How does Nginx reverse proxy multiple ports to different directories on the same port?

how do I configure the reverse proxy for Nginx to proxy multiple ports to different directories on the same port?

I have apps a, b, and c running on ports 8001, 8002, and 8003, respectively. The
server does not have a domain name configured, so the access addresses are ip:8001 , ip:8002 and ip:8003 .
now I want to implement it in Nginx, open only one port 80, and then access different services through different directories.
I expect the access address to become ip:80/a , ip:80/b and ip:80/c . And all resource requests under this application are based on this path.
such as ip:80/a can jump to ip:80/a/login instead of ip:80/login , notice the difference in the directory.
my / etc/nginx/conf.d/default.conf is as follows:

server {
    listen       80;
    server_name  localhost;
    location /a {
        proxy_pass http://127.0.0.1:8001/;
    }
    location /b {
        proxy_pass http://127.0.0.1:8002/;
    }
    location /c {
        proxy_pass http://127.0.0.1:8003/;
    }
}

according to my configuration above, enter ip:80/a to see that the application of ip:8001 has been successfully proxied. Just look at the home page and everything is normal.
but a jump to a multi-level directory such as ip:80/a/user/** fails and becomes ip:80/user/** .
I have also tried to follow the official documentation, using regular configuration of location or using rewrite, can not achieve the effect I want.
Thank you for your advice.

server { listen 80; server_name sub1.example.com; location / { proxy_pass http://127.0.0.1:8001; } } server { listen 80; server_name sub2.example.com; location / { proxy_pass http://127.0.0.1:8002; } } ......