RGB Gradients Generation The Challenge

Given the two uppercase hexadecimal strings (both 6 characters long, XXXXXX and YYYYYY) representing RGB values (ranging from 000000 to FFFFFF inclusive), and a positive non-zero integer N, display a linear transition of the N+2 colors generated from XXXXXX to YYYYYY that would result in a color gradient.

Example

Input

FF3762
F08800
9


Output

Please note in our example, I've requested 9 interim steps between the two colors, therefore 11 lines will be displayed from initial color to the final color

FF3762
FD3F58
FC474E
FA4F44
F9573A
F75F31
F66727
F46F1D
F37713
F17F09
F08800


Caveats

While I've gone with a simple linear process of deriving the integer values for the interim colors before converting them back into hexadecimal, your methods may vary. Please consider the various ways one could round up/down your numbers accordingly.

Testing

To make this interesting, I've provided a snippet to allow testing of your code, inclusive of a button to provide you with two random colors to test your code against. Displaying your results is optional, but it's encouraged!



c1=()=&gt;('00000'+(Math.random()*(1&lt;&lt;24)|0).toString(16)).slice(-6);

$("#col").click(function(){
  alert("Your two colors are: "+c1()+" and "+c1()+".");
});
        
$("#colors").blur(function(){
  $("#test").empty();
 var colArr = $("#colors").val().split("\n");
 for(c in colArr){
   $("#test").append('&lt;div class="tester" style="background-color:#'+colArr[c]+';"&gt;'+colArr[c]+'&lt;/div&gt;')
  }
  
});
.tester{height: 20px;
width: 60px;padding: 4px;border: 1px solid black;}
&lt;script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"&gt;&lt;/script&gt;
&lt;button id="col"&gt;Your two colors&lt;/button&gt;&lt;br /&gt;
&lt;textarea id="colors"&gt;&lt;/textarea&gt;
&lt;div id="test"&gt;

&lt;/div&gt;




1) You can access two random colors for your test by clicking on the "Your two colors" button.
2) The number of interim steps will be the same as the number of characters in your PPCG username inclusive of spaces, in the case of "WallyWest" it would be 9 (as per my example above).
3) Run your code with the two colors and the number and once you have your generated list, you have the option of pasting your output into the textarea and tabbing away from it to get your generated color gradient.

My example is shown here:



I must admit, that looks pretty awesome!

Please note: As I mentioned, showing your testing of your output using the snippet is optional, but it's encouraged! :)

Output

The list output must be in the form of N+2 sets of 6 digit hex numbers separated by line feeds (\n) as shown in my example above. Output can be in the form of separate lines, space/comma separated list, an array or whatever is best suited for your language... (Thanks @nimi for the heads up) Please remember, that if you plan on testing your code with the snippet, however you separate each "color" is up to you.

Rules

This is code-golf, so the shortest solution in bytes will be crowned the winner. No loopholes, naturally. Input must accept the two strings and a number (which as I said will be equivalent to the number of letters in your username on PPCG, thus your resulting output will always be a minimum of three lines long.
JavaScript (ES6), 130 bytes



g=
(f,t,n)=&gt;[...Array(++n+1)].map((_,i)=&gt;f.replace(/../g,(e,j)=&gt;((`0x${e}`*(n-i)+`0x${t[j]+t[j+1]}`*i)/n|256).toString(16).slice(1)))
;
p=_=&gt;g(f.value,t.value,+n.value).map(e=&gt;o.insertRow().insertCell().appendChild(document.createTextNode(e)).parentNode.bgColor=e);
&lt;input id=f value=e14f09&gt;&lt;input id=t value=9a04f6&gt;&lt;input id=n value=4 type=number&gt;&lt;input type=button onclick=p() value=Go!&gt;&lt;table id=o bgcolor=black cellpadding=4&gt;