how to post category_id on desinger table laravel

hi i have 3 table 1st is products 2nd is category 3rd is designer

products and category is many to many relationship product belongsto designer & designer hasMany products designer belongsto category & category hasMany designers

here is my table

product

Schema::create('products', function (Blueprint $table) {
        $table->increments('id');
        $table->timestamps();
        $table->string('image');
        $table->string('stock');
        $table->string('title');
        $table->string('slug')->unique();
        $table->string('gender');
        $table->text('description');
        $table->integer('price');
        $table->integer('user_id')->unsigned();
        $table->foreign('user_id')->references('id')->on('users')
                    ->onDelete('restrict')
                    ->onUpdate('restrict');

        $table->dateTime('published_at');
    });

designers table

Schema::create('designers', function (Blueprint $table) {
        $table->increments('id');

        $table->string('name')->unique();
        $table->string('slug')->unique();
        $table->timestamps();
    });

category table

Schema::create('categories', function (Blueprint $table) {
        $table->increments('id');
        $table->string('name')->unique();
        $table->timestamps();
    });

    Schema::create('category_product', function (Blueprint $table) {

        $table->integer('category_id')->unsigned()->index();
        $table->foreign('category_id')->references('id')->on('categories')
                    ->onDelete('restrict')
                    ->onUpdate('restrict');

        $table->integer('product_id')->unsigned()->index();
        $table->foreign('product_id')->references('id')->on('products')
                    ->onDelete('restrict')
                    ->onUpdate('restrict');

        $table->timestamps();
    });

adding missing column in products table

Schema::table('products', function (Blueprint $table) {
        $table->integer('designer_id')->unsigned();
        $table->foreign('designer_id')->references('id')->on('designers')
                    ->onDelete('restrict')
                    ->onUpdate('restrict');
    });

adding missing column in designer

Schema::table('designers', function (Blueprint $table) {
        $table->integer('category_id')->unsigned();
        $table->foreign('category_id')->references('id')->on('categories')
                    ->onDelete('restrict')
                    ->onUpdate('restrict');
    });

here is my controller

public function productpost(Request $request){

    $this->validate($request, [
        'title' => 'required|max:255',
        'description' => 'required',
        'price' => 'required',
        'image' => 'image|required',
    ]);

    $designer_name = $request->designer;
    $designer_slug = str_random(40);
    $designer = designer::where('name', $designer_name)->firstOrCreate(
            ['name' => $designer_name], ['slug' => $designer_slug]
        );
    $designer->name = $designer_name;
    $designer->slug = $designer_slug;
    $designer->save();
    $designer_id = $designer->id;
    $product = new Product;
    $product->title = $request->title;
    $product->designer_id = $designer_id;
    $product->description = $request->description;
    $product->price = $request->price;
    $product->stock = $request->stock;
    $product->gender = $request->gender;
    $product_slug = str_random(40);
    $product->slug = $product_slug;
    $product->user_id = Auth::user()->id;
    $product->published_at = Carbon::now()->format('Y-m-d');
    if($request->hasFile('image')) {
        $file = Input::file('image');
        //getting timestamp
        $timestamp = str_replace([' ', ':'], '-', Carbon::now()->toDateTimeString());
        $name = $timestamp. '-' .$file->getClientOriginalName();
        $file->move(public_path().'/images/product/', $name);
        $product->image = $name;
        $thumb = Image::make(public_path().'/images/product/' . $name)->resize(1200,1800)->save(public_path().'/images/product/thumb/' . $name, 90);  
    }
    $product->save();
    $productsearch = product::where('slug', $product_slug)->firstorfail();
    $product_id = $productsearch->id;
    $categoryname = $request->category;
        foreach ($categoryname as $name) {
            $category = category::firstOrNew(['name' => $name]);
            $category->designer_id = $designer_id;
            $category->save();
            $category->products()->attach($product_id);
        }

    return Redirect::back()->with('status', 'Post Success');

missing is product need designerid
designer need category_id category need product_id how to solve this on controller thank you

via Chebli Mohamed