InputStream -> OutputStream

Here is what I need to do. Inside a servlet I have an InputStream that is the result of calling getInputStream on a Process. This is stdout from a C program that I call. I also have an OutputStream. This comes from Response.getOutputStream. What I need to do is pipe the stream from the InputStream through the OutputStream.
Any ideas?

Write a loop to read bytes from the input stream, and write those bytes to the output stream:
int val; while ((val = inStream.read()) != -1) outStream.write(val);
For improved efficiency, modify the loop to use read(byte[]) and write(byte[]) instead. It may well also be useful to put this method in a separate thread.