How do I write Makefile to compile c project with bin lib obj subfolders

Question

This is my project structure

build/
  bin/
    z.exe
  lib/ 
    libx.a
    liby.a
    libz.a
  obj/
    x.o
    y.o
    z.o

src/
  module_1/
    x.h
    x.c
  module_2/
    y.h
    y.c
  module_3/
    z.h
    z.c

I want to compile my project so that the build directory has these subfolder (bin, lib, obj)

How do I write Makefile for this? (Spent 2 days cannot figure that out)

module_3 is the entry point with main function in z.c

I want all modules become libraries for later testing them

NOTE:

default include in modules is relative to the project directory

src/module_3/z.c

#include "src/module_1/x.h"

...