recursive binflip check

bool valid(int prev, int k, int after, int powerUsed) {
  if (k == 0 && powerUsed == 0)
    return true;
  if (powerUsed == 0)
    return false;
  // printf("call %d %d %d %d\n", prev, k, after, powerUsed);
  int toUse = pow(2, powerUsed - 1);
  if (toUse > k) {
    int shifted = toUse - k;
    vector<bool> vals;
    if (prev >= shifted) {
      vals.pb(
          valid(prev - shifted, shifted, after + k, powerUsed - 1));
    }
    if (after >= shifted) {
      vals.pb(
          valid(prev + k, shifted, after - shifted, powerUsed - 1));
    }
    for (auto x : vals)
      if (x)
        return true;
    return false;
  } else {
    return valid(prev + toUse, k - toUse, after, powerUsed - 1) || valid(prev, k - toUse, after + toUse, powerUsed - 1);
  }
}