I need a function to generate random integers. (assume Java `long` type for now, but this will be extended to `BigInteger` or `BitSet` later.)

The tricky part is there is a parameter P that specifies the (independent) probability of any bit in the result being 1.

If P = 0.5 then we can just use the standard random number generator. Some other values of P are also easy to implement. Here's an incomplete example:

```
Random random = new Random();

// ...

long nextLong(float p) {
    if      (p == 0.0f)   return 0L;
    else if (p == 1.0f)   return -1L;
    else if (p == 0.5f)   return random.nextLong();
    else if (p == 0.25f)  return nextLong(0.5f) & nextLong(0.5f);
    else if (p == 0.75f)  return nextLong(0.5f) | nextLong(0.5f);
    else if (p == 0.375f) return nextLong(0.5f) & nextLong(0.75f); // etc
    else {
      // What goes here??
      String message = String.format("P=%f not implemented yet!", p);
      throw new IllegalArgumentException(message);
    }
}

```

Is there a way to generalise this for any value of P between 0.0 and 1.0?