Regular expression to remove one parameter from query string

I'm looking for a regular expression to remove a single parameter from a query string, and I want to do it in a single regular expression if possible.

Say I want to remove the foo parameter. Right now I use this:

/&?foo\=[^&]+/

That works as long as foo is not the first parameter in the query string. If it is, then my new query string starts with an ampersand. (For example, "foo=123&bar=456" gives a result of "&bar=456".) Right now, I'm just checking after the regex if the query string starts with ampersand, and chopping it off if it does.

Example edge cases:

Input                    |  Expected Output
-------------------------+--------------------
foo=123                  |  (empty string)
foo=123&bar=456          |  bar=456
bar=456&foo=123          |  bar=456
abc=789&foo=123&bar=456  |  abc=789&bar=456

Edit

OK as pointed out in comments there are there are way more edge cases than I originally considered. I got the following regex to work with all of them:

/&foo(\=[^&]*)?(?=&|$)|^foo(\=[^&]*)?(&|$)/

This is modified from Mark Byers's answer, which is why I'm accepting that one, but Roger Pate's input helped a lot too.

Here is the full suite of test cases I'm using, and a Javascript snippet which tests them:

$(function() {
    var regex = /&foo(\=[^&]*)?(?=&|$)|^foo(\=[^&]*)?(&|$)/;
    
    var escapeHtml = function (str) {
        var map = {
          '&': '&