How to forward proxy twice

[ldy]

The network topology diagram is like this：
Client Machine C --> Nginx Machine B（installed connect_module）--> Nginx Machine A（installed connect_module） --> target website

Machine A can access the external network，Machine B can access Machine A，Machine C can access Machine B，How to configure make Machine C can access https website？I tried this configuration，Machine C can access http website，but cannot access https website。

# Machine A configuration，After this，Machine B can access http/https website
server {
	listen  8080;

	# dns resolver used by forward proxying
	resolver  114.114.114.114;

	# forward proxy for CONNECT request
	proxy_connect;
	proxy_connect_allow            443 80;
	proxy_connect_connect_timeout  10s;
	proxy_connect_read_timeout     10s;
	proxy_connect_send_timeout     10s;

	# forward proxy for non-CONNECT request
	location / {
		proxy_pass $scheme://$host;
		proxy_set_header Host $host;
	}
}

# Machine B configuration，After this，Machine C can access http website
server {
	listen                           8081;
	#server_name                     localhost;
	#resolver                        Machine A ipv6=off;
        #proxy_connect;
	#proxy_connect_allow            443 80;
	#proxy_connect_connect_timeout  10s;
	#proxy_connect_read_timeout     10s;
	#proxy_connect_send_timeout     10s;
	location / {
		proxy_pass $scheme://Machine A:8081;
		proxy_set_header Host $host;
		proxy_set_header Referer $http_referer;    
		proxy_set_header X-Real-IP $remote_addr;
		proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
		proxy_set_header X-Forwarded-Proto $scheme;
	}
}

I have tried multiple configuration methods in Machine B，still cannot make Machine C access https website，can you tell me where I went wrong？

[chobits]

It might be unavailable to cascade two proxy_connect agent.

The first proxy_connect agent will extract raw data from CONNET tunnel, then it forwards the flow to 2nd proxy_connect agent. The 2nd proxy_connect agent also tries to extract the raw data from the tunnel, but there is no tunnel (CONNECT request) only raw data, so it fails.

So a possible way is to change one of the proxy_connect agent to pure tcp proxy agent.