How to redirect from one url to another in nginx?

Question

linux

How to make the following redirection in nginx:
from site.ru to newsite.ru
from site.ru/page to newsite.ru/new/page
The option I use does not work:
server {
listen 80;
server_name site.ru;
location / {
rewrite ^(.*) newsite.ru/$1 permanent;
}
location /page {
rewrite ^(.*) newsite.ru/new/page/$1 permanent;
}
}
UPD: I noticed such a strange thing, above in the config I have a redirect from old.site.ru to newsite.ru/old/, so now with the redirect that I described above opens: newsite.ru/old/new/page/, then there is, as I understand it, a redirect occurs, only the name of the nginx server is substituted from the previous redirect.
There is an opinion that regular expressions should help in this case, but how to use them correctly for this specific config does not fit in my head.

Answer 1

So try:

server_name old.site.ru www.old.site.ru;
location / {
        rewrite ^(.*)$ http://newsite.ru/old/$1 permanent;
        }
}

Answer 2

server {
    server_name site.ru;
    rewrite ^ http://newsite.ru$request_uri? permanent;
}