= 1 << index - 1
  end
  x
  }

# 基底を求める
bases = []
xs.each do |x|
  bases.each do |base|
    x = [x, x ^ base].min
  end
  bases << x if x != 0
end

# 解く
y = S.join.reverse.to_i(2)

bases.each do |base|
  y = [y, y ^ base].min
end

if y != 0
  puts 0
  exit
end

rank = bases.size
puts 2.pow(N - rank, 998244353)