Here is what I want to do, in nginx conf language:

server {
listen 80;

server_name www.example.com;

# root when path query arg is present
if ($arg_path) {
root /var/www/example/$arg_path;
}

# root when path query arg is not present (default)
if (!$arg_path) {
root /var/www/example/default;
}
}