for (int i = 0; i < k; i++) {
  vector<int> b(a.size());
  for (int mask = 0; mask < 1 << k; mask++) {
    if (((mask >> i) & 1) == 0) {
      int first = a[mask];
      int second = a[mask | (1 << i)];
      b[mask] = first - second;
      b[mask | (1 << i)] = first + second;
    }
  }
  a = b;
}